Multiprocessing and Scalability · 17. Broadcasting Indexing Objects on air Channel. Advantages....

Mobile and Heterogeneous databases Broadcasting

A.R. HursonComputer Science

Missouri Science & Technology

1

Note, this unit will be covered in ninelectures. In case you finish it earlier, thenyou have the following options:

1) Take the early test and start CS6302.module102) Study the supplement module

(supplement CS6302.module9)3) Act as a helper to help other students in

studying CS6302.module9Note, options 2 and 3 have extra credits as noted in courseoutline.

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Broadcasting

Glossary of prerequisite topics

Familiar with the topics?No Review

CS6302.module9.background

Yes

Remedial actionYes

NoTake the Module

Take Test

Pass?

Glossary of topics

Familiar with the topics?Yes

Pass?

Take Test

Yes

Options

Lead a group of students in this module (extra credits)?

Study more advanced related topics (extra credits)?

Study next module?

No

{

Extra Curricular activities

Enforcement of background

{Current ModuleAt the end give a

test, record the score, and impose remedial

action if not successful

No

Broadcasting

3

You are expected to be familiar with: Mobile DataAccess Systems, if not, you need to

study CS6302.module7.

4

Wireless Communication & Mobility

Previous module introduced mobility and wirelesscommunication in traditional multidatabase platform.As you recall, we distinguished three classes of data andthree classes of services.

This module will concentrate on “public data” and“broadcasting” as a means to make public data availableto the users.

Within the scope of broadcasting, we will talk aboutchallenges and potential solutions.

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Broadcasting

Broadcasting

Many applications are directed towardspublic information that are characterized bythe: Massive number of users, Similarity and simplicity in the requests, and Fact that data is modified by a few (at the

server level).

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Broadcasting

The reduced bandwidth attributed to thewireless environment places limitationson the rate and amount ofcommunication.

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8

Broadcasting

Broadcast-Based Service In such an environment, broadcasting has

been suggested as a possible solution forquery processing. In broadcasting, public data is broadcast over the

air channel. A mobile host unit, in search of data, could tune

to the appropriate frequency upon which the datais being broadcast.

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Broadcasting

Broadcast-Based Service Lower Bandwidth: Response time is independent of

the number of users accessing a channel — it scales upas the number of users increases.

Limited Energy Resources: Less energy is consumedto receive (to pull) an information from the air channelthan sending (to push) the information.

Limited Storage Medium: Air channel can beconsidered as a persistent storage medium.

10

Broadcasting

Broadcast-Based Service ─ Challenges Power Consumption ─ Application of index and

organization of objects on broadcast channel (s). Network Latency ─ Application of parallel channels to

reduce broadcast length: Distribution of Objects over parallel channels, Creation of Conflicts.

Broadcasting contents ─ Application specific domain.

Broadcast-Based Service Application of Index in Single and Parallel

Broadcast Channel(s), Data Organization on Single and Parallel

Broadcast Channel(s), Heuristic and Theoretical conflict resolution

schemes, Conflict resolution in the face of replication.

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Broadcasting

Broadcasting

Retrieving information from the air channelhas two requirements: Minimizing the overall response time at the

mobile unit, and Minimizing the amount of power consumed in

the retrieval process at the mobile unit.

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Broadcasting

Indexing Objects on air Channel An index is a mechanism that speeds up associative

searching. It has been extensively used in traditionalfile and database systems.

An index can be formally defined as a function thattakes a key value and provides an address referring tothe location of the associated data. Its main advantagelies in the fact that it eliminates the need for anexhaustive search through the pages of the data on thestorage medium.

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Broadcasting

Indexing Objects on air Channel B-trees, B+-trees, and hash tables are some of

the most common data structures that havebeen used to implement indexes.

In databases, an index is used during the queryoptimization stage as part of query processing.Normally, a query engine generates multipleplans that can be used to access the requireddata.

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Broadcasting

Indexing Objects on air Channel Similarly, within the scope of broadcasting, an index is

an auxiliary information pointing to the location orpossible availability of a data item on the broadcast andhence, allowing mobile unit to predict the arrival timeof the data item requested.

The prediction of the arrival time enables the mobileunit to switch its operational mode into an energy-saving mode.

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Broadcasting

Indexing Objects on air Channel In short, an indexing mechanism facilitates

object retrieval from the air channel(s),reducing power consumption.

It should be noted that the advantages ofindexing schemes come at the expense ofcomputational overhead and increased lengthof the broadcast (response time).

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Broadcasting

Indexing Objects on air Channel

Advantages Disadvantages

Provides auxiliary information that allows mobile users to predict arrival time of objects.

Longer Broadcast.

Enables utilization of different operational modes (active, nap, doze, etc).

Longer response time.

Reduces power consumption (less tune-in time). Computational overhead due to complexity in retrieval, allocation,and maintenance of the indexes.

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Broadcasting

Indexing Objects on air Channel ─ Signature-BasedIndexing A signature is an abstraction of the information stored

in a record or a file. The basic idea behind the application and use of

signatures in a broadcast channel is to add a controlpart to the contents of an information frame.

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Broadcasting

Indexing Objects on air Channel ─ Signature-Based Indexing A hash function is applied to the contents of the information

frame, generating a bit vector and superimposing it on the dataframe.

A signature partially reflects the data content of a frame. Inshort, this technique creates a set of signatures for data frameson a broadcast and interleaves them with their associated dataframe.

Different allocation schemes of signatures on a broadcastchannel have been studied in the literature; Single signature, Integrated signature and Multi-level signature.

20

Broadcasting

Indexing Objects on air Channel ─ Signature-Based Indexing In the single signature scheme, the signature frame is

broadcast before the corresponding data frame. In the integrated signature scheme, a signature is

constructed for a group of consecutive frames calleda frame group.

The multi-level signature scheme is a combination ofthe single and integrated signature methods in whichthe upper level signatures are integrated signaturesand the lower level signatures are single signatures.

21

Broadcasting

Indexing Objects on air Channel ─ Signature-BasedIndexing During the retrieval process, a query is resolved by generating

a signature based on the user’s request. The query signature is then compared against the signatures of

the data frames in the broadcast. A successful match indicates a possible hit. Consequently, the

content of the corresponding information frame is checkedagainst the query to verify that it corresponds to the user’sdemands.

If the data of the frame corresponds to the user’s request, thedata is recovered; otherwise, the corresponding informationframe is ignored.

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Broadcasting

Indexing Objects on air Channel ─ Signature-Based Indexing In general, the signature based scheme reduces the

access time and the tune-in time when pullinginformation from the air channel.

By checking the signature, the mobile unit partiallydetermines the validity of the content of aninformation frame ─ if the data frame does notcorrespond to the query, the mobile unit switchesfrom active mode to doze mode and waits until thenext signature is transmitted.

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Broadcasting

Indexing Objects on air Channel ─ Signature-BasedIndexing As part of the studies done on signature-based indexing

schemes, the three aforementioned signature-based schemeshave been analyzed with respect to each other using the accesstime and tune-in time as the performance metrics: With fixed signature size, the multi-level scheme has the best

tune-in time performance at the expense of a longer access time. The integrated scheme, on the other hand, has the best average

access time, but its tune-in time depends on the similarity amongthe information frames.

Finally, the simple scheme has an adequate access time and tune-in time.

In general, in comparison to broadcasting without using indexing,all three signature-based schemes improved tune-in timeperformance significantly with a reasonable access timeoverhead.

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Broadcasting

Indexing Objects on air Channel ─ Tree-Based Indexing As noted before, an index is auxiliary information representing

one or several data attributes pointing to the location of datacollection (i.e., information frames) sharing the same commonattribute value(s).

This auxiliary information is usually organized as a tree inwhich the lowest level of the tree points to the location of theinformation frames on the broadcast channel.

With this concept in mind, the frames on the broadcast are oftwo kinds: Data frames and Index frames.

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Broadcasting

Indexing Objects on air Channel ─ Tree-BasedIndexing A broadcast channel is a sequential medium and

hence, to reduce the mobile unit active and tune-intime, and consequently to reduce the powerconsumption, the index frames are usually replicatedand interleaved with the data frames. Otherwise, therequest would have to wait for the beginning of thenext broadcast cycle an increase in the queryresponse time.

One study investigated two index replicationschemes: Distributed indexing and (1, m) indexing

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Broadcasting

Indexing Objects on air Channel ─ Tree-BasedIndexing In distributed indexing, the index is partitioned and

interleaved in the broadcast cycle. Each part of theindex in the broadcast is followed by itscorresponding data frame(s).

In (1, m) indexing, the entire index is interleaved mtimes during the broadcast cycle the whole indexis broadcast before every 1/m fraction of the cycle.

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Broadcasting

Indexing Objects on air Channel ─ Tree-BasedIndexing A series of analysis for both methods were carried

out and compared with the algorithms that providedthe best case for tune-in time and response time.

It was concluded that, in general, the (1, m) indexingscheme reduces power consumption at the expenseof an increase in the response time.

The distributed indexing scheme, relative to the (1,m) indexing scheme, increases the response time at amuch lower rate at the expense of higher powerconsumption.

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Broadcasting

Indexing Objects on air Channel ─ Tree-Based Indexing Previous work has shown that the tree-based indexing schemes

are more suitable for the application domains where informationis accessed from the broadcast channel randomly, and thesignature-based indexing schemes are more suitable in retrievingsequentially structured data elements.

In addition, tree-based indexing schemes have shown superiorityover the signature-based indexing schemes when user request isdirected towards interrelated objects clustered on the broadcastchannel(s). Furthermore, tree-based indexing schemes relative tosignature-based indexing schemes are more suitable in reducingthe overall power consumption.

A tree-based indexing provides global information regarding thephysical location of the data frames on the broadcast channel. Onthe other hand, signature-based indexing schemes are moreeffective in retrieving data frames based on multiple attributes.

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Broadcasting

Indexing Objects on air Channel

Feature Signature -based Indexing

Tree -based Indexing

Less power consumption √

Longer length of broadcast √ √

Computational overhead √ √

Longer response time √ √

Shorter tune-in time √

Random data access √

Sequentially structured data √

Clustered data retrieval √

Multi-attribute retrieval √

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Broadcasting

Indexing Objects on air Channel ─ Object OrientedIndexing In general, in the presence of an indexing mechanism

one can adapt the following protocol for retrieving dataobjects from the air channel(s) in order to minimize thepower consumption.

The protocol involves the following steps: Initial probe: The client tunes into the broadcast channel to

determine when the next index tree is broadcast. Search: The client accesses the index and determines the offset

for the requested objects. Retrieve: The client tunes into the channel and downloads all

the required data objects.

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Broadcasting

Indexing Objects on air Channel ─ Object Oriented Indexing Object-oriented indexing is normally implemented via a multi-

level tree. We can classify the possible implementation techniques into two

general schemes: Single-class indexing and Hierarchical indexing.

In the single-class scheme, multiple multi-level trees areconstructed, each representing one class. In this case, the leafnodes of each tree point to objects belonging only to the classindexed by that tree.

The hierarchical-based scheme constructs one multi-level treerepresenting an index for all classes. The same query has to onlynavigate the common tree.

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Broadcasting

Indexing Objects on air Channel ─ ObjectOriented Indexing

Single-Class-Based IndexTrees

… …

:.

… …

…

…

Objects From a Single Class

:.

:.

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Broadcasting

Indexing Objects on air Channel ─ ObjectOriented Indexing

… … …Inner Nodes

… … … …

Data …

Hierarchical-Based Index Trees

Objects From Multiple Classes

Leaf Nodes :.:.:.

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Broadcasting

Indexing Objects on air Channel ─ Object OrientedIndexing We assume an air-channel page as the storage granule on the air

channel. Due to the sequential nature of the air channel, the allocation of the

nodes of a multi-level tree has to follow the navigational path usedto traverse the tree, starting at the root. Therefore, an orderingscheme is used to sequentially map the nodes on the air channel.Similarly, data objects are allocated onto air channel pagesfollowing their index.

Note that, it is possible to interleave and distribute the index pagesand associated data pages in a variety of methods.

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Broadcasting

Indexing Objects on air Channel ─ Object OrientedIndexing

Previous D n I1

In Dn

Single Class Scheme

I3

I2

…

D 2D 1

D3 Next I1

Previous D

Hierarchical Scheme

IH D Next I H

I i Index of single class iDiData of single class i

IH Hierarchical index

D Data of all classes

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Broadcasting

Indexing Objects on air Channel ─ Object OrientedIndexing (Hierarchical Method) In this scheme, whether the domain of the query covers one class

or all classes along the hierarchy, the same index structure has tobe traversed.

Any request has to probe the channel first, read one page, and getan offset to the first page of the index.

The modules of the mobile unit can then go into doze mode. Oncethe index is reached the modules are brought back into activemode.

A number of index pages are read and offsets to the requiredobjects are obtained. The offsets are followed and the requiredobjects are retrieved. In the interim between the retrieval ofobjects, the modules are brought into doze mode.

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Broadcasting

Indexing Objects on air Channel ─ Object Oriented Indexing(Hierarchical Method)

Hierarchical ProtocolProbe onto channel and get offset to the next index activeReach the index dozeRetrieve the required index pages activeReach the required data pages dozeRetrieve required data pages active

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Broadcasting

Indexing Objects on air Channel ─ Object OrientedIndexing (Single Class Method) Single-Class Protocol

Probe onto channel and get offset to the next index activeReach the index dozeRetrieve offsets to the indexes of required classes activefor every required class

Reach the index dozeRetrieve the required index pages activeReach the required data dozeRetrieve required data pages active

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Broadcast-Based Service ─ Simulation A simulator was developed to evaluate the feasibility and

effectiveness of the proposed algorithms. The NASDAQ database with 4290 securities is used as the source

data for the objects on the broadcast. The simulator views the parallel air channels as a two-dimensional

N × M array, where N and M represent the number of parallel airchannels and the number of objects on a broadcast, respectively.

For each simulation run, user requests are generated, randomly,requesting K objects on the broadcast.

For every simulated configuration, the simulator is run 1000 times,and the average number of every estimated performance metric iscalculated and reported.

Broadcasting

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Broadcasting

Indexing Objects on air Channel ─ Object OrientedIndexing Response Time Degradation Relative to the No-

Indexing SchemeAggregation/Hierarchical

Aggregation/Single

Inheritance/Hierarchical

Inheritance/Single

1.17 1.05 1.1 1.02

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Broadcasting

Indexing Objects on air Channel ─ Object OrientedIndexing Response Time vs. Number of Retrieved Classes

0

20

40

60

80

100

120

140

160

12.5 25 50 75 87.5 100

Percentage of Retrieved Classes

Res

pons

e T

ime

(Sec

.)

Aggr/SnglAggr/HierInher/SnglInher/Hier

Chart2

12.512.512.512.5

25252525

50505050

75757575

87.587.587.587.5

100100100100

Aggr/Sngl

Aggr/Hier

Inher/Sngl

Inher/Hier


Response Time (Sec.)

28.4765625

62.03125

67.5140625

139.8217447917

32.2265625

63.39296875

82.1

140.9602213542

40.0026041667

64.296875

93.3

142.206640625

47.2

66.2109375

110.4

145.1132161458

52.4674479167

67.0916294643

118.7

146.1540364583

56

67.3082589286

129.9

147.0432291667

PCRAS

Data Rate1048576bits/sec

Power Active0.13W

Power Doze0.0066W

Response TimeActive TimeEnergy

AggregationInheritanceAggregationInhertianceAggregationInheritance

In PagesIn SecIn PagesIn SecIn PagesIn mSecIn PagesIn mSecIn mJoules

PercentagePrcnt Cls RtrAggr/SnglAggr/HierAggr/SnglAggr/HierInher/SnglInher/HierInher/SnglInher/HierAggr/SnglAggr/HierAggr/SnglAggr/HierInher/SnglInher/HierInher/SnglInher/HierAggr/SnglAggr/HierInher/SnglInher/Hier

0.12512.57,29015,880286217,28435,794681401615615718206978196416454932

0.25258,25016,229326321,01836,086821413518138713828149109230427560944

0.55010,24116,460406423,88536,405931425723223896546254180291435647961

0.757512,08316,950476628,26237,14911014585323311248763338245352452770988

0.87587.513,43217,175526730,38737,41511914695373711459672377281392461830999

110014,33617,231566733,25437,64313014711140432157112814393164234649111,010

PCRAS

Aggr/Sngl

Aggr/Hier

Inher/Sngl

Inher/Hier

Percentage Classes to Retrieve

Seconds

Aggr/Sngl

Aggr/Hier

Inher/Sngl

Inher/Hier


m Seconds

Aggr/Sngl

Aggr/Hier

Inher/Sngl

Inher/Hier


m Joules

42

Broadcasting

Indexing Objects on air Channel ─ Object OrientedIndexing Active Time vs. Number of the Retrieved Classes

0

100

200

300

400

500

600

12.5 25 50 75 87.5 100


Act

ive

Tim

e (m

Sec

.)


Chart9

12.512.512.512.5

25252525

50505050

75757575

87.587.587.587.5

100100100100

Aggr/Sngl

Aggr/Hier

Inher/Sngl

Inher/Hier


Active Time (m Sec.)

23.75

49.21875

37.65625

45

117.28515625

63.28125

144.62890625

98

190.75

80.859375

257.65625

156.25

263.75

115.9598214286

353

209

322

137.109375

435

257.8125

378

149.609375

500

292.96875

PCRAS


Power Active0.13W

Power Doze0.0066W





0.12512.57,29015,880286217,28435,79468140613244910123845191415450928

0.25258,25016,229326321,01836,08682141301611763372514598227426560942

0.55010,24116,460406423,88536,405931424921191816640258156288434648958

0.757512,08316,950476628,26237,14911014568302641169054353209344451772984

0.87587.513,43217,175526730,38737,415119146823532213711166435258386460837996

110014,33617,231566733,25437,6431301479738378150128755002934164639191,007

PCRAS

Aggr/Sngl

Aggr/Hier

Inher/Sngl

Inher/Hier


Seconds

Aggr/Sngl

Aggr/Hier

Inher/Sngl

Inher/Hier


m Seconds

Aggr/Sngl

Aggr/Hier

Inher/Sngl

Inher/Hier


m Joules

43

Broadcasting

Indexing Objects on air Channel ─ ObjectOriented Indexing Energy Improvement Relative to the No-Index

SchemeAggregation/Hierarchical

Aggregation/Single

Inheritance/Hierarchical

Inheritance/Single

17.5 18.9 18.4 19

44

Broadcasting

Indexing Objects on air Channel ─ Object OrientedIndexing Detailed Energy Consumption

0

200

400

600

800

1,000

1,200

12.5 25 50 75 87.5 100


Ener

gy (m

Jou

les)


Chart10

12.512.512.512.5

25252525

50505050

75757575

87.587.587.587.5

100100100100

Aggr/Sngl

Aggr/Hier

Inher/Sngl

Inher/Hier


Energy (m Joules)

190.8760625

415.47984375

450.23959375

928.376515625

227.1683007812

426.2025

559.7072070313

942.4306609375

287.5557375

434.337421875

647.57478125

957.845078125

344.06675

451.3016294643

772.2002

983.5378265625

386.01995625

459.7240513393

837.099

996.430703125

416.2452

462.6963058036

919.04

1006.63765625

PCRAS


Power Active0.13W

Power Doze0.0066W





0.12512.57,29015,880286217,28435,79468140613244910123845191415450928

0.25258,25016,229326321,01836,08682141301611763372514598227426560942

0.55010,24116,460406423,88536,405931424921191816640258156288434648958

0.757512,08316,950476628,26237,14911014568302641169054353209344451772984

0.87587.513,43217,175526730,38737,415119146823532213711166435258386460837996

110014,33617,231566733,25437,6431301479738378150128755002934164639191,007

PCRAS

Aggr/Sngl

Aggr/Hier

Inher/Sngl

Inher/Hier


Seconds

Aggr/Sngl

Aggr/Hier

Inher/Sngl

Inher/Hier


m Seconds

Aggr/Sngl

Aggr/Hier

Inher/Sngl

Inher/Hier


m Joules

45

Broadcasting Object Organization on the Air Channel

Organizing data objects on the air channel as a means to reduceaccess latency.

An appropriate data placement algorithm should attempt todetect data locality and cluster related data close to one another.

The objects in an object-oriented paradigm are normallyassociated with one another through semantic links ─inheritance, aggregation, or association.

An object-clustering algorithm takes advantage of suchrelationships and attempts to map a complex object into a linearsequence of objects along the semantic links.

Object Organization on the Air Channel Object clustering to minimize the access delay ─

Taking object connectivity (degree of dependence amongobjects) into account.

How to map a weighted graph (complex object) onto a onedimensional air channel to reduce access latency?

Cluster Objects Based on connectivity: Strict Linearity ─ ApproximateLinearOrder Varying Levels of Connectivity ─ PartiallyLinearOrder

Issues of concern: Linearity Replication

46

Broadcasting

47

Broadcasting

Object Organization on the Air Channel A complex object can be expressed as a

hierarchy or a directed acyclic graph (DAG) inwhich objects are represented as the nodes andlinks are the relationships among these objects.

Within the scope of disk storage medium, it hasbeen shown that clustering objects based ontheir semantic connectivity can improve theresponse time by an order of magnitude.

48

Broadcasting

Object Organization on the Air Channel ─ AnExample

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Clustering Method Resulting Sequence

Depth First abensofgpqhrmcijdkl

Breadth First abrcdefgqhijklmnsop

Children- Depth First abrcdefgqhmnsopijkl

Level Clustering acibgqprmenosjdlkfh

49

Broadcasting

Object Organization on the Air Channel ─ DifferentClustering Methods

Clustering Method Resulting Sequence

Depth First abensofgpqhrmcijdkl

Breadth First abrcdefgqhijklmnsop

Children- Depth First abrcdefgqhmnsopijkl

Level Clustering acibgqprmenosjdlkfh

50

Broadcasting

Object Organization on the Air Channel In spite of the differences between a disk

and an air channel, from a databaseperspective, the goal in organizinginformation on the air channel is still thesame as that of the disk ─ to reduce theresponse time for accessing a series ofobjects requested.

51

Broadcasting

Object Organization on the Air Channel In order to achieve this goal, the object organization on

an air channel has to meet the following three criteria: Linear ordering: The air channel is a one-dimensional sequential

access structure. This fact requires that the object ordering be linear. Minimum linear distance between related objects: multiple objects

might be retrieved based on their connection patterns. Reducing thedistance among these objects along the broadcast reduces the responsetime and power consumption.

More availability for popular objects: Generally, requests to datafollow the 20/80 rule, providing more availability for popular objectscan be achieved by simply replicating such objects .

52

Broadcasting

Object Organization on the Air Channel ─ AnExample a

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53

Broadcasting

Object Organization on the Air Channel ─ AnExample Linear Individual Costs Total

Sequence ab ac ad ae bf bg bh ch cj ei ij Cost1 abfgchdeij 1 4 6 7 1 2 4 1 5 1 1 332 abfgcheijd 1 4 9 6 1 2 4 1 4 1 1 343 abcdefghij 1 2 3 4 4 5 6 5 7 4 1 42

4 abgfeichjd 1 6 9 4 2 1 6 1 2 1 3 365 acdeijbhgf 6 1 2 3 3 2 1 6 4 1 1 30

6 adeicjbhgf 6 4 1 2 3 2 1 3 1 1 2 26

7 adecbihgfj 4 3 1 2 4 3 2 3 6 3 4 358 adecbhgfij 4 3 1 2 3 2 1 2 6 6 1 319 adecijbhgf 6 3 1 2 3 2 1 4 2 2 1 27

10 adbfgcheij 2 5 1 7 1 2 4 1 4 1 1 2911 adceijbhgf 6 2 1 3 3 2 1 5 3 1 1 2812 aeidcjbhgf 6 4 3 1 3 2 1 3 1 1 3 2813 aedcbihgfj 4 3 2 1 4 3 2 3 6 4 4 3614 aedcijbhgf 6 3 2 1 3 2 1 4 2 3 1 28

a

edcb

i

j

hgf

54

Broadcasting

Object Organization on the Air Channel ─ An Example Refer to the previous table, the abfgchdeij sequence objects a and

d are separated by the sequence bfgch and thus have a cost of 6. The right-most column represents the total cost associated with

each individual linear sequence. An optimal sequence is the linear sequence with the minimum total

sum. In a query where multiple related objects are retrieved, a minimum

average linear distance translates into smaller average responsetime. In this example, the optimum linear sequence achieves atotal sum of 26.

55

Object Organization on the Air Channel One method in obtaining an optimal linear sequence is

to enumerate and calculate all possible linear sequenceswith their associated costs and then choose thesequence with the minimum cost.

Naturally, such a solution, though simple, iscomputationally impractical.

In practice heuristic rules are used to generate a linearsequence with a reasonable cost.

Broadcasting

56

Object Organization on the Air Channel ─ StrictLinearity ─ ApproximateLinearOrder

Independent Node: An independent node is a nodethat has either one or no parent.

In example on slide 52, node e is an independent nodewhereas node h is not.

A graph containing only independent nodes makes up aforest.

Broadcasting

57

Object Organization on the Air Channel ─ Strict Linearity ─ApproximateLinearOrder Prioritize node based on their number of descendants in

ascending order — the node with the least number ofdescendants is given a higher priority.

Once a node is selected, all of its descendants should bevisited and placed on the sequence in a depth firstmanner, without any interruption from breadth siblings.

If a node has a non-independent child, with all of itsparents already visited, the non-independent childshould be inserted in the linear sequence before anyindependent child.

Broadcasting

58

Object Organization on the Air Channel ─ Strict Linearity ─ApproximateLinearOrder ApproximateLinearOrder Algorithm

Traverse DAG using DFS traversal and as each node is traversed Append the traversed node N to the sequence Remove N from {nodes to be traversed} if {non-independent children of N having all their parents in the sequence} ≠ ∅ Set ← {non-independent children of N having all their parents in

the sequence} else if {independent children of N} ≠ ∅ Set ← {independent children of N} NextNode ← node ∈ Set | node has least # of descendants among

the nodes in Set.

Broadcasting

59

Object Organization on the Air Channel ─ Strict Linearity ─ApproximateLinearOrder

The algorithm assumes a greedy strategy andstarts by selecting a node with an in-degree ofzero and out-degree of at least one.

Applying ApproximateLinearOrder algorithm to thegraph of slide 52 generates either the fifth or eleventhsequence (slide 53). This is dependent on whether c ord was chosen first as the child with the least number ofindependent-children.

Broadcasting

60

Object Organization on the Air Channel ─ Varying Levels ofConnectivity ─ PartiallyLinearOrder

In a complex object, objects are connected throughsemantic links with different degrees of connectivity.The frequency of accesses of objects in an object-oriented database reveals that some patterns are morefrequently traversed than others.

The algorithm PartiallyLinearOrder assumes a weightedDAG as its input and produces a linear sequence.

Broadcasting

61

Object Organization on the Air Channel ─ Varying Levels ofConnectivity ─ PartiallyLinearOrder The algorithm combines the nodes (single_node) of the

graph into multi_nodes in a descending order of theirconnectivity.

The insertion of single_nodes within a multi_noderespects the linear order at the granularity level of thesingle_nodes.

The multi_nodes are merged (with multi_nodes orsingle_nodes) at the multi_node granularity,recursively, without interfering with internal orderingsequences of a multi_node.

Broadcasting

62

Object Organization on the Air Channel ─ Varying Levels of Connectivity ─PartiallyLinearOrder PariallyLinearOrder Algorithm

for every weight ws in descending order for every two nodes N1 & N2 connected by ws merge Ni & Nj into one multi_node for every multi_node MN wm = ws - 1 for every weight wm in descending order while ∃ adjacent_node AN connected to MN if ∃ an edge in both directions between MN & AN compute WeightedLinearDistanceMN_AN & WeightedLinearDistanceAN_MN merge MN & AN into one multi_node, based on the appropriate direction

Broadcasting

63

Object Organization on the Air Channel ─ VaryingLevels of Connectivity ─ PartiallyLinearOrder

a

edcb

i

j

hgf

3

3

3

32 2

1

2

1

21

Original Graph

Broadcasting

64

Object Organization on the Air Channel ─ VaryingLevels of Connectivity ─ PartiallyLinearOrder

ach

edbf

ijg

2

1

2

2

21

1

First and Second iterations

b f g a c h e i j d

Third iteration

Broadcasting

a

edcb

i

j

hgf

3

3

3

32 2

1

2

1

21

Original Graph

65

Object Organization on the Air Channel

0

2

4

6

8

10

12

14

16

400 1200 2000 2800 3600 4400 5200 6000 6800 7600

Number of Objects

Ave

rage

Acc

ess D

elay

(Sec

.)

Children Depth First

PartLinOrder

ApproxLinOrder

Broadcasting

Chart4

4004000.5151290894

8008000.9710245132

120012001.5323934555

160016001.9695863724

200020002.4386920929

240024002.9068460464

280028003.397146225

320032004.0070075989

360036004.4064083099

400040004.8279161453

440044005.3714294434

480048005.8468732834

520052006.3271303177

560056006.8458423615

600060007.3416957855

640064007.6775436401

680068008.2197856903

720072008.6224727631

760076009.2089147568

800080009.6173028946


PartLinOrder

ApproxLinOrder

Number of Objects

Average Access Delay (Sec.)

0.7478065491

0.5956707001

1.4874181747

1.1758861542

2.167517662

1.7435445786

2.9210519791

2.3002843857

3.5640993118

2.880487442

4.3533496857

3.3522310257

5.039981842

3.919465065

5.5851917267

4.4843883514

6.4912242889

5.1224651337

7.1238555908

5.7068462372

7.8835411072

6.2830114365

8.609828949

6.8458805084

9.1740055084

7.470913887

10.0819225311

8.1295375824

10.5791149139

8.4140205383

11.2520189285

8.8864564896

12.088470459

9.5177173615

12.6827278137

9.9269456863

13.8358402252

10.5339832306

14.382311821

11.4190301895

num

Children Depth FirstPartLinOrderApproxLinOrder

4007841326246065401520.74780654910.59567070010.5151290894

8001559671123300610181931.48741817471.17588615420.9710245132

12002272807182823916068312.1675176621.74354457861.5323934555

16003062945241202320652612.92105197912.30028438571.9695863724

20003737229302041025571543.56409931182.8804874422.4386920929

24004564818351506930480494.35334968573.35223102572.9068460464

28005284804410985735621665.0399818423.9194650653.397146225

32005856498470222242016525.58519172674.48438835144.0070075989

36006806542537129446204546.49122428895.12246513374.4064083099

40007469904598406250624377.12385559085.70684623724.8279161453

44008266492658821556323527.88354110726.28301143655.3714294434

48009028060717842661308918.6098289496.84588050845.8468732834

52009619642783382166344779.17400550847.4709138876.3271303177

5600105716628524438717838610.08192253118.12953758246.8458423615

6000110930068822740769832610.57911491398.41402053837.3416957855

6400117985979318125805048811.25201892858.88645648967.6775436401

6800126756809980050861907012.0884704599.51771736158.2197856903

72001329880410409157904131812.68272781379.92694568638.6224727631

76001450793011045682965624713.835840225210.53398323069.2089147568

800015080947119737211008447314.38231182111.41903018959.6173028946

num


PartLinOrder

ApproxOptimalLinOrder

Number of Objects


szd


PartLinOrder

ApproxLinOrder

Number of Objects


ppo

Children Depth FirstOptPartialNonLinOrderApproxOptimalLinOrder

[2:2:2]9578737733437862902329.13499546056.99460792545.9988327026

[6:0:0]137281089292800.0130920410.01038742070.0088500977

[0:6:0]4378852356519830027634.17599868773.40003776552.8636579514

[0:0:6]23328921184941841586597522.248192787217.637428283715.1309728622

[3:3:0]2290394176333914885882.18428993231.68165111541.4196281433

[3:0:3]120322259391708796733511.47482395178.95663070687.5982427597

[0:3:3]1410475811219901936858813.451345443710.70013141638.9345817566

ppo


OptPartialNonLinOrder


Object Size Distribution [S:M:L]


rpf






nnr


107933497697995358334287.56597232826.65660190585.5631904602

209595106787911366030689.15060615547.51410770426.2971763611

30105313789311159745559810.0435047158.87981319437.110212326

401170221310260511837524611.16009998329.78518581397.9872570038

501329861510936628920197912.682547569310.42998123178.7756910324

6014458089129589311032098213.788308143612.35859966289.8428554535

7015546461129875891064783214.826260566712.385930061310.1545639038

8017761218144815321193682616.938417434713.810665130611.3838443756

nnr




Percentage of Popular Objects

Average Access Time (Sec.)

odd


11216248911069851936718011.599053382910.55703258518.9332389832

29103419791314465327088.68169689187.54656219486.2300758362

39918981702788957710399.45947742466.70231723795.5036916733

4113699576250675552417110.84323596955.96110820775.2682600021

5134725666299645535259812.84844017036.0078096395.1046352386

6174224376498565573499716.61533069616.1975145345.4693193436

7202213556358444575043519.28458690646.06388473515.4840421677

8232566816607216566337222.17929935467.56135864266.4812149048

9281224646589300585980026.81967163097.54085540776.7060089111

10318375736789236616841830.36267566687.76966400157.0591941833

11354526687325979679163933.81029891979.08257741938.4201151848

12387994127758327673673437.00200271619.61859235768.3520452499

13420993867289194683855740.14910316479.73212394719.1304586411

14446474467711117697278842.579122543310.29545192729.3096763611

15469614898059058682263644.785965919510.76000328069.1092018127

16492587447744274704858646.976799011210.33972129829.4108776093

17509483778086274725370748.588158607510.79634056099.6847436905

18537894318216695752828351.297598838810.970471382110.0513422012

19556176148585816837277653.041090011611.463301086411.1788619995

20593043719012513812953056.557055473312.033003044110.8540935516

21605685229380549843758057.762643814112.524384117111.2653846741

22629764289074864866869960.059001922612.116250610411.5739618301

23651223539913259909787262.1055154813.235628700312.1469696045

246822773310748818928350765.067036628714.351220321712.3948190689

odd




Replication Frequency


lvd


[10:0]8582447620261447057768.18485927585.91527366644.48777771

[9:1]8925420683237055985998.51194381716.51585578925.3392400742

[8:2]9078371735027162695378.65780925757.00976467135.9790964127

[7:3]9902814797414969286549.44405937197.60474109656.6076793671

[6:4]10415394848860678786209.93289375318.09536552437.5136375427

[5:5]105550269349764835168010.06605720528.91662979137.9647827148

[4:6]111256129786678931271110.61021041879.33330345158.8812932968

[3:7]1171207310558765992937611.16950321210.06962299359.4693908691

[2:8]11923337108815171063257511.370980262810.377423286410.1400136948

[1:9]12613283115871981146988912.028964042711.050413131710.9385385513

[0:10]14715399144043841445763214.03369808213.737091064513.7878723145

lvd




Next-Node Ratio [C:R]


bwd







[9:0:0:0]14715399144043841445763214.03369808213.737091064513.7878723145

[6:1:1:1]11896996107945641032304011.345859527610.29449844369.8448181152

[1:6:1:1]7659425498151436833827.30459690094.75074195863.5127468109

[1:1:6:1]7663814511710934100897.30878257754.88005542763.252114296

[1:1:1:6]7250184460224432628946.914314274.38904190063.111738205




Out-Degree Distribution [0:1:2:3]







AverageWeakNormalStrong

100015348051648356162574012619831.46370410921.57199478151.55042648321.2035207748

200030149223216378318395625212632.87525367743.06737709053.03645706182.404463768

300044702324672483476584138608534.26314544684.45602703094.54506015783.6819963455

400060099316443940642542951499435.73151683816.14542007456.12776660924.9113683701

500074822587978466781818063651517.13563728337.60885810857.4559974676.0702810287

Average

Weak

Normal

Strong

Number of Objects


64K128K256K512K1M2M

4005401528.24206542974.12103271482.06051635741.03025817870.51512908940.2575645447

800101819315.53639221197.7681961063.8840980531.94204902650.97102451320.4855122566

1200160683124.518295288112.2591476446.1295738223.0647869111.53239345550.7661967278

1600206526131.51338195815.7566909797.87834548953.93917274481.96958637240.9847931862

2000255715439.019073486319.50953674329.75476837164.87738418582.43869209291.2193460464

2400304804946.509536743223.254768371611.62738418585.81369209292.90684604641.4534230232

2800356216654.354339599627.177169799813.58858489996.794292453.3971462251.6985731125

3200420165264.11212158232.05606079116.02803039558.01401519784.00700759892.0035037994

3600462045470.50253295935.251266479517.62563323978.81281661994.40640830992.203204155

4000506243777.246658325238.623329162619.31166458139.65583229064.82791614532.4139580727

4400563235285.942871093842.971435546921.485717773410.74285888675.37142944342.6857147217

4800613089193.549972534246.774986267123.387493133511.69374656685.84687328342.9234366417

52006634477101.23408508350.617042541525.308521270812.65426063546.32713031773.1635651588

56007178386109.533477783254.766738891627.383369445813.69168472296.84584236153.4229211807

60007698326117.467132568458.733566284229.366783142114.6833915717.34169578553.6708478928

64008050488122.840698242261.420349121130.710174560515.35508728037.67754364013.8387718201

68008619070131.516571044965.758285522532.879142761216.43957138068.21978569034.1098928452

72009041318137.95956420968.979782104534.489891052217.24494552618.62247276314.3112363815

76009656247147.342636108473.671318054236.835659027118.41782951359.20891475684.6044573784

800010084473153.876846313576.938423156738.469211578419.23460578929.61730289464.8086514473

64K

128K

256K

512K

1M

2M

Number of Objects


66


0

5

10

15

20

25

[2:2:2] [6:0:0] [0:6:0] [0:0:6] [3:3:0] [3:0:3] [0:3:3]


Ave

rage

Acc

ess D

elay

(Sec

.)


Broadcasting

Chart5

[2:2:2][2:2:2][2:2:2]

[6:0:0][6:0:0][6:0:0]

[0:6:0][0:6:0][0:6:0]

[0:0:6][0:0:6][0:0:6]

[3:3:0][3:3:0][3:3:0]

[3:0:3][3:0:3][3:0:3]

[0:3:3][0:3:3][0:3:3]


PartLinOrder

ApproxLinOrder



9.1349954605

6.9946079254

5.9988327026

0.013092041

0.0103874207

0.0088500977

4.1759986877

3.4000377655

2.8636579514

22.2481927872

17.6374282837

15.1309728622

2.1842899323

1.6816511154

1.4196281433

11.4748239517

8.9566307068

7.5982427597

13.4513454437

10.7001314163

8.9345817566

num


4007841326246065401520.74780654910.59567070010.5151290894

8001559671123300610181931.48741817471.17588615420.9710245132

12002272807182823916068312.1675176621.74354457861.5323934555

16003062945241202320652612.92105197912.30028438571.9695863724

20003737229302041025571543.56409931182.8804874422.4386920929

24004564818351506930480494.35334968573.35223102572.9068460464

28005284804410985735621665.0399818423.9194650653.397146225

32005856498470222242016525.58519172674.48438835144.0070075989

36006806542537129446204546.49122428895.12246513374.4064083099

40007469904598406250624377.12385559085.70684623724.8279161453

44008266492658821556323527.88354110726.28301143655.3714294434

48009028060717842661308918.6098289496.84588050845.8468732834

52009619642783382166344779.17400550847.4709138876.3271303177

5600105716628524438717838610.08192253118.12953758246.8458423615

6000110930068822740769832610.57911491398.41402053837.3416957855

6400117985979318125805048811.25201892858.88645648967.6775436401

6800126756809980050861907012.0884704599.51771736158.2197856903

72001329880410409157904131812.68272781379.92694568638.6224727631

76001450793011045682965624713.835840225210.53398323069.2089147568

800015080947119737211008447314.38231182111.41903018959.6173028946

num


PartLinOrder


Number of Objects


szd


PartLinOrder

ApproxLinOrder

Number of Objects


ppo


[2:2:2]9578737733437862902329.13499546056.99460792545.9988327026

[6:0:0]137281089292800.0130920410.01038742070.0088500977

[0:6:0]4378852356519830027634.17599868773.40003776552.8636579514

[0:0:6]23328921184941841586597522.248192787217.637428283715.1309728622

[3:3:0]2290394176333914885882.18428993231.68165111541.4196281433

[3:0:3]120322259391708796733511.47482395178.95663070687.5982427597

[0:3:3]1410475811219901936858813.451345443710.70013141638.9345817566

ppo



ApproxLinOrder



rpf


PartLinOrder

ApproxLinOrder



nnr


107933497697995358334287.56597232826.65660190585.5631904602

209595106787911366030689.15060615547.51410770426.2971763611

30105313789311159745559810.0435047158.87981319437.110212326

401170221310260511837524611.16009998329.78518581397.9872570038

501329861510936628920197912.682547569310.42998123178.7756910324

6014458089129589311032098213.788308143612.35859966289.8428554535

7015546461129875891064783214.826260566712.385930061310.1545639038

8017761218144815321193682616.938417434713.810665130611.3838443756

nnr


PartLinOrder

ApproxLinOrder



odd


11216248911069851936718011.599053382910.55703258518.9332389832

29103419791314465327088.68169689187.54656219486.2300758362

39918981702788957710399.45947742466.70231723795.5036916733

4113699576250675552417110.84323596955.96110820775.2682600021

5134725666299645535259812.84844017036.0078096395.1046352386

6174224376498565573499716.61533069616.1975145345.4693193436

7202213556358444575043519.28458690646.06388473515.4840421677

8232566816607216566337222.17929935467.56135864266.4812149048

9281224646589300585980026.81967163097.54085540776.7060089111

10318375736789236616841830.36267566687.76966400157.0591941833

11354526687325979679163933.81029891979.08257741938.4201151848

12387994127758327673673437.00200271619.61859235768.3520452499

13420993867289194683855740.14910316479.73212394719.1304586411

14446474467711117697278842.579122543310.29545192729.3096763611

15469614898059058682263644.785965919510.76000328069.1092018127

16492587447744274704858646.976799011210.33972129829.4108776093

17509483778086274725370748.588158607510.79634056099.6847436905

18537894318216695752828351.297598838810.970471382110.0513422012

19556176148585816837277653.041090011611.463301086411.1788619995

20593043719012513812953056.557055473312.033003044110.8540935516

21605685229380549843758057.762643814112.524384117111.2653846741

22629764289074864866869960.059001922612.116250610411.5739618301

23651223539913259909787262.1055154813.235628700312.1469696045

246822773310748818928350765.067036628714.351220321712.3948190689

odd


PartLinOrder

ApproxLinOrder



lvd


[10:0]8582447620261447057768.18485927585.91527366644.48777771

[9:1]8925420683237055985998.51194381716.51585578925.3392400742

[8:2]9078371735027162695378.65780925757.00976467135.9790964127

[7:3]9902814797414969286549.44405937197.60474109656.6076793671

[6:4]10415394848860678786209.93289375318.09536552437.5136375427

[5:5]105550269349764835168010.06605720528.91662979137.9647827148

[4:6]111256129786678931271110.61021041879.33330345158.8812932968

[3:7]1171207310558765992937611.16950321210.06962299359.4693908691

[2:8]11923337108815171063257511.370980262810.377423286410.1400136948

[1:9]12613283115871981146988912.028964042711.050413131710.9385385513

[0:10]14715399144043841445763214.03369808213.737091064513.7878723145

lvd


PartLinOrder

ApproxLinOrder



bwd


PartLinOrder

ApproxLinOrder




[9:0:0:0]14715399144043841445763214.03369808213.737091064513.7878723145

[6:1:1:1]11896996107945641032304011.345859527610.29449844369.8448181152

[1:6:1:1]7659425498151436833827.30459690094.75074195863.5127468109

[1:1:6:1]7663814511710934100897.30878257754.88005542763.252114296

[1:1:1:6]7250184460224432628946.914314274.38904190063.111738205


PartLinOrder

ApproxLinOrder




PartLinOrder

ApproxLinOrder




100015348051648356162574012619831.46370410921.57199478151.55042648321.2035207748

200030149223216378318395625212632.87525367743.06737709053.03645706182.404463768

300044702324672483476584138608534.26314544684.45602703094.54506015783.6819963455

400060099316443940642542951499435.73151683816.14542007456.12776660924.9113683701

500074822587978466781818063651517.13563728337.60885810857.4559974676.0702810287

Average

Weak

Normal

Strong

Number of Objects


64K128K256K512K1M2M

4005401528.24206542974.12103271482.06051635741.03025817870.51512908940.2575645447

800101819315.53639221197.7681961063.8840980531.94204902650.97102451320.4855122566

1200160683124.518295288112.2591476446.1295738223.0647869111.53239345550.7661967278

1600206526131.51338195815.7566909797.87834548953.93917274481.96958637240.9847931862

2000255715439.019073486319.50953674329.75476837164.87738418582.43869209291.2193460464

2400304804946.509536743223.254768371611.62738418585.81369209292.90684604641.4534230232

2800356216654.354339599627.177169799813.58858489996.794292453.3971462251.6985731125

3200420165264.11212158232.05606079116.02803039558.01401519784.00700759892.0035037994

3600462045470.50253295935.251266479517.62563323978.81281661994.40640830992.203204155

4000506243777.246658325238.623329162619.31166458139.65583229064.82791614532.4139580727

4400563235285.942871093842.971435546921.485717773410.74285888675.37142944342.6857147217

4800613089193.549972534246.774986267123.387493133511.69374656685.84687328342.9234366417

52006634477101.23408508350.617042541525.308521270812.65426063546.32713031773.1635651588

56007178386109.533477783254.766738891627.383369445813.69168472296.84584236153.4229211807

60007698326117.467132568458.733566284229.366783142114.6833915717.34169578553.6708478928

64008050488122.840698242261.420349121130.710174560515.35508728037.67754364013.8387718201

68008619070131.516571044965.758285522532.879142761216.43957138068.21978569034.1098928452

72009041318137.95956420968.979782104534.489891052217.24494552618.62247276314.3112363815

76009656247147.342636108473.671318054236.835659027118.41782951359.20891475684.6044573784

800010084473153.876846313576.938423156738.469211578419.23460578929.61730289464.8086514473

64K

128K

256K

512K

1M

2M

Number of Objects


67


0

2

4

6

8

10

12

14

16

[10:0] [9:1] [8:2] [7:3] [6:4] [5:5] [4:6] [3:7] [2:8] [1:9] [0:10]


Ave

rage

Acc

ess D

elay

(Sec

.)


Broadcasting

Chart6

[10:0][10:0][10:0]

[9:1][9:1][9:1]

[8:2][8:2][8:2]

[7:3][7:3][7:3]

[6:4][6:4][6:4]

[5:5][5:5][5:5]

[4:6][4:6][4:6]

[3:7][3:7][3:7]

[2:8][2:8][2:8]

[1:9][1:9][1:9]

[0:10][0:10][0:10]


PartLinOrder

ApproxLinOrder



8.1848592758

5.9152736664

4.48777771

8.5119438171

6.5158557892

5.3392400742

8.6578092575

7.0097646713

5.9790964127

9.4440593719

7.6047410965

6.6076793671

9.9328937531

8.0953655243

7.5136375427

10.0660572052

8.9166297913

7.9647827148

10.6102104187

9.3333034515

8.8812932968

11.169503212

10.0696229935

9.4693908691

11.3709802628

10.3774232864

10.1400136948

12.0289640427

11.0504131317

10.9385385513

14.033698082

13.7370910645

13.7878723145

num


4007841326246065401520.74780654910.59567070010.5151290894

8001559671123300610181931.48741817471.17588615420.9710245132

12002272807182823916068312.1675176621.74354457861.5323934555

16003062945241202320652612.92105197912.30028438571.9695863724

20003737229302041025571543.56409931182.8804874422.4386920929

24004564818351506930480494.35334968573.35223102572.9068460464

28005284804410985735621665.0399818423.9194650653.397146225

32005856498470222242016525.58519172674.48438835144.0070075989

36006806542537129446204546.49122428895.12246513374.4064083099

40007469904598406250624377.12385559085.70684623724.8279161453

44008266492658821556323527.88354110726.28301143655.3714294434

48009028060717842661308918.6098289496.84588050845.8468732834

52009619642783382166344779.17400550847.4709138876.3271303177

5600105716628524438717838610.08192253118.12953758246.8458423615

6000110930068822740769832610.57911491398.41402053837.3416957855

6400117985979318125805048811.25201892858.88645648967.6775436401

6800126756809980050861907012.0884704599.51771736158.2197856903

72001329880410409157904131812.68272781379.92694568638.6224727631

76001450793011045682965624713.835840225210.53398323069.2089147568

800015080947119737211008447314.38231182111.41903018959.6173028946

num


PartLinOrder


Number of Objects


szd


PartLinOrder

ApproxLinOrder

Number of Objects


ppo


[2:2:2]9578737733437862902329.13499546056.99460792545.9988327026

[6:0:0]137281089292800.0130920410.01038742070.0088500977

[0:6:0]4378852356519830027634.17599868773.40003776552.8636579514

[0:0:6]23328921184941841586597522.248192787217.637428283715.1309728622

[3:3:0]2290394176333914885882.18428993231.68165111541.4196281433

[3:0:3]120322259391708796733511.47482395178.95663070687.5982427597

[0:3:3]1410475811219901936858813.451345443710.70013141638.9345817566

ppo



ApproxLinOrder



rpf


PartLinOrder

ApproxLinOrder



nnr


107933497697995358334287.56597232826.65660190585.5631904602

209595106787911366030689.15060615547.51410770426.2971763611

30105313789311159745559810.0435047158.87981319437.110212326

401170221310260511837524611.16009998329.78518581397.9872570038

501329861510936628920197912.682547569310.42998123178.7756910324

6014458089129589311032098213.788308143612.35859966289.8428554535

7015546461129875891064783214.826260566712.385930061310.1545639038

8017761218144815321193682616.938417434713.810665130611.3838443756

nnr


PartLinOrder

ApproxLinOrder



odd


11216248911069851936718011.599053382910.55703258518.9332389832

29103419791314465327088.68169689187.54656219486.2300758362

39918981702788957710399.45947742466.70231723795.5036916733

4113699576250675552417110.84323596955.96110820775.2682600021

5134725666299645535259812.84844017036.0078096395.1046352386

6174224376498565573499716.61533069616.1975145345.4693193436

7202213556358444575043519.28458690646.06388473515.4840421677

8232566816607216566337222.17929935467.56135864266.4812149048

9281224646589300585980026.81967163097.54085540776.7060089111

10318375736789236616841830.36267566687.76966400157.0591941833

11354526687325979679163933.81029891979.08257741938.4201151848

12387994127758327673673437.00200271619.61859235768.3520452499

13420993867289194683855740.14910316479.73212394719.1304586411

14446474467711117697278842.579122543310.29545192729.3096763611

15469614898059058682263644.785965919510.76000328069.1092018127

16492587447744274704858646.976799011210.33972129829.4108776093

17509483778086274725370748.588158607510.79634056099.6847436905

18537894318216695752828351.297598838810.970471382110.0513422012

19556176148585816837277653.041090011611.463301086411.1788619995

20593043719012513812953056.557055473312.033003044110.8540935516

21605685229380549843758057.762643814112.524384117111.2653846741

22629764289074864866869960.059001922612.116250610411.5739618301

23651223539913259909787262.1055154813.235628700312.1469696045

246822773310748818928350765.067036628714.351220321712.3948190689

odd


PartLinOrder

ApproxLinOrder



lvd


[10:0]8582447620261447057768.18485927585.91527366644.48777771

[9:1]8925420683237055985998.51194381716.51585578925.3392400742

[8:2]9078371735027162695378.65780925757.00976467135.9790964127

[7:3]9902814797414969286549.44405937197.60474109656.6076793671

[6:4]10415394848860678786209.93289375318.09536552437.5136375427

[5:5]105550269349764835168010.06605720528.91662979137.9647827148

[4:6]111256129786678931271110.61021041879.33330345158.8812932968

[3:7]1171207310558765992937611.16950321210.06962299359.4693908691

[2:8]11923337108815171063257511.370980262810.377423286410.1400136948

[1:9]12613283115871981146988912.028964042711.050413131710.9385385513

[0:10]14715399144043841445763214.03369808213.737091064513.7878723145

lvd


PartLinOrder

ApproxLinOrder



bwd


PartLinOrder

ApproxLinOrder




[9:0:0:0]14715399144043841445763214.03369808213.737091064513.7878723145

[6:1:1:1]11896996107945641032304011.345859527610.29449844369.8448181152

[1:6:1:1]7659425498151436833827.30459690094.75074195863.5127468109

[1:1:6:1]7663814511710934100897.30878257754.88005542763.252114296

[1:1:1:6]7250184460224432628946.914314274.38904190063.111738205


PartLinOrder

ApproxLinOrder




PartLinOrder

ApproxLinOrder




100015348051648356162574012619831.46370410921.57199478151.55042648321.2035207748

200030149223216378318395625212632.87525367743.06737709053.03645706182.404463768

300044702324672483476584138608534.26314544684.45602703094.54506015783.6819963455

400060099316443940642542951499435.73151683816.14542007456.12776660924.9113683701

500074822587978466781818063651517.13563728337.60885810857.4559974676.0702810287

Average

Weak

Normal

Strong

Number of Objects


64K128K256K512K1M2M

4005401528.24206542974.12103271482.06051635741.03025817870.51512908940.2575645447

800101819315.53639221197.7681961063.8840980531.94204902650.97102451320.4855122566

1200160683124.518295288112.2591476446.1295738223.0647869111.53239345550.7661967278

1600206526131.51338195815.7566909797.87834548953.93917274481.96958637240.9847931862

2000255715439.019073486319.50953674329.75476837164.87738418582.43869209291.2193460464

2400304804946.509536743223.254768371611.62738418585.81369209292.90684604641.4534230232

2800356216654.354339599627.177169799813.58858489996.794292453.3971462251.6985731125

3200420165264.11212158232.05606079116.02803039558.01401519784.00700759892.0035037994

3600462045470.50253295935.251266479517.62563323978.81281661994.40640830992.203204155

4000506243777.246658325238.623329162619.31166458139.65583229064.82791614532.4139580727

4400563235285.942871093842.971435546921.485717773410.74285888675.37142944342.6857147217

4800613089193.549972534246.774986267123.387493133511.69374656685.84687328342.9234366417

52006634477101.23408508350.617042541525.308521270812.65426063546.32713031773.1635651588

56007178386109.533477783254.766738891627.383369445813.69168472296.84584236153.4229211807

60007698326117.467132568458.733566284229.366783142114.6833915717.34169578553.6708478928

64008050488122.840698242261.420349121130.710174560515.35508728037.67754364013.8387718201

68008619070131.516571044965.758285522532.879142761216.43957138068.21978569034.1098928452

72009041318137.95956420968.979782104534.489891052217.24494552618.62247276314.3112363815

76009656247147.342636108473.671318054236.835659027118.41782951359.20891475684.6044573784

800010084473153.876846313576.938423156738.469211578419.23460578929.61730289464.8086514473

64K

128K

256K

512K

1M

2M

Number of Objects


68


0

2

4

6

8

10

12

14

16

[9:0:0:0] [6:1:1:1] [1:6:1:1] [1:1:6:1] [1:1:1:6]Out-Degree Distribution [0:1:2:3]

Aver

age A

cces

s Dela

y (S

ec.) Children Depth First

PartLinOrderApproxLinOrder

Broadcasting

Chart7

[9:0:0:0][9:0:0:0][9:0:0:0]

[6:1:1:1][6:1:1:1][6:1:1:1]

[1:6:1:1][1:6:1:1][1:6:1:1]

[1:1:6:1][1:1:6:1][1:1:6:1]

[1:1:1:6][1:1:1:6][1:1:1:6]


PartLinOrder

ApproxLinOrder



14.033698082

13.7370910645

13.7878723145

11.3458595276

10.2944984436

9.8448181152

7.3045969009

4.7507419586

3.5127468109

7.3087825775

4.8800554276

3.252114296

6.91431427

4.3890419006

3.111738205

num


4007841326246065401520.74780654910.59567070010.5151290894

8001559671123300610181931.48741817471.17588615420.9710245132

12002272807182823916068312.1675176621.74354457861.5323934555

16003062945241202320652612.92105197912.30028438571.9695863724

20003737229302041025571543.56409931182.8804874422.4386920929

24004564818351506930480494.35334968573.35223102572.9068460464

28005284804410985735621665.0399818423.9194650653.397146225

32005856498470222242016525.58519172674.48438835144.0070075989

36006806542537129446204546.49122428895.12246513374.4064083099

40007469904598406250624377.12385559085.70684623724.8279161453

44008266492658821556323527.88354110726.28301143655.3714294434

48009028060717842661308918.6098289496.84588050845.8468732834

52009619642783382166344779.17400550847.4709138876.3271303177

5600105716628524438717838610.08192253118.12953758246.8458423615

6000110930068822740769832610.57911491398.41402053837.3416957855

6400117985979318125805048811.25201892858.88645648967.6775436401

6800126756809980050861907012.0884704599.51771736158.2197856903

72001329880410409157904131812.68272781379.92694568638.6224727631

76001450793011045682965624713.835840225210.53398323069.2089147568

800015080947119737211008447314.38231182111.41903018959.6173028946

num


PartLinOrder


Number of Objects


szd


PartLinOrder

ApproxLinOrder

Number of Objects


ppo


[2:2:2]9578737733437862902329.13499546056.99460792545.9988327026

[6:0:0]137281089292800.0130920410.01038742070.0088500977

[0:6:0]4378852356519830027634.17599868773.40003776552.8636579514

[0:0:6]23328921184941841586597522.248192787217.637428283715.1309728622

[3:3:0]2290394176333914885882.18428993231.68165111541.4196281433

[3:0:3]120322259391708796733511.47482395178.95663070687.5982427597

[0:3:3]1410475811219901936858813.451345443710.70013141638.9345817566

ppo



ApproxLinOrder



rpf


PartLinOrder

ApproxLinOrder



nnr


107933497697995358334287.56597232826.65660190585.5631904602

209595106787911366030689.15060615547.51410770426.2971763611

30105313789311159745559810.0435047158.87981319437.110212326

401170221310260511837524611.16009998329.78518581397.9872570038

501329861510936628920197912.682547569310.42998123178.7756910324

6014458089129589311032098213.788308143612.35859966289.8428554535

7015546461129875891064783214.826260566712.385930061310.1545639038

8017761218144815321193682616.938417434713.810665130611.3838443756

nnr


PartLinOrder

ApproxLinOrder



odd


11216248911069851936718011.599053382910.55703258518.9332389832

29103419791314465327088.68169689187.54656219486.2300758362

39918981702788957710399.45947742466.70231723795.5036916733

4113699576250675552417110.84323596955.96110820775.2682600021

5134725666299645535259812.84844017036.0078096395.1046352386

6174224376498565573499716.61533069616.1975145345.4693193436

7202213556358444575043519.28458690646.06388473515.4840421677

8232566816607216566337222.17929935467.56135864266.4812149048

9281224646589300585980026.81967163097.54085540776.7060089111

10318375736789236616841830.36267566687.76966400157.0591941833

11354526687325979679163933.81029891979.08257741938.4201151848

12387994127758327673673437.00200271619.61859235768.3520452499

13420993867289194683855740.14910316479.73212394719.1304586411

14446474467711117697278842.579122543310.29545192729.3096763611

15469614898059058682263644.785965919510.76000328069.1092018127

16492587447744274704858646.976799011210.33972129829.4108776093

17509483778086274725370748.588158607510.79634056099.6847436905

18537894318216695752828351.297598838810.970471382110.0513422012

19556176148585816837277653.041090011611.463301086411.1788619995

20593043719012513812953056.557055473312.033003044110.8540935516

21605685229380549843758057.762643814112.524384117111.2653846741

22629764289074864866869960.059001922612.116250610411.5739618301

23651223539913259909787262.1055154813.235628700312.1469696045

246822773310748818928350765.067036628714.351220321712.3948190689

odd


PartLinOrder

ApproxLinOrder



lvd


[10:0]8582447620261447057768.18485927585.91527366644.48777771

[9:1]8925420683237055985998.51194381716.51585578925.3392400742

[8:2]9078371735027162695378.65780925757.00976467135.9790964127

[7:3]9902814797414969286549.44405937197.60474109656.6076793671

[6:4]10415394848860678786209.93289375318.09536552437.5136375427

[5:5]105550269349764835168010.06605720528.91662979137.9647827148

[4:6]111256129786678931271110.61021041879.33330345158.8812932968

[3:7]1171207310558765992937611.16950321210.06962299359.4693908691

[2:8]11923337108815171063257511.370980262810.377423286410.1400136948

[1:9]12613283115871981146988912.028964042711.050413131710.9385385513

[0:10]14715399144043841445763214.03369808213.737091064513.7878723145

lvd


PartLinOrder

ApproxLinOrder



bwd


PartLinOrder

ApproxLinOrder




[9:0:0:0]14715399144043841445763214.03369808213.737091064513.7878723145

[6:1:1:1]11896996107945641032304011.345859527610.29449844369.8448181152

[1:6:1:1]7659425498151436833827.30459690094.75074195863.5127468109

[1:1:6:1]7663814511710934100897.30878257754.88005542763.252114296

[1:1:1:6]7250184460224432628946.914314274.38904190063.111738205


PartLinOrder

ApproxLinOrder




PartLinOrder

ApproxLinOrder




100015348051648356162574012619831.46370410921.57199478151.55042648321.2035207748

200030149223216378318395625212632.87525367743.06737709053.03645706182.404463768

300044702324672483476584138608534.26314544684.45602703094.54506015783.6819963455

400060099316443940642542951499435.73151683816.14542007456.12776660924.9113683701

500074822587978466781818063651517.13563728337.60885810857.4559974676.0702810287

Average

Weak

Normal

Strong

Number of Objects


64K128K256K512K1M2M

4005401528.24206542974.12103271482.06051635741.03025817870.51512908940.2575645447

800101819315.53639221197.7681961063.8840980531.94204902650.97102451320.4855122566

1200160683124.518295288112.2591476446.1295738223.0647869111.53239345550.7661967278

1600206526131.51338195815.7566909797.87834548953.93917274481.96958637240.9847931862

2000255715439.019073486319.50953674329.75476837164.87738418582.43869209291.2193460464

2400304804946.509536743223.254768371611.62738418585.81369209292.90684604641.4534230232

2800356216654.354339599627.177169799813.58858489996.794292453.3971462251.6985731125

3200420165264.11212158232.05606079116.02803039558.01401519784.00700759892.0035037994

3600462045470.50253295935.251266479517.62563323978.81281661994.40640830992.203204155

4000506243777.246658325238.623329162619.31166458139.65583229064.82791614532.4139580727

4400563235285.942871093842.971435546921.485717773410.74285888675.37142944342.6857147217

4800613089193.549972534246.774986267123.387493133511.69374656685.84687328342.9234366417

52006634477101.23408508350.617042541525.308521270812.65426063546.32713031773.1635651588

56007178386109.533477783254.766738891627.383369445813.69168472296.84584236153.4229211807

60007698326117.467132568458.733566284229.366783142114.6833915717.34169578553.6708478928

64008050488122.840698242261.420349121130.710174560515.35508728037.67754364013.8387718201

68008619070131.516571044965.758285522532.879142761216.43957138068.21978569034.1098928452

72009041318137.95956420968.979782104534.489891052217.24494552618.62247276314.3112363815

76009656247147.342636108473.671318054236.835659027118.41782951359.20891475684.6044573784

800010084473153.876846313576.938423156738.469211578419.23460578929.61730289464.8086514473

64K

128K

256K

512K

1M

2M

Number of Objects


69

Object Organization on Parallel Channels The broadcast length is a factor that affects the

average response time in retrieving objectsfrom the air channel.

The broadcast length can be reduced if objectsare broadcast along the parallel air channels.

Reduced average response time could alsotranslate into lower power consumption.

Broadcasting

70

Object Organization on Parallel Channels Formally we are intended to assign the objects

from a weighted DAG onto multiple channels,while: Preserving dependency implied by the edges, Minimizing the overall broadcast time (load

balancing) and Clustering related objects close to one another

(improving the response time).

Broadcasting

71

Object Organization on Parallel Channels Assuming that all channels have the same data rate, one

can draw many analogies between object organizationon parallel channels and static task scheduling in ahomogeneous multiprocessor environment:

Tasks are represented as a directed graph D ≡ (N, A),where nodes (N) and directed edges (A) representingprocesses and dependence among the processes,respectively.

An optimal solution to such a problem is proven to beNP hard and hence, in many solutions, heuristics havebeen developed to generate a “suitable solution”.

Broadcasting

Object Organization on Parallel Channels We are intended to assign the objects from a weighted

DAG onto multiple channels, while: Preserving dependency implied by the edges, Minimizing the overall broadcast length (load balancing) and Clustering related objects close to one another (improving the

response time).

Largest Object First (LOF) Clustering Critical-Path (CCP)

72

Broadcasting

73

Object Organization on Parallel Channels ─Largest Object First This algorithm relies on a simple and localized

heuristic by giving priority to larger objects. Consider a 2-channel environment and three

objects A, B, and C with the followingrelationships among the sizes of the objects A >B > C.

Broadcasting

74

Object Organization on Parallel Channels ─ LargestObject First

B AC

AC B

Random allocation Allocation based on the Largest Object First Heuristic

Broadcasting

75

Object Organization on Parallel Channels ─ LargestObject First

The algorithm follows the following procedure;Recursively, a "proper" node with in-degree of zero ischosen (initially the root) and assigned to a "proper"channel.

A “proper” channel is the one with the smallest overallsize.

A “proper” node is the largest node with in-degree ofzero.

Broadcasting

76

Object Organization on Parallel Channels ─ LargestObject First Largest Object First Algorithm

Repeat until all nodes are assignedAssign a free node with the largest weight whose

parents are fully allocated to the least-loadedchannel

Remove all out-edges of assigned node from the dagInsert resulting free nodes into the list of free nodes.

Broadcasting

77

Object Organization on Parallel Channels ─ ClusteringCritical-Path

AssignWeights(DAG) Algorithm for every node i

Calculate Wi Weight of each node is calculated based on the:

Size of the node, Maximum weight of its children, Number of children with in-degree 1 and in-degree > 1, and Degree of connectivity among objects.

Broadcasting

78

Object Organization on Parallel Channels ─Clustering Critical-Path Critical Path Algorithm

AssignWeights(DAG) repeat until all the nodes have been processed

Select the free node N with the largest weight if all parents of N are fully allocated on the channels

place it on the currently least-loaded channel else

fill up the least-loaded channel(s) with nulls up to theend of the last allocated parent of N then place N on it.

Broadcasting

79

Object Organization on Parallel Channels

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

1 2 3 4 5 6 7 8

Number of Channels

Ave

rage

Res

pons

e Ti

me

Per O

bjec

t (S

ec.) LOF

CCP

Broadcasting

Chart1

5.99912643435.9991264343

3.03976608242.75

2.262

1.821.58

1.71.32

1.521.1428589004

1.461.053625241

1.41.0009916975

LOF

CCP

Number of Channels

Average Response Time Per Object (Sec.)

Sheet1

BADACE

CEBD

BADAD

CEBCE

BA

C

A

CB

C

DG

D

CG

NumChnnls

Response Single6290540

Delay Single6290232

Data Rate1048576

Previous WorkCurrent Work

LOFCCPRatio/SingleRatio/SingleCCP/LOF% ImprvNumChnnlsLOFCCPLOFCCPOODLOFCCPLOFCCPFRelatedRandomAvg. access delayRelatedRandomAvg. access delay

11257191257191.001.000.000.0016,290,5406,290,5406.006.00[5:1:1:1]1,622,1471,603,2731.551.5301,707,0001,896,8371,513,0951.631.811.44

26370257629.59887322871.972.180.1110.5423,187,4262,883,5843.042.75[3:3:1:1]1,761,6081,627,3901.681.550.11,707,0821,869,5441,522,5321.631.781.45

347361.052164907941912.43554416632.653.000.1313.0032,369,7822,097,1522.262.00[2:2:2:2]1,908,4081,656,7501.821.580.21,703,9361,842,2521,543,5041.631.761.47

438140.316345191333110.82407989143.303.800.1515.1941,908,4081,656,7501.821.58[1:5:1:1]1,929,3801,709,1791.841.630.31,702,8871,814,9601,543,3221.621.731.47

535625.570212541427662.20745914983.534.540.2928.7951,782,5791,384,1201.701.32[1:3:3:1]2,001,6271,799,3561.911.720.41,680,8671,787,6671,583,3501.601.701.51

631853.4510135664239503.955.250.3333.0061,593,8361,198,3741.521.14[1:1:5:1]2,098,2011,878,0002.001.790.51,656,7501,760,3751,656,6691.581.681.58

730596.0779472414220804.115.690.3938.5771,530,9211,104,8061.461.05[1:1:3:3]2,327,8391,920,9912.221.830.61,623,9131,733,0821,690,3051.551.651.61

829338.7048809164209774.295.990.4039.8681,468,0061,049,6161.401.00[1:1:1:5]2,708,4722,012,2172.581.920.71,616,0891,705,7901,723,8591.541.631.64

0.81,667,9131,678,4971,746,9281.591.601.67

0.91,706,0871,651,2051,762,6561.631.571.68

11,707,0001,623,9131,810,0001.631.551.73

NumChnnls

LOF

CCP

Number of channels

Average response time per object (Sec.)

Comparison

LOF

CCP

Out-degree distribution


NumChannels

&A

Page &P

Related

Avg. access delay

Random

Factor of load balacing vs. clustering related objects


Average access delay (Sec.)

&A

Page &P

Related

Random

Factor of load balancing vs. clustering related objects


Basic Single6290540


LOFCCPRatio/SingleRatio/SingleCCP/LOF% ImprvLOFCCP

11257191257191.001.000.000.006,290,5406,290,540

263702625001.972.010.021.923,187,4263,127,282

343642426002.882.950.022.452,183,6932,131,555

434125330003.683.810.033.411,707,4961,651,205

528835273004.364.610.065.621,442,8031,365,997

625818239504.875.250.087.801,291,8431,198,374

723901220805.265.690.088.251,195,9231,104,806

822740209775.535.990.088.401,137,8301,049,616

80

Object Organization on Parallel Channels

1.50

1.70

1.90

2.10

2.30

2.50

2.70

Aver

age R

espo

nse

Tim

e Per

Obj

ect

(Sec

.)

Out-Degree Distribution

LOF

CCP

Broadcasting

Chart2

[5:1:1:1][5:1:1:1]

[3:3:1:1][3:3:1:1]

[2:2:2:2][2:2:2:2]

[1:5:1:1][1:5:1:1]

[1:3:3:1][1:3:3:1]

[1:1:5:1][1:1:5:1]

[1:1:3:3][1:1:3:3]

[1:1:1:5][1:1:1:5]

LOF

CCP

Out-Degree Distribution

Average Response Time Per Object (Sec.)

1.547

1.529

1.68

1.552

1.82

1.58

1.84

1.63

1.9089

1.716

2.001

1.791

2.22

1.832

2.583

1.919

Sheet1

BADACE

CEBD

BADAD

CEBCE

BA

C

A

CB

C

DG

D

CG

NumChnnls

Response Single6290540

Delay Single6290232

Data Rate1048576


LOFCCPRatio/SingleRatio/SingleCCP/LOF% ImprvNumChnnlsLOFCCPLOFCCPOODLOFCCPLOFCCPFRelatedRandomAvg. access delayRelatedRandomAvg. access delay

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Multiprocessing and Scalability · 17. Broadcasting Indexing Objects on air Channel. Advantages....

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