Multipoint relaying for flooding broadcast messages in mobile wireless networks

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Multipoint relaying for flooding broadcast messages in mobile wireless networks

Amir Qayyum, Laurent Viennot, Anis Laouiti

To cite this version:

Amir Qayyum, Laurent Viennot, Anis Laouiti. Multipoint relaying for flooding broadcast mes- sages in mobile wireless networks. 35th Annual Hawaii International Conference on System Sciences (HICSS’2002), Jan 2002, Maui, United States. pp.3866 - 3875. �inria-00471699�

Mobile Wireless Networks

Am ir Qayyum , Laurent Viennot, Anis Laouiti

ProjetHiperom,INRIARoquenourt,B.P.105,78153LeChesnayCedex,Frane

Email:Amir.Qayyuminria.fr,Laurent.Viennotinria.fr,Anis.Laouitiinria.fr

Abstrat

Inthispaperwedisussthemehanismofmul-

tipoint relays (MPRs) to eÆiently do the ood-

ingof broadastmessagesinthe mobilewireless

networks. Multipoint relaying is a tehnique to

reduethenumberofredundant re-transmissions

while diusing a broadast message in the net-

work. Wedisuss theprinipleand thefuntion-

ing of MPRs, and propose a heuristi to selet

theseMPRsinamobilewirelessenvironment.We

also analyze the omplexityof this heuristiand

prove thatthe omputationof a multipoint relay

setwithminimalsizeisNP-omplete. Finally,we

present some simulation results to show the eÆ-

ienyofmultipointrelays.

keywords: multipointrelays,mobilewireless

networks,oodingofbroadastmessages

1 In trod u tion

Theresearhrelatingtomehanismsandproto-

olsusedinthewirednetworksisbeomingma-

ture. As a result, these mehanisms and proto-

olsarenowlassiedaordingtotheir relative

domainsofappliation,basedonperformanere-

sultsobtainedinthosespeiareas.

For mobile wireless networks, the researh is

still in its earlier stage. There is less onsen-

sus about the appliability of dierent existing

tehniques and algorithms in these new type of

networks. To obtain a satisfatory performane

fromthesetehniquesoralgorithms,theymustbe

madeadequate tothis newand hallengingenvi-

ronment.

Speially,ad-horadionetworkshaveanin-

herent apaity for broadasting, i.e., with one

emission, anode anreah all thenearby nodes.

Using this apability for optimizing broadast

messages insuhnetworksisa hallangingtask.

A ompromise has to be made between a small

number of emissions and thereliability. Several

tehniques are desribedin theliterature tolimit

or optimize the ooding of broadast traÆ [1℄,

[2℄,[3℄,[4℄,[5℄,[6℄,[7℄.Someresultsofompari-

sonbetweenthesetehniquesanbefoundin[8℄.

Our paper disusses in detail the mehanism of

\multipointrelaying"asoneofthepossiblesolu-

tion,rstpresentedin[2℄. Comparisonwithother

tehniquesisreservedforfuturework.

1.1 Requirem ents of a mobile wire-

less environm ent

In\mobile"\wireless"networks,eahofthese

two words put before us a list of requirements,

and the daunting task is to fulll them to their

best. Themobilityimpliesthelimitedlifetimeof

neighborhoodortopologyinformationreeivedat

anytime,beauseofthemovementofnodes.This

impliesthattheinformationbeupdatedregularly,

otherwise it beomes invalid. More frequently

nodesanbehandledorretlyandeÆiently.

Thewirelessnatureof themediumimpliesthe

limited bandwidth apaity available in a fre-

quenyband. Itisfurtherredued bythehighbit

errorrate inradiotransmissions. Thismakesita

sare and hene a preious resoure. Every ef-

fortisdonetoonsumeitveryprudently. Hene,

while designing a protool using wireless links,

themaintaskistoreduetheunneessary useof

thisbandwidth.

Therefore,the requirementsof thesetwoenvi-

ronments are ompletely opposite to eah other.

Mobility requires more traÆ to be send in

the network to keep the nodes informed of the

hanges, and atthe same time, wireless medium

doesnotallowtobeusedabundantlyforunnees-

sarytraÆ.Theompromiseistomanagethemo-

bilityofnodeswhileusingminimumoftheband-

widthresoures.

1.2 Flooding of broadast messages

in the network

The type of ontrol traÆ that is generated to

manage the mobility of nodes in a network is

mostlytheinformationthatanodedelaresabout

itsrelativemovement,itsnewposition,oritsnew

neighborhood,et. Sometimes, thisinformation

is useful only in the neighborhood of the node

whih is delaring the information. Therefore,

the information is not required to be propagated

inwholeof thenetworktoreaheverynode. But

inmanyases, notonlytheimmediateneighbors

ofthedelaringnode,buttheotherfarawaynodes

alsoneedtoknowthetopologialhangesour-

ringanywhereinthenetwork.Inthesesituations,

lotof messagepassingisrequiredinthenetwork

to keep the information onsistent and valid at

eah node, by regularlyannouning the hanges

duetomobility,orfailureoflinks,et.

Theannounementsaboutlinkhangesaredes-

tined to eahnode of the network. But often all

thenodesofnetworkarenotintheradiorangeof

beamehanismtoreahthefarawaynodesinor-

der tokeepthem informed of the latest hanges.

Theoneptofintermediatenodeswhihserveas

relays to pass the messages between the soure

andthedestinationisoneofthesolution.

If a message is for a spei destination, the

determinationofintermediatenodesissimple:all

the nodeswhih formthe path(if it exists)from

thesoureuptothedestinationaretheintermedi-

atenodes. Thesenodesagreeuponamehanism

to re-transmit the message, on their turn, so that

themessageissuessfullytransfered tothedes-

tination. Dierentroutingprotoolsdesignate,in

dierent ways,these intermediatenodes for uni-

astpaketforwarding.

The problem arises when a paket is not des-

tined to a spei node, rather it is a broadast

message for all the nodes in the network. The

task of determining the intermediate nodes who

willforwardthe paketis nottrivialinthis ase.

Thenodesshouldbehavesuhthatthemessageis

reahed to every node in thenetwork. Asimple

solution is that eah node re-transmits the mes-

sage, when it reeives the rst opy of the mes-

sage. Fig 1 shows an example where a paket

originatedbynodeSisdiusedupto3-hopswith

24 retransmissions. The paket is retransmitted

by all the intermediate nodes in order to diuse

it in the network. This tehnique is known as

\pureooding". It is simple,easy toimplement,

andgivesahighprobabilitythateahnode,whih

is notisolatedfromthenetwork,willreeive the

broadast message. The inonveniene of this

tehnique is that it onsumes a large amount of

bandwidthbeauseofsomanyredundant retrans-

missions.

In ertain onditions, and partiularly in the

\wireless"networks,theavailabilityoflimitedre-

souresintermsofbandwidthapaityrequiresto

restritthetraÆasmuhaspossible. Ifthison-

straintofwirelessmediumisnotonsideredwhile

designing an algorithm, the network may suer

fromperformane degradationsduetohighover-

S

node retransmitting

49 retransmissions

to diffuse a message

upto 3-hops

Figure 1: Diusion of a broadast message

usingpureooding

loadsor ongestion,whentheooding ofbroad-

ast pakets is launhed in the network. On one

hand,broadastmessagesneedsomemehanism

of ooding, speially in mobile environment to

keepthemobilenodesremaininontatbyregu-

larlydiusingtheupdates. Butontheotherhand,

it is not appreiatable either to aet the atual

workingofthesystemduetothisadditionalon-

troltraÆ.

Every protool uses some kind of ooding of

ontrol messages, for its funtioning [9℄, [10℄.

It beomes very advantageous to optimize the

resoure onsumption of the ooding proess.

Many tehniques are desribed in the literature

tolimittheoodingofbroadasttraÆandeah

tehniquehasitsownareaofappliationandhas

its own advantagesand disadvantages. Here, we

willdisuss themehanismof \multipointrelay-

ing"asoneofthepossiblesolution.

2 M u ltip oin t relay in g

The onept of \multipoint relaying" is to re-

due the number of dupliate re-transmissions

while forwarding a broadast paket. This teh-

nique restrits the numberof re-transmitters to a

smallsetof neighbornodes,insteadof allneigh-

S

11 retransmissions

to diffuse a message

upto 3-hops

retransmitting nodes

Figure 2: Diusion of a broadast message

usingmultipointrelays

bor, like in pureooding. This setis kept small

as muh as possible by eÆiently seleting the

neighbors whihovers(in terms of one-hop ra-

dio range) the same network region as the om-

pleteset of neighborsdoes. This smallsubset of

neighbors is alled multipointrelaysof agiven

networknode. Thetehniqueofmultipointrelays

(or MPRs) provides an adequate solution to re-

due ooding of broadast messages in the net-

work, while attaining the same goal of transfer-

ring the message to every node in the network

with a high probability. Fig 2 shows an exam-

ple wherea broadast message of node S is dif-

fused in thenetworkusingthe multipointrelays.

In thisase,ittookonly11 retransmissionsfora

messagetoreahupto3-hops.

Multipoint relaying tehnique works in a dis-

tributed manner, designed in view of the mobile

and disperse nature of the networknodes. Eah

node alulates its own set of multipoint relays,

whihis ompletelyindependent of othernodes'

seletion of theirMPRs. Eah nodereats when

its neighborhood nodes hange and aordingly

modiesitsMPRsettoontinueoveringitstwo-

hopneighbors.

Animportantaspetofthemultipointrelaysis

the manner in whih these multipoint relays are

seleted by eah node. The goal is to ahieve

the maximum performane by seleting an opti-

mal set of MPRs by eah node. Butthis task is

notatrivialone.Ifthemehanismofseletingthe

MPRs istoo simple, it maynotselet eÆiently

the MPRs in a dynami and omplex situation,

andthe expeted performane gainwouldnotbe

ahieved. If the algorithm of MPR seletion is

veryomplexandsophistiatedtoprovideanear

tooptimalMPRset,itmaybeomediÆulttoim-

plementit. Ahighlysophistiatedalgorithmmay

generateitsownontroltraÆ,togatherinforma-

tionfor itsfuntioning,whihbeomesompara-

ble tothe saving inooding of messages. Thus,

theremustbeaompromiseindesigningsuhan

algorithmfortheseletionofmultipointrelays:it

should be easy to implement, and it should give

neartooptimalMPRsetin\majority"ofases.

Theinformationrequired toalulatethemul-

tipointrelaysisthesetof one-hopneighborsand

the two-hop neighbors, i.e. the neighbors of

the one-hop neighbors. To obtain the informa-

tionaboutone-hopneighbors,mostprotoolsuse

someformofHELLOmessages,thataresentlo-

ally by eah node to delare its presene. In a

mobileenvironment,these messagesaresent pe-

riodiallyasakeepalivesignalstorefreshthein-

formation. To obtaintheinformation of two-hop

neighbors,onesolutionmaybethateahnodeat-

tahesthelistofitsownneighbors,whilesending

itsHELLOmessages.Withthisinformation,eah

nodeanindependentlyalulateitsone-hopand

two-hop neighbor set. One a node has its one-

and two-hop neighbor sets, it an selet a mini-

mumnumberof one-hopneighborswhihovers

allitstwo-hopneighbors.

2.1 Heuristi for the seletion of mul-

tipoint relays

Weproposehereoneheuristifortheseletion

of multipointrelays. To seletthe multipointre-

laysforthe nodex,let usallthetheset of one-

hopneighbors of nodex as N(x), andthe setof

itstwo-hopneighborsasN (x). Lettheseleted

multipoint relay set of node x be MPR (x). The

heuristianbestatedas:

1. Start with an empty multipoint relay set

MPR (x)

2. Firstseletthoseone-hopneighbornodesin

N(x)asmultipointrelayswhiharetheonly

neighbor of some node in N 2

(x), and add

these one-hop neighbor nodes to the multi-

pointrelaysetMPR (x)

3. While there still exist some node in N 2

(x)

whihisnotoveredby themultipointrelay

setMPR (x):

(a) For eah node in N(x) whih is not

in MPR (x), ompute the number of

nodes that it overs amongthe unov-

erednodesinthesetN 2

(x)

(b) Add that node of N(x) in MPR (x) for

whihthisnumberismaximum.

Toanalyzetheaboveheuristi,rstnotiethat

the seond step permits to selet some one-hop

neighbor nodes as MPRs whih must be in the

MPR (x)set.OtherwisetheMPR (x)willnotover

all the two-hop neighbors. These nodes will be

seleted asMPRs inthe proess, sooneror later.

Therefore, iftheseondstepis omitted,themul-

tipoint relay set an still be alulated with su-

ess, i.e. it willoverall thetwo-hopneighbors.

Thepreseneofstep2isforoptimizingtheMPR

set. Those nodes whih are neessary to over

the two-hop setN 2

(x) areall seletedin the be-

ginning,whihhelpstoreduethenumberofun-

overednodesofN 2

(x)atthestartof thenormal

reursiveproedureofstep3.

om p u tation of m u ltip oin t

relay s

This setion is devoted to the analysis of the

omputation of the multipoint relays. We will

show that unfortunately, nding a multipoint re-

layset with minimal size is NP-hard. Neverthe-

lesswewillseethattheaboveheuristiiswithin

alogn fator fromoptimality. Letus rstgivea

formaldenitionoftheproblem.

3.1 Form al denitions

If x is a node of the network, we denote by

N(x) the set of its one-hop neighbors. N(x) is

alledtheneighborhood of x. (Here weonsider

that x 2= N(x).) Let N 2

(x)denote the two-hop

neighborsofx.

If y is a one-hop neighbor of x, we also say

thatxoversy. Orwewillsimplysaythatyis a

neighbor of x. Moreover, if S and T aresets of

nodes,wesaythatSoversT ieverynodeinT

isoveredbysomenodeinS.AsetSN(x)is

amultipointrelaysetfor xifS oversN 2

(x),or

equivalently[

y2N(x)

N(y) N(x) [

y2S N(y).

Amultipoint relay set for a node x is optimal if

itsnumber of elementsis minimalamongall the

multipointrelaysetforx.Weallthisnumberthe

optimalmultipointrelaynumberforx.

3.2 NP-ompleteness

We prove that the following problem is NP-

omplete:

MultipointRelay: Given anetwork (i.e. the

setofone-hopneighborsforeahnode),anodex

of thenetworkandan integerk,isthere amulti-

pointrelaysetforxofsizelessthank?

First of all, notie that this problem is easier

thantheproblemofndinganoptimalmultipoint

relayset.Ifanoptimalsetisknown,simplyom-

putingitssizeandomparingittokallowstoan-

tipointRelayProblemisNP-omplete.

ItisobviouslyinNPsinetakingarandomset

inN(x),oneaneasilyhekinpolynomialtime

if itisa multipointrelaysetand ifits sizeisless

thank. ToprovethatitisNP-omplete,weprove

thatthefollowingDominatingSetProblemwhih

isknowntobeNP-omplete[11℄anberedued

to the Multipoint Relay Problem in polynomial

time:

DominatingSetProblem: Givenagraph(i.e.

a set of nodes and a set of neighbors for eah

node)andanumberk,isthereadominatingsetof

ardinality lessthan k? Where adominatingset

isasetSofnodessuhthatanynodeofthegraph

iseitherinSorintheneighborhoodofsomenode

inS.

LetGbeagraphwithnodesetV andletM(x)

denotetheneighborhoodof anyx 2 V. Weon-

strutaredutionasfollows. Letusmakeaopy

of V and denote witha prime the opies: x 0

de-

notestheopyofxforanyx 2V andS 0

denotes

thesetofopiesoftheelementsofanysetSV

(V 0

denotes the set of all the opies). Let s be

an element neither in V nor in V 0

. Consider a

networkwhere the nodes are fsg [V [V 0

and

where the neighborhoods are the following (see

Figure3.2foranexample):

N(s) = V;

N(x) = fx 0

g[M(x) 0

forx2V;

N(x 0

) = fxg[M(x)forx2V

Suh a data struture an easily be omputed

inpolynomialtime. We laimthattheanswer to

the Multipoint Relay Problem for the node s of

theomputednetworkwiththe integer k isvalid

for the Dominating Set Problem for the onsid-

ered graph with the same integer k. It is suÆ-

ient toprovethat anymultipointrelaysetS for

the network is assoiated with a dominating set

of the graph with same ardinality. S is a sub-

set of N(s) = V. We show that S itself is a