Routing Indices For Peer-to-Peer Systems

Svetlana Strunjas

University of Cincinnati

May,2002

Outline

Motivation and background

P2P systems

Routing Indices

Experimental results

Conclusions

Motivation

Create efficient and feasible

distributed – index search mechanism for P2P systems

Background

Napster – centralized indices (vulnerable to attack and difficult to scale)

Gnutella – queries flood significant part of the network(simple but very costly approach)

Background(cont’d 1)

Freenet – each node builds an index with the location of recently requested documents (queries are restricted to the specific documents and it takes time for node to build an effective index)

Background(cont’d 2)

Oceanstore – distributed – index approach similar to Routing Indices(special case of Compound RIs)

Key difference is in static network and queries on document identifier (Oceanstore) versus dynamic network and queries on content of document(Routing Indices)

Background(cont’d 3)

Selecting a neighbor for forwarding query using Routing Indices is generalization of the Bellman-Ford algorithm

Bellman – Ford algorithm -transmits packet between two nodes through the shortest route -destination of packet is pre-defined(IP routing) Routing Indices -transmit packet from node to node in order to find best answer to the query -destination of packet is not pre-defined , but instead depends on query contained in packet

P2P Systems(Introduction)

Formed by a large number of nodes that can join or leave the system at any time and have equal capabilities

Each node has local documents database which can be accesed through local index

The local index receives content queries and returns pointer to the document with requested content

Query Processing in Distributed P2P Systems

Users submit queries to any node along with the stop condition

Node receives query , evaluates the query against it’s own database ,returns pointer to any results , and , if the stop condition is not reached , forwards the query to neighbor(s)(parallel or sequentially)

Routing IndicesIntroduction

RI allows a node to select “best“ neighbors to send a query to

It is data structure(and associated algorithm) which ,for given query , returns a list of neighbors , rank according to their goodness for query

Goodness reflects the number of documents in “nearby” nodes

Routing Indices Types

Compound Routing Indices(CRI)

Hop-count Routing Indices(HRI)

Exponential Routing Indices(ERI)

Compound Routing Indices(example)

CRI(cont’d1)

Documents are on zero or more topics,and queries request documents on particular topic

Each node has a local index for quickly finding local documents

CRI contain the number of documents along each path and the number of documents of each topic of interest

CRI(“goodness” estimators)

Measure of “goodness” of the neighbor , for given query , is number of documents that can be found in that path

Estimated number of results along each path is given by formula:

CRI(drawbacks)

CRI do not take into account the difference in cost due to the number of hops necessary to reach the document

Are not applicable if we have cycles in network

Using RI

 

RIs with four topics of interests : database,network,theory and languages

Storage space required

It can be adjusted by increasing or decreasing the level of summarization of index

For centralized systems it is C*(T+1)*N bytes For distributed systems it is C*(T+1)*B*N C – number of categories T – counter size in bytes B – branching factor N – number of nodes

Creating (maintaining)RIs

Disconnection from Network

150 75 0 75 125 1500 110 80 70 165

Algorithm for Creating/Updating RIs

There are two phases :

1.Newly connected node sends a summary of its local index to its new neighbors (creation phase)

2.The node waits for update messages or for changes on its local index ; after updating its RI , the node sends a new aggregate RIs to all its neighbors

Algorithm for Answering Queries

It runs every time query is receivedQuery is given together with stop conditionThere are three phases: 1.Node attempts to answer the query using its local db

2.If not enough results are obtained to reach stop condition , the

algorithm ranks all the neighbors using estimating function

3.Node sends the query to each neighbors sequentially,checking if

the stop condition was reached whenever each query returns

Hop-count RI

Store aggregated RI for each “hop” up to a maximum number of hops(horizon of the RI)

Hop-count RI(cont’d1)

Goodness of neighbor is defined as ratio between the number of documents available through that neighbor and the number of messages required to get those documents

Simple model that allows us to compute this ratio is regular-tree model

Hop-count RI(cont’d2)

Model assumes that all nodes are connected to exactly F+1 nodes , except ones at the leaves which are connected to only one

Goodness of the neighbor is given by formula:

goodness() – estimating function for CRINi[j] –RI entry for j hops through i-th neighborF-fanoutH-horizon

Hop-count RI(drawbacks)

HRI performances can be negatively affected by the lack of information beyond the horizon

Higher storage and transmission cost than CRI

Exponentially Aggregated RI

Stores the result of applying the regular-tree cost formula to hop-count RI

Exponentially Aggregated RI(cont’d)

Each entry of the ERI for node N contains a value computed as:

th – height of the assumed regular treegoodness() – estimating function for CRIsN[j] – summary of the local index of neighbor j of NT – topic of inerest for entry

With ERIs we can keep information for all nodes

accessible from each neighbor in the RI,while HRI’s do not have

any information beyond horizon

Cycles in P2P Network

There are three approaches for dealing with cycles: No-op solution

Cycle avoidance solution

Cycle detection and recovery

No-op solution

Works only with the HRI and ERI

If there are cycles CRI algorithm can be trapped in an infinite loop

NO-op solution (cont’d1)

10 15

20

G1=21.67G2=23.58

NO-op solution (cont’d2)

In HRI cycles longer than horizon will not affect the RI

If we use regular-tree cost model we can limited effect of short cycles

In HRI and ERI difference between two values of goodness introduced by cycle is very small(algorithm will not propagate updates which are not much different than old value)

Cycle avoidance solution

Do not allow nodes to create an update connection to other node if such connection creates the cycle

Drawback : Absence of global information causes suboptimal update network

Cycle detection and recovery

Detects cycles sometime after they are formed and takes recovery actions to eliminate the effect of the cycles

Cycles are detected using unique message identifier

Recovery procedure can decrease accuracy of the RI

Experimental Results(Introduction)

Results are obtained using different models for

elements of search mechanismSteps of experiment:

1.Setting P2P system as network of nodes T, where each node

contains set of documents

2.Users send requests consisting of query Q and stopCondition

to a node of P2P system

3. search mechanism answers requests by obtaining a set of documents of size

stopCondition that matches Q

4.search mechanism allows for update such as addition of nodes and new

documents

Experimental Results(Techniques and measure of cost)

Search techniques : CRI , HRI , ERI,

No-RI(for comparison purposes)

Measure of cost:numbers of messages generated

Experimental Results(Network topologies)

Topology of network defines number of nodes and how they are connected

In this model , three kinds of topologies are considered:

1.Tree 2.Tree with added cycles 3.Power-law graph

Experimental Results(Distribution of documents)

Distributions for modeling the location of document results :

1.Uniform distribution( all nodes have the same probability of having each document result)

2.80/20 biased distribution ( assigns uniformly 80% of the document results to the 20% of nodes , and the remaining 20% of the documents to the remaining 80% of nodes)

Experimental Results(Simulation parameters)

Experimental Results(Comparison of CRI,HRI and ERI)

Experimental Results(Number of results)

Experimental Results(Effects of overcounts)

Experimental Results(Effects of cycles)

Experimental Results(Network topology)

Experimental Results(Updates and network topology)

Experimental Results(Updates and cycle policy)

Experimental Results(Updates per minute)

Conclusions

ERI and HRI offer significant improvements versus not using an RI,while keeping update costs low

Routing indices (in particular ERI and HRI can help improve the search performance of current and future P2P systems

References:

[1] A.Crespo , H. Garcia-Molina.Routing Indices For Peer-to-Peer Systems(2001).The 22nd International Conference on Distributed Computing Systems ,Vienna , Austria.

[2] J.F.Kurose , K.W.Ross.(1999).”Routing Principles”.Computer Networking – A Top Down Approach Featuring Internet, 2nd ed. , Addison Wesley,4.