ﬁPervasive communication environments: the BIONETS ... · N But RF connectivity is subject to...

CREATE-NETvia Solteri 38, Trento

Italy

“Pervasive communication environments:the BIONETS perspective - 1st part”

F. De [email protected]

Autonomous Computingin Smart Environments

University of Fribourg, 23 - 24 November 2006

“Pervasive communication environments: the BIONETS perspective” 1/56

Wireless sensor networks

N “Recent advances in micro-electro-mechanical systems (MEMS) technology, wire-less communications, and digital electronics have enabled the development of lowcost, low-power, multifunctional sensor nodes that are small in size and commu-nicate untethered in short distances.” [Ak]

N Sensed phenomena with a wide spectra:

• temperature, humidity, pressure• mechanical stress• position speed and direction of an object• . . .

N Advantage of WSNs: sampling locally a field, with spatial resolution dependingon the sensor nodes density

N Temporal resolution: each sensor can report a time series of data


Wireless sensor networks

N Applications: environmental monitoring, military (surveillance, tracking), healthmonitoring, home automation ...

N Typical features required to sensors:

• cheap: < 1 $ per sensor• extremely low powered• the smaller the better• support very dense deployment• ease of deployment (often called self-organization)

N Once deployed, maintainance should be minimal

N If cost permits, better replace/add new units

N Power consumption: sensing, processing and communications.


Sensors nodes - Building Health Monitoring

courtesy of Ing. David Tacconi

N Application: Torre Aquila - Trento, his-torical building

N Remote server collecting data on: tem-perature, pressure and misallignementof building structure

N Sensor node: CrossBow Mica MoteN Sensing board: xy accelometer, micro-

phone, termometerN Node mounting full OS: Tiny-OS UC

Berkely

• Radio messaging• Multi-hopping from mote to mote• Low power modes• Sensor measurements and signal

processing of external peripherals


Sensor nodes - Building Health Monitoring

courtesy of David Tacconi

N Development: nesC on the PC

N Base station: allows the aggregation ofsensor network data onto a PC

N Base station acts as a sink

N Accelometer shoots when perturbationoccurs

N Avoid wasting resources for “normalconditions”: run-length encoded data


Directed diffusion

N Sensor network achitecture is data centric

N Directed diffusion [Es1,Es2]: reference paradigmN Sensors execute certain tasks, referenced according to predefined attributesN Elements of directed diffusion [Es1]: interests, names, data messages, gradients

and reinforcementsN Iterest messages generated at sinks:

type = wheeled vehicle // detect vehicle location

interval = 20 ms // send events every 20 ms

duration = 10 seconds // for the next 10 seconds

rect = [-100, 100, 200, 400] // from sensors within rectangle

N Data messages are generated by sensors responding to interests:type = wheeled vehicle // type of vehicle seen

instance = truck // instance of this type

location = [125, 220] // node location

intensity = 0.6 // signal amplitude measure

confidence = 0.85 // confidence in the match

timestamp = 01:20:40 // event generation time


Directed diffusion

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Interest I Source

Sink

I entryStore interest

N No source-destination pairs as in IP

N Kind of semantic addressing matchingthe application

N Sink node express interest propagatinga query (initial flooding)

N Initial gradient setup is exploratory, i.e.low update rate requested

N Any potential source node stores the en-try in a local cache

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SinkData matches I

N +/- Reinforcement of routes

N Loop avoidance


Conveying data

N Conveying data across the network becomes the first step in order to make themavailable at the sink: we would like to make it “efficiently”

N From the application down to the bit transmission, collecting data in pervasive/sensorizedenvironments: Where is the bottleneck?

N What we do want from the network architecture is

• No need for fixed topology• Mobile units do take part to the network topology• No wiring• Easy replacement/maintainance

N Also, we would like to be free to add/replace/switch-off as many nodes as wewant with no need for reconfiguration

N But, packing all this nice features altogheter usually has a price ... efficiency

N Not enough: devices should last the longest the possible, i.e., make a parsimo-nious use of batteries.


RoutingN Traditional techniques for ad-hoc networks

• Flooding: robust and fast but expensive; MAC problems with broadcast(ex. 802.11)

• Proactive Routing Techniques: determine routes independent of traffic pat-tern. Destination-Sequenced Distance-Vector (DSDV)(Bellman-Ford)

N nodes maintain each destination in network,N control traffic

• Reactive: determine routes when needed. Dynamic Source Routin (DSR),Ad-Hoc on demand Distance Vector routing (AODV)

N source node broadcasts route request packets RREQsN destination and intermediate node with reply RREP packetsN route metrics: hops, link quality ...

N Not suitable for sensor networs: energy constraints the applicability of routemaintainance, topology simply “aslept”

N Directed diffusion: data centric paradigms [KamSurvey]


MAC solutions

N TDMA/FDMA: requires syncronization and scheduling, collision free

N Random Access (ALOHA): slot-less or slotted

N Carrier sense multiple access (CSMA): slotted or slot-less

N Polling: master/slave

Problem: idle listening consumes a lot of energySolutions: sleep as much as possibleNodes do not sleep when they carrier sense: refined techniques

N TynyOS S-MAC: periodic listen and sleep, fixed duty cycle, need to synchronizeneighboring nodes schedules

N TynyOS T-MAC: adaptive duty-cycle

N TinyOS B-MAC: wake up and check channel status, send long preambles


Off the shelf MAC: CSMA/CA

N The “ancient” standard for ad-hoc networks is represented by the IEEE802.11xfamily

N The reason for its success: plug-and-play, ad-hoc mode and cheap hardware im-plementation

N The basic mechanism for medium access control is the well known CSMA/CAprotocol

N Basically the de-facto standard of wireless technologies

N No wonder: fashionable also IEEE802.15.4 - Zigbee used for Mica Motes

N What is going to happen for large size deployments under CSMA/CA, does itscale?

N Known results under saturation conditions


CSMA/CA

N Mechanism: a node listens to the medium (CS: Carrier Sense)

N When the medium is perceived idle for longer than a DIFS: transmit

N If the medium is busy: freeze the counter and decrement after one idle slot

N If no ACK is coming back: either error or collision, retry

N Retry up to a maximum number of attempts

PacketArrival

Case Idle

Case Busy

DIFS

DIFS DataBusy BackoffACK

DataACK


Limit performances of CSMA/CA

N Bianchi’s model or also fixed point analysis duable in saturation [Bianchi,KumMior]

N The system is bounded by the number of nodes

N Listening to the medium and to freezing the backoff counter has a cost: delay

N Basically: service time is increased at each alien tranmission

N Even worse: collisions and retransmissions are overheard due to the protocol

N Closed form analysis for the service time consumption of the system [ZaDe1]

ws = Ts +nc

∑

j=1

Tc,j + τB

N Channel sensing becomes a dramatic waste of energy [ZaDe2]


Service time of CSMA/CA

n=10

n=30 n=50 n=70n=100

TheorySimulation×

1

0.8

0.6

0.4

0.2

00 0.2 0.4 0.6 0.8 1

Fw

s(t

)

Figure 1: Cumulative Distribution Function of the service time ws (n =10, 30, 50, 70, 100, packet–length of 600 bytes.


Service time of CSMA/CA

20

15

10

5

00 0.04 0.08 0.12

t [s]

×10

−3

TheorySimulation

p ws(t

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0

1

2

3

4

5

×10

−3

0.0168

b)

a)

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Figure 2: a) Mass distribution function b) Detail of the third spike.


Idle mode impact on energy consumption

number of stations

Nor

mal

ized

life

β0 = βS

β0 = 1/2 βS

β0 = 0

Basic access modeRTS/CTS

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

Figure 3: Normalized Life of stations: basic access mode (solid line) and RTS/CTSaccess mode (dashed line), β0 = 0, β0 = 1/2βS and β0 = βS .


.

Ad-hoc Networks


Wireless Ad-hoc networks

N The most flexible network architecture we canthink about: ad-hoc means shaped to obtain aparticular aim.

N Example: deploying a wireless sensor networkwould be made much easier made [SmartDust]style, the configuration of the network beingdictated by the landscape peculiarities

N What kind of network would one obtain?

N There exist strict constraints on the scalabilityof ad-hoc networks

N Several studies on the capacity and connectiv-ity of ad-hoc networks since 2000 cornerstonework [GuptaKumar]


Static ad-hoc networks

N Several connectivity models

N Simplistic view: two nodes communicate if they are within radio range (Booleanmodel)

N But RF connectivity is subject to interference, links actually depend on everyother transmission

N Success depends on interferers: if node i transmits to node j

N Physical model: SNIR(i , j) = Pi /|Xi−Xj |α

N0+γP

k 6=i Pk /|Xi−Xk |α> β

N Protocol model: |Xj − Xj | < (1 + ∆)|Xj − Xk |, for any other node k

For both models Gupta and Kumar proved that the order of capacity for randomnetworks unitary sphere/disk is

λ(n) = Θ(1/√

n log n)



N Consequences: it seems we cannot design our favorite “pervasive” ad-hoc net-works disregarding scalability issues

N Even with “perfect scheduling algorithm which knows the locations of all nodesand all traffic demandes, and coordinates wireless transmissions temporally andspatially to avoid collisions which would otherwise result in lost packets”

N Proof in [GuptaKumar]: upper and lower bound

N Three factors into play (protocol model):

• length of routes: we have to traverse several relays• number of nodes• area “occupied” by useful transmissions

Possible solution is locality as suggested in [GuptaKumar]: sources communicatingonly to nearby nodes (smart homes)



N Later result [DT]: connectivity and the capacity depends on the attenuation func-tion l(|Xi − Xj |)

N Everything can be expressed in terms of the interference ratio

SNIR(i , j) =Pi l(|Xi − Xj |)

N0 + γ∑

k 6=i Pk l(|Xi − Xj |)> β

N Physical reasons force the attenuation function to be bounded l(x) < M

N The trade off is between capacity (β) and connectivity (γ)

N Dousse and Thiran: if the attenuation function is positive and bounded, then thetransport capacity is bounded above by a constant, independently of the numberof nodes

N Uniform traffic matrix: O(1/n)


Effect of Relays

1st hope: Gastpar and Vetterli [GV]: coding can improve ad-hoc network capacity

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N One source-destination pair

N The remaining n − 2 nodes act as relays

N Relays cooperate with source and destination in orderto make them communicate

N Allow for arbitrary complex coding schemes

N Half duplex scheme: source transmits every two timeslots

N Signal model as in [GK], Gaussian relay network,power of noise N

N Power of the source ≤ P, (cumulative) power of therelays ≤ (n − 2)P


Effect of Relays

The result holds asymptotically: upper and lower bound match as n diverges

N Upper bound: broadcast channel bounds Cupper ≤ 14 log2(1 + (

∑nk=2 α2

k )P/N)

N No relay closer than r0 > 0 to the source: then fading coefficients αk are boundedunder suitable assumptions

N Lower bound: constructive scheme;

• At t + 1 relays repeat signal received from source in slot t , scaling downpower accordingly

• Destination decodes: Xn(t + 1) = γ1Yn(t) + γ2Yn(t + 1)

• Finally: Clower ≥ 14 log2(P/D1), D1 = PN

N+Pf

N [Gastpar - Vetterli] The capacity Clower ≤ C ≤ Cupper , upper and lower boundconverge and C is in the form:

log(1 + ||α||P/N)


The impact of mobility

N 2nd hope: work from Glossglauser and Tse [2002]

N Search for a mechanism that does not degrade with the number of nodes.

N Technical assumptions:

• n nodes in the unit circle of unitary area• fixed pairs Source-Destination• nodes follow i.i.d trajectories• node positions are uniform over the disk at each point in time (this does not

scale with the number of nodes)• slotted time model• Success: SNIR(i , j) = Pi γij

N0+(1/L)P

k 6=i Pk γkj> β

• γij = |Xi − Xj |−α, α > 2



N From the static case: typical length of S-D paths is√

n

N Relaying is the bottleneck? Let us try to transmit directly.

N But, it does not scale: in [GT] the maximum number of successful allowed trans-missions per slot is Θ(1).

N This is bad: throughput per session is smaller than n−1/(1+α/2) and α > 2.(o(

√n))

N Hence some relaying is due.

N Key intuition: relay the less the possible.

N How less?



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The two-hop relaying protocol proposed in [GT]:

N Step 1: source node has the packet

N Step 2: first hop, source node handes off the packet toa relay neighbor

N Step 3: second hop, the relay neighbor deliver thepacket to the destination

This scheme under suitable assumptions provides a con-stant long term source destination throughput, i.e. Gloss-gauser and Tse proved that using mobility in wise man-ner, one can make per session throughput a constant inthe number of nodes Θ(1).


The impact of mobilityN Constructive proof in [GT] pivoted on the 2-hop relay protocolN The protocol works picking a sender density θ ∈ (0, 1)

N Pick randomly a set of nS sources out of n nodes, nS = θn

N The remaining nR = n − nS are designated receiversN Keep only Nt sources such that interference permit transmissionN Implement half duplex (odd and even time slots)N The 2-hop protocol is able to sustain Θ(n) feasible source-destination pairs Nt (!)N Due to symmetry: probability that feasible S-D pair i and j is picked is Θ(1/n)

N Throughput per feasible pair: Θ(1/n)

N Sum up on the n − 1 possible relay “paths” the result in follows

[Glossglauser-Tse] The two-phased algorithm achieves a throughput per S-D pair ofΘ(1), i.e. there exist a constant c > 0 such that

limn→∞

Pr{λ(n) = cR is feasible} = 1



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GT

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n

√

nlog n

1/√

n log n1/n 1

D(n)

T (n)

N Mobility enhances capacity: at which cost?

N In [GT] already pointed out: delay would di-verge.

N El Gamal et. al. [ElGa] in 2004: formalizationof the trade-off between throughput and delay

N Three schemes on the unit torus

N Static ad-hoc (Scheme 1):

↓ D(n) = Θ(√

n/ log n) T (n) = Θ(1/√

n log n) ↓

N Pure mobility (Scheme 2):

↑ D(n) = O(n) T (n) = Θ(1) ↑



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N Scheme for covering the intermediate caseN Divide the unit torus into a(n) cells; each cell

divided into b(n) = Θ(log n/n) subcellsN Cellular TDMA scheme proposed in [ElGa]:

Θ(na(n)) packet time slots per cell slot (speedand packet length shrink with n)

N Split each packet time slot into two subslotsN Subslot A: send to destination if in the same

cell, otherwise, send along cells along segmentSR to a relay picked randomly

N Subslot B: each node picks another node atrandom in the same cell and send a packet des-tined to it

[El Gamal et al.] If v (n) = o(√

log n/n) then the scheme

T (n) = Θ(1/√

na(n) log n), D(n) = O(1/a1/2(n)v (n))

where a(n) = O(1) and a(n) = Γ(log n/n)


Connectivity issues

N Deep result: connectivity and capacity are strictly related in ad-hoc networks[DFT]

N Percolation theory: Bn = [o,√

n]2, extendend model, Poisson point processN Full connectivity within Bn has a cost: radius has to increase as log n

N Conversely, for every positive fraction of nodes 0 < θ < 1, there exist r > 0such that a connected cluster of nodes contains a fraction θ of the nodes

Discarding part of the nodes things get better:

[Dousse, Franceschetti, Thiran] (LB) For any 0 < θ < 1, there exist a rate R > 0independent of n, such that there exist a subset of the nodes of size nθ in which eachnode can send data to any other node at rate R w.h.p.

[Dousse, Franceschetti, Thiran](UB) For any rate R > 0, the fraction of nodes thatcan send data to any destination at that rate is at most θ w.h.p., where θ = P[I ≥N0P (22R − 1)], where I is the shot noise defined by I =

∑

x∈N l(||x||), and N is aPoisson process with unit density (θ < 1).


.

Processing and communications



N Sensing: huge variability of random field

N High sample rate means large amounts of data to be collected and processed

N Sampling should be fast enough to guarantee both accuracy and delivery

N The trade-off is between communications and processing

• Concrete example [KaiserW]: 1GHz carrier frequency; antenna elevationof 1/2 wavelength; BPSK transmission, 10−6 BER, distance loss α = 4,Rayleigh fading, ideal (nonoise) receiver.

• Energy: 1Kb a distance of 100 m is approximately 3 J.• Processor: 100 MIPS/W executes 3 million operations

Quite clear: if possible process locally and save on communications



N Simple(istic) example: majority voting in a n sensors WSNs

N Two events: E = {0, 1}; typical alarm detection

N Estimation: decide 1 if the number of ones detected is less than the number of 0s

Sink

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0

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• Assume: transmitted bits dictate the cost

• First strategy: send data to sink and decide

C = 1(n − 1) + 2(n − 1 − 2) + 3(n − 1 − 3) +

. . . + log(n − 1)(n − 1 − 2log(n−1)−1) = Θ(n log2 n)

• Second strategy: each node evaluates the majorityoutcome of children, and encodes the number ofvotes: C = Θ(n log n)

• small gain but ...


Majority voting

N Again on majority voting: in colocated networks

N Approximated hypothesis testing is possible using batch conflict resolution: col-lisions do carry information on the number of contending nodes

N Data collection at the sink: collect and decide if N0 > N1 or viceversa

N [PZ] trade off between MAC and Application layer: let the application be awareof the Medium Access Control

N Leverage the information about the number of transmitters

N Stop contention as soon as the majority estimation error probability is below acertain threshold

N Still packetized solution: practically feasible


Majority voting

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• Tree split algorithms; best im-plementations achieve almost halfchannel capacity

• No carrier sensing: every sensortosses a coin

N tail: transmitN head: skip the slot and toss again

• Channel has three states:I(dle),C(ollision),S(uccess)

• Need return channel to feedbacktransmission result


Majority voting

N Number of sensors N is unknown: just jumped into the sensor field

N Start collecting N0 and N1: eventually 2 binary split trees with p0 and p1

N TDMA collecting first 1s and then 0s

N n0 number of sensor tossing 0 (they transmit): say Np0

N Bernoulli trials: P{n0 = Np0 |N = N0} =( N0

Np0

)

pN00 (1 − p0)N−N0

N Most likely value: moda = b(N + 1)pcN For small p0, 1/p0 of them: P{N = N0|n0 = Np0} ∼ p0 P{n0 = Np0 |N = N0}N Maximum likelihood approximate majority voting

N0 = bNp0/p0c N1 = bNp1/p1c

N [PZ] upper bound to the error probability: stop batch resolution the upper boundis below a threshold


Wireless networks as estimators

N Change of perspective: do you really need the sink node and elaborate only afterdata are collected there?

N Answer: no, there exist certain cases when the estimation can be made availableat each node [Gian]

N Good news for pervasive communication/computing environmentsN Using gossip propagation: only communicate with neighbors and propagate hop

by hop (no need for end to end communication)N Notice: no packetized communication assumed, can be done “bitwise”N M sensors deployed: general not colocated multihop communicationsN Sensor network to estimate s ∈ Rp

N Assumption of a linear model on the observations xj ∈ RLj

xj = Hjs + nj

N nj random vector noise with given covariance matrix Σ


Wireless networks as estimators

N Need additional hypothesis on full rank of H = [HT1 HT

2 . . . HTM ]T

N BLUE estimator s = Cx, C = (HT Σ−1H)−1

HT Σ−1

N Ambitious task: can you find a BLUE estimate at each sensor (if needed in infiniteiterations)?

N Answer: yes and exchanging “messages” only with the neighborhood

N Two fully distributed algorithms:

• full knowledge on C

• local knowledge on Hj

N Through iterative optimizations consensus is achieved, meaning that every sensorconverges to the s [Gian]

N Notice: in order to build the algorithm, solutions can be found constraining theoptimization to obtain consensus, i.e. same estimate, in sensors’ neighborhoodonly


In-network computation

N Limit performances of sensor networks when computing is accounted for [Kum2,Kum3]

N Target: communicate a given function f n : χn → Yn to the sink(s)

N Nodes take measures in a finite set χ and can communicate blocks of measures

N No channel errors accounted for

N [Kum2] under protocol model: important insight in improvements achievablewith current technologies

N The big question: how fast can you sample the function of the field? Rate ofcomputing allowed by a sensor network Rnmax

N Proved strong dependence on:

• topology: colocated vs multi-hop random planar• computed function



N Independence from the data arrival order: symmetric functions

N Type sensitive functions:

• functions such that, from a given number of sensor readings on, there exista fraction of the readings that are sufficient to discriminate output values,i.e. to state that they are different

• sample functions: mean, median, mode• ex. χ = 1, 100, mean function: fix the first half values, put remaining 1/2

values either 1 or 100

N [Kum2] In colocated networks, for any possible collision free strategy,

Rnmax = Θ(1/n)

N [Kum2] In random planar networks, under suitable covering radius scaling, w.h.p.

Rnmax = Θ(1/ log n)



N Type threshold functions:

• functions such that there exist a reference type vector θ such that (element-wise) larger data frequencies do not affect the reference function

• sample functions: max,min,range• ex. max , θ = 1

N [Kum2] In colocated networks, for any possible collision free strategy,

Rnmax = Θ(1/ log n)

N [Kum2] In random planar networks under suitable covering radius scaling, w.h.p.

Rnmax = Θ(1/ log log n)

N Type threshold functions are exponentially easier to compute than type sensitivefunctions


.

Location Detection


Location detection

N Location detection is a very popular application of WSNs

N Existing examples of indoor location detection systems:

• Infrared: Olivetti Research Laboratory Active Badge location system. Abadge periodically emits a unique ID using diffused IR received by one ofseveral receivers scattered throughout a building;

• Ultrasound: Active Bat or MIT Cricket measure time-of-flight of ultra-sound with respect to a reference signal;

• RF propagation: Microsoft RADAR pre-computed SNR map and comparesreceived signals; distances from base stations are triangulated to obtain theposition;

Emergency response: robustness is a key issue, and location detection systems shouldprove robust to multiple sensor failures.


Location detection

N A location detection system designed through Identifying codes [Lev]

N System makes use of a robust modification of identifying codes built over anarbitrary topology,

N location tracking: observer transmits IDs and the system determines his location

N Let us focus on the dual location service: observer can determine his location

N Transmitters occupy certain positions: each transmitter periodically broadcasts aunique ID

N Observer waits T at his current position collects the ID’s from the packets hereceives

N Collisions can be efficiently solved by common MAC protocols within T

N The covered locations are all those areas receiving a set of IDs (problem of iden-tifying graphs)


Location detection

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ID(d) = {d}

ID(e) = {c, d}

ID(f ) = {b, d}

ID(g) = {a, d}


Location detection

N Procedure: model a physical environment with a graph G = (V , E),N vertices V indicate locatable regionsN edges E connect regions with RF connectivityN A non-empty subset C ⊆ V is called a code, its elements are called codewords.N Given a code C, the identifying set of a vertex v ∈ V is defined to be

IC(v ) = B(v ) ∩ C. (1)

N Code C is called an identifying code if for every u, v ∈ V

IC(u) 6= IC(v );

N C is irreducible if deletion of any codeword from C results in a code that is nolonger an identifying code.

N G = (V , E) is distinguishable if an identifying code exists for it


Location detection

N Location detection in general relies on irregular graphs

N Distinguishability can be enforced a posteriori

N Generation of an optimal identifying code is NP-complete.N Problem: Given a distinguishable graph G = (V , E), compute a subset C of V

such that C is an identifying code for G and C is irreducible.

ID-CODE(G, a)C = Vif C is not an identifying code

do EXITfor each vertex x ∈ a, taken in order

do D = C \ {x}if ∃ u, v ∈ V such that ID(u) = ID(v )

C = C

else C = Dreturn C


Location detection

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N Vertices visited a = {f , g, d , e, a, b, c}, then C = {a, b, c}N Conversely with a = {a, b, c, d , e, f , g}, then C = {d , e, f , g}N The code C returned by ID-CODE is irreducible.N Complexity is O(|V |2 log |V |)


Location detection

The case for robustness:

N Destruction of ID-transmitting vertices through the emergency agent (e.g. , fire,water, explosion).

N Variation of radio paths due to changes in building structure (e.g. , walls collaps-ing, furniture shifting, people moving).

N Failure of ID reception due to medium access control scheme limitations.

N Due to reflections or some other channel variations due to extreme conditions,some spurious packets may come to the observer.

Def. 1 An identifying code C over a given graph G = (V , E) is said to be r -robust if

IC(u) ⊕ A 6= IC(v ) ⊕ B

for all u, v ∈ V and A, B ⊆ V with |A|, |B| ≤ r .


Location detection

N A ⊕ B = (A ∪ B) \ (A ∩ B)

N dmin(C) , minu,v∈V |IC(u) ⊕ IC(v )|

N A code C is r -robust if and only if

dmin(C) ≥ 2r + 1.

N The maximum robustness achievable by an identifying code over a graph G =(V , E) is given by dmin(V ), and is upper bounded by the sum of the degrees ofany two vertices in the graph.

N Of course the problem is still NP − complete

N Quite simple to modify the greedy algorithm presented before


Location detection

N r -ID-CODE algorithm generates r -robust identifying codes for an arbitrary graph

N Not every graph has a r -robust code

N But deletion of a node from a code decreases dmin(C)

N The robust version of the algorithm:

r -ID-CODE(G, a, r )C = Vif dmin(C) ≤ 2r

do EXITfor each vertex x ∈ a

do D = C \ {x}if dmin(D) ≤ 2r

C = C

else C = Dreturn C


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(h) 0-robust code.

N 0-robust code requires 16 transmitters among the 64 points of resolution

N 1-robust code requires 32


Location detection

0 200 400 600 800 10000

0.1

0.2

0.3

0.4

Number of nodes

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N Fraction of sensorized locations scales at the increase of the number of locations

N Asking for robustness costs in the size of the code, i.e. number of sensorizedlocations

N Complexity is O(|V |3)


BibliographyN [Ak] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam and E. Cayirci, “Wireless sensor networks: a

survey”, Elsevier Computer Networks, Vol 38, 2002, pp. 393-422

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N [Es1] C. Intanagonwiwat, D. Estrin, R. Govidan and Fabio Silva, “Impact of Network Density onData Aggregation in Wireless Sensor Networks”

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N [GuptaKumar] P. Gupta and P. R. Kumar, “The Capacity of Wireless Networks”, IEEE Trans. onInformation Theory, Vol. 46, No. 2, March 2000.

N [DT] O. Dousse and P. Thiran, “Connectivity vs Capacity in Dense Ad Hoc Networks”, in the pro-ceedings of INFOCOM 2004, Hong Kong.

N [GT] M. Glossglauser and D. Tse, “Mobility Increases the Capacity of Ad Hoc Wireless Networks”,IEEE/ACM trans. on Networking, Vol. 10, no. 4, August 2002.

N [GV] M. Gaspar and M. Vetterli, “On the Capacity of Wireless NEtworks: the Relay Case”, in theproceedings of INFOCOM 2002, New York.


N [ElGa] A. El Gamal, J. Mammen, B. Prebhakar and D. Shah, “Throughtput-Delay Trade-off in Wire-less Networks”, in the proceedings of INFOCOM 2004, Hong Kong.

N [DFT] O. Dousse, M. Franceschetti and P. Thiran, “On the Throughput Scaling of wireless RelayNetworks”, IEEE Transactions on information Theory, Vol. 52, No. 6, June 2006.

N [PZ] E. Bottega, P. Popowsky, M. Zorzi H. Yomo and r. Prasad, “Hypothesis Testing over a RandomAccess Channel in Wireless Sensor Networks ”, in the proceedings of EURASIP EUSIPCO 2006,Florence.

N [Gian] I. Schizas, A. Ribeiro and G. B. Giannakis “Distributed Estimation with Ad Hoc WirelessSensor Networks”, in the proceedings of EURASIP EUSIPCO 2006, Florence.

N [Lev] M. Karpovsky, K. Chakrabarty and L. Levitin, “A New Class of Codes for Identification ofVertices inGraphs”, IEEE Transactions on Information Theory", Vol. 44, no. 2, 1998, pp. 599-611"

N [SFR] S. Ray, R. Ungrangsi, F. De Pellegrini, A. Trachtenberg and D. Starobinski, “Robust LocationDetection in Emergency Sensor Networks”, in the proceedings of IEEE INFOCOM 2003.

N [SchPap] D. S. Scherber and H. Papadopoulos, “Distributed Computing of Averages over Ad-hocNetworks”, IEEE JSAC, vol. 23, No. 4, April 2005.

N [Kum2] A. Giridhar and P. R. Kumar, Computing and Communicating Functions over Sensor Net-works”, IEEE JSAC, pp. 755-764, vol. 23, no. 4, April 2005.

N [Kum3] A. Giridhar and P. R. Kumar, Towards a Theory of In-Network Ccomputation in WirelessSensor Networks”, IEEE Communications Magazine, vol. 44, no. 4, pp. 98-107, April 2006.

N [ZaDe1] A. Zanella and F. De Pellegrini, “Statistical Analysis of the Service Time in Saturated IEEE802.11 Networks”, IEEE Communication Letters, March 2005.


N [ZaDe2] A. Zanella and F. De Pellegrini, “Mathematical Analysis of IEEE 802.11 Energy Efficiency”,in the proceedings of WPMC 2004.

N [KuMior] A. Kumar, E. Altman, D. Miorandi and M. Goyal, “New Insights from a Fixed Point Anal-ysis of Single Cell IEEE 802.11 WLANs", to appear in IEEE/ACM Trans. on Networking.

N [Bianchi] Giuseppe Bianchi, “Performance Anaylsis of the IEEE 802.11 Distributed CoordinationFunction", IEEE Journal on Selected Areas in Communications, Vol. 18, Number 3, March 2000.

N [KamSurvey] J. N. Al-Karaki and A. E. Kamal, “Routing Techniques in Wireless Sensor Networks: ASurvey", IEEE Wireless Communications, pp. 6-28, vol. 11, no. 6, 2004.

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