Efficient Broadcast in MANETs Using Network Coding and Directional Antennas

Transcription

1 Effiint Brost in MANETs Using Ntwork Coing n Dirtionl Antnns Shuhui Yng Dprtmnt of Computr Sin Rnsslr Polythni Institut Troy, NY 28 Ji Wu n Mihl Cri Dprtmnt of Computr Sin n Enginring Flori Atlnti Univrsity Bo Rton, FL 3343 Astrt In this ppr, w onsir th issu of ffiint rosting in moil ho ntworks (MANETs) using ntwork oing n irtionl ntnns. Ntwork oing-s rosting fouss on ruing th numr of trnsmissions h forwring no prforms in th multipl sour/multipl mssg rost pplition, whr h forwring no omins som of th riv mssgs for trnsmission. With th hlp of ntwork oing, th totl numr of trnsmissions n ru ompr to rosting using th sm forwring nos without oing. W xploit th usg of irtionl ntnns to ntwork oing-s rosting to furthr ru nrgy onsumption. A no quipp with irtionl ntnns n ivi th omniirtionl trnsmission rng into svrl stors n turns som of thm on for trnsmission. In th propos shm using irtionl ntnn, forwring nos slt lolly only n to trnsmit rost mssgs, originl or o, to rstrit stors. W lso stuy two xtnsions. Th first xtnsion pplis ntwork oing to oth ynmi n stti forwring no sltion pprohs. In th son xtnsion, w sign two pprohs for th singl sour/singl mssg issu in th ntwork oing-s rost pplition. Prformn nlysis vi simultions on th propos lgorithms using ustom simultor is prsnt. I. INTRODUCTION Brosting is th most frquntly us oprtion in moil ho ntworks (MANETs) for th issmintion of t n ontrol mssgs in mny pplitions. Usully, ntwork kon is onstrut for ffiint rosting to voi th rost storm prolm us y simpl lin flooing, whr only slt nos, ll forwring nos, tht form th virtul kon, forwr t to th ntir ntwork. In MANETs, th forwring no st for rost is usully slt in loliz mnnr, whr h no trmins its own sttus of forwring or non-forwring s on lol informtion [6], or th sttus of no is signt y its nighors [7]. A smllr-siz forwring no st is onsir to mor ffiint u to th ru numr of trnsmissions in th ntwork, whih hlps to llvit th intrfrn n lso onsrvs nrgy. Th onnt ominting st () s virtul kon hs n wily stui [], whr h no is ithr forwring no or nighor to forwring no in th st, n th st is onnt. Fining minimum is NP-omplt. In [6], Li t l. xploit ntwork oing in th rost pplition. Thy ppli oing mthos to trministi forwring no sltion pprohs to gin rution in th numr of trnsmissions, fousing on ruing th numr of trnsmissions h forwring no prforms. Ntwork oing [5] is fin s llowing intrmit nos to pross th inoming informtion flows. Whn forwring no, i y rtin pproh, ns to forwr svrl mssgs to ll of its nighors whil som nighors lry hv som of th mssgs, this no n omin som of th mssgs to ru th numr of forwrings, n h nighor n still gt vry mssg vi oing. For instn, no gts two mssgs from nos n rsptivly. In orr to lt n hv h othr s mssg, ns to forwr oth th mssgs s tritionl forwring no. With ntwork oing, only ns to forwr on o mssg ontining oth originl mssgs through th XOR oprtion, n n n o th mssg with th hlp of thir own mssgs through th XOR oprtion. Not tht th ntwork oing works only whn thr r multipl mssgs rost t th sm tim in th ntwork. In [8], Yng, Wu, n Di fous on ruing th totl numr of forwring irtions/stors of forwring nos. Using irtionl ntnns, th omniirtionl trnsmission rng of h no n ivi into svrl stors n th trnsmission n prform only in slt stors. Thrfor, y ruing th totl numr of trnsmission stors of th forwring nos in th ntwork, th intrfrn n llvit s wll s th nrgy onsumption. In this ppr, w try to omin th ffiiny of oth ntwork oing n irtionl ntnns to hiv ffiiny in rosting. W nlyz th prformn of ths two mthos n sign n lgorithm Effiint Brost using Ntwork Coing n Dirtionl Antnns (), whr h no is its forwring sttus using only lol informtion n limit piggyk rost stt informtion. Th propos sign is not simply th omintion of th two xisting mthos. W tk th vntg of th intrtionl ffts of thm to hiv n vn ttr prformn. Aitionlly, w moify th xisting irtionl ntnn mtho to ynmi mo. As shown in Figur (), thr r four mssgs, A, B, C, n D gnrt from nos,,, n, rsptivly. W ssum tht no is slt for forwring using forwring no sltion mtho. Thrfor, ns to forwr ll four mssgs, osting 4 trnsmissions totlly. In ntwork oing-s rosts,

2 II III () I IV A B C D () P P 2 I II III IV Fig.. () A smpl ntwork, () nighor rption tl of no, n () trnsmission tl of no using oing n irtionl ntnns. s on 2-hop nighorhoo informtion, n onstrut nighor rption tl s in () to ror th rost stt informtion of th riv mssgs. For instn, whn sns out mssg A, not only, ut lso gts it. Thrfor, is ovr no of mssg A n thr is in th gri t lin, olumn A. Bs on th tl, thn os ths four mssgs into two omin mssgs to forwr, P (= A C) n P 2 (= B D) ( is th XOR oprtion) using som ntwork oing lgorithms. Oviously, vry othr no n o ths two omin mssgs togthr with th mssgs it lry hs in orr to gin ll four of th originl mssgs. For instn, no hs mssg A, B, n C. Whn rivs P 2, it n us P 2 B to xtrt mssg D. n us P A n P 2 B to otin C n D. With th hlp of irtionl ntnns, th omniirtionl trnsmission rng of n ivi into K stors (K is 4 in this xmpl), s th sh lins show in (). Thn n rstrit th trnsmissions of th two omin mssgs in only som of th stors, s shown in tl (). For instn, P only ns to trnsmitt in stors I, II, n IV.Ifw lt th onsumption of th trnsmission of on mssg in on stor th unit nrgy onsumption, tritionl rosting whr trnsmits ll four mssgs omniirtionlly, osts 6. Brosting with ntwork oing osts 8. Th rost with ntwork oing n irtionl ntnns osts 6. Othr thn th forwring nos, th sour nos n lso rstrit th trnsmissions to slt stors to furthr ru th totl nrgy onsumption s long s th mssg n rh forwring no. Although th forwring no/g sltion n th furthr ntwork oing prours r inpnnt, w show tht iffrnt unrlying forwring no sltion pprohs fft th ffiiny of ntwork oing signifintly. In, w sign th ynmi vrsion of th unrlying forwring no/g sltion pproh. W thn us stti vrsion without piggyk informtion for it to nlyz th prformn n troffs. W fin out tht th nrgy onsrvtion of th ynmi n stti vrsions r omprl, lthough th ynmi on is slightly ttr. Howvr, sin th stti vrsion hs lss ovrh, it is mor prtil. Also, th ntwork oing-s rost pproh [6] works only whn thr r multipl sours with multipl mssgs in th ntwork. W propos two pprohs s nothr xtnsion to to l with th singl sour with singl mssg () pplition; th piplin-s pproh (PB) n th sprout pproh (SO). W lso isuss th til implmnttion thniqus in th propos lgorithm, suh s th timing issu n th nighorhoo informtion isovry issu. Th ontriutions of this ppr r th following: ) W prsnt th vntgs of th omintion of th ntwork oing n irtionl ntnn pprohs for ffiint rost n vlop th lgorithm. 2) W xtn th lgorithm to stti forwring no/g sltion vrsion to stuy th prformn vrition. 3) W propos two pprohs for th singl sour with singl rost mssg pplition. 4) W isuss som implmnttion thniqus in n onut prformn nlysis through simultions on th propos lgorithms. II. RELATED WORKS AND PRELIMINARIES A. Brost in MANETs Both proilisti [5] n trministi [7], [3], [6] pprohs hv n propos for ffiint rost. Proilisti pprohs us limit nighorhoo informtion (lol informtion) n rquir rltivly high rost runny to mintin n ptl livry rtio. Dtrministi pprohs slt fw forwring nos to hiv full livry n most r loliz, whr h no trmins its sttus (forwring or non-forwring) s on its h-hop nighorhoo informtion (for smll vlus of h, suh s 2 or 3). Th ision of forwring nos n m unr oth stti n ynmi lol viws. In th stti pprohs, only topology informtion is onsir, whrs in ynmi ons, rost stt informtion of th nighorhoo is lso piggyk. Th onpt n ppli for rosting. Wu n Li [7] propos th first loliz solution for onstution. Png n Lu [8] prsnt sll rost lgorithm whr th sttus of forwring no is omput on-th-fly. In [3], Stojmnovi t l. xtn [7] to ynmi vrsion. Su n Mrsi [4] vlop ynmi pproh without using koff ly. Lou n Wu [7] vis totl/prtil ominnt pruning (TDP/PDP) mtho s on 2-hop topology n rost stt informtion. Wu n Di [6] furthr propos gnri formtion pproh, whih n prform in oth ynmi n stti mos. B. Ntwork Coing Ntwork oing [], [5] n us to llow th intrmit nos to omin pkts for forwring. Thrfor, ntwork oing n us for ffiint rosting y ruing th totl numr of trnsmissions. In [3], Frgouli t l. quntifi th nrgy svings tht ntwork oing hs th potntil to offr in rosting. Thy lso propos n implmntl mtho for prforming th ntwork oing, rssing som prtil issus suh s stting th forwring

3 ftor n mnging gnrtions. In [9], protiv ompnstion pkt is prioilly rost, onstrut from unforwr mssgs using ntwork oing to improv th livry rtio of th proilisti rost pproh. In [6], Li t l. ppli ntwork oing to trministi rost pproh ll prtil ominting pruning (PDP) [7] in multipl-sour rost pplition. Thy prov tht using only XOR oprtion, th oing lgorithm is NP-omplt n vlop gry XOR-s pproh for simpliity. Th R-Solomon o ws xploit to sign n optiml R-Solomon o-s lgorithm. C. Dirtionl Antnns Th most populr irtionl ntnn mol is illy storiz, s in [4], whr th fftiv trnsmission rng of h no is qully ivi into K non-ovrlpping stors, whr on or mor suh stors n swith on for trnsmission or rption. Th hnnl pity whn using irtionl ntnns n improv, n th intrfrn n ru. Som proilisti pprohs for rosting using irtionl ntnns r propos in [4], [], [2]. In [2], Di n Wu propos loliz rost protool using irtionl ntnns, whih is sour-s. In [8], Yng, Wu, n Di put forwr th irtionl ntwork kon for ffiint rosting using th irtionl ntnn mol in stti mnnr whr th kon is suitl for ny sour no in th ntwork. Thy sign th onpt of irtionl onnt ominting st (D) for th onstrution of irtionl ntwork kon. D xtn th pproh for rost with th hlp of irtionl ntnns. Th minimum D prolm is prov to NPomplt. Using D, not only forwring nos ut lso forwring gs of h forwring no r signt. Th totl nrgy onsumption is ru, s wll s th intrfrn. Thy vlop th no n g ovrg onition for th D prolm. All of th ov shms ssum n omniirtionl rption mo. III. BROADCAST WITH NETWORK CODING AND DIRECTIONAL ANTENNAS In this stion, w first xtn th pproh vlop in [8] to onstrut th irtionl onnt ominting st (D) to ynmi vrsion, whr th onstrut D is sour-s. W thn omin th ntwork oing with th ynmi D to vlop th. A. Dynmi Dirtionl Connt Dominting St (DD) In [8], th onpt of using irtionl ntwork kon for ffiint rost in onjuntion with irtionl ntnns ws propos. Th omniirtionl trnsmission rng of h no is ivi into K stors n h forwring no only ns to swith on svrl stors for trnsmission whil th ntir ntwork gts th rost mssg. Th irtionl onnt ominting st (D) is propos for th onstrution of irtionl ntwork kon, whr h no trmins lolly not only its sttus of forwring or non-forwring, ut lso its forwring outgoing gs if it is forwring no. Not tht th ntwork is mol s irt grph. Thn in rost initit from ny sour no, th sour uss ominiirtionl trnsmission (or irtionl trnsmission if it tts forwring no in tht irtion) to sn th mssg to nighoring forwring no. Thn forwring nos forwr th mssg towrs only thir orrsponing forwring gs, n th ntir ntwork gts th mssg. Th D is irtionl ntwork kon ssuming tht K is infinit, n h outgoing g is trnsmission stor. Whn K is finit, th stors tht ontin slt forwring gs r simply swith on for trnsmission to gt irtionl ntwork kon. Not tht whn K is, th D prolm turns into th prolm. A minimum D prolm is to fin D with th lst forwring gs whih is prov to NP-omplt. If th nrgy onsumption of trnsmission in ny irtion is fix, ruing th numr of forwring gs gurnts th smllst nrgy onsumption in th pplition of rosting using irtionl ntnns. Th no/g ovrg onition propos in [8] onstruts D for givn ntwork lolly t h no in stti mnnr. Th onstrut D is for ny sour no in th ntwork. Aftr th xhng of Hllo mssgs, h no mks ision s on only lol topology informtion in th initiliztion phs for th rost pplition strts. Hr, w xtn this mtho to ynmi vrsion, whr h no mks ision s not only on topology informtion ut lso rost stt informtion piggyk in riv rost mssgs. It is its forwring sttus n orrsponing forwring gs for h riv rost mssg. In our propos ynmi no/g ovrg onition, h rost mssg piggyks with it th informtion of its q most-rntly visit nos (q is smll numr suh s 2 or 3). A visit no for mssg is no tht hs forwr th mssg. Corrsponingly, visit g for mssg is n g tht hs forwr th mssg. Thn, whn no pplis th ovrg onition to trmin its sttus for riv mssg, it onsirs th informtion of visit nos/gs of this mssg s wll s lol topology informtion. Th ynmi vrsion of th no n g ovrg onitions rsml th stti ons [8] xpt tht th no n g prioritis r upt s on th piggyk rost stt informtion. Not tht th upt nw priority is only vli for th orrsponing mssg. Thrfor, no my hv iffrnt sttus (visit or not, forwring or not) n prioritis for iffrnt mssgs. In th following, n unmrk sttus rprsnts non-forwring sttus. A ominting nighor mns tht thr is n inoming g from tht nighor. A sornt nighor mns tht thr is n outgoing g to tht nighor. Not tht h no v hs priority p(v) n suh priority is totlly orr within its h-hop nighorhoo, whih oul th no ID, no gr, or nrgy lvl s on iffrnt pplitions. Dynmi No Covrg Conition. No v is unmrk if, for ny two ominting n sornt nighors, u n w, irt rplmnt pth xists onnting u to w suh tht () h intrmit no on th rplmnt pth hs

4 u t x w u x s f s f () v v () w () () Fig. 2. Dirt rplmnt pths in () no ovrg, n () g ovrg with visit nos. Fig. 3. () Forwr nos, () forwring nos n forwring gs. highr priority thn v (inluing visit nos), n (2) u hs highr priority thn v if thr is no intrmit no. Eg Priority Assignmnt. For h g (v w), th priority of this g is P (v w) =(P (v),p(w)). Th priority of n g is tupl s on th lxigrphi orr. Th first lmnt is th priority of th strt no of this g n th son on is th priority of th n no. Thrfor, thr is totl orr for ll th gs. For xmpl, P (x y) >P(w v), if n only if, (P (x) >P(w)) or (P (x) =P (w) n P (y) >P(v)). Dynmi Eg Covrg Conition. Eg (v w) is unmrk if irt rplmnt pth xists onnting v to w vi svrl intrmit gs with highr prioritis thn (v w) or visit gs. AsshowninFigur2,v is th urrnt no n lk nos r visit ons. Assum th priority is s on th lphti orr, i.., P () > P(). () shows two typs of irt rplmnt pths from u to w using th no ovrg onition. Whn u is irtly onnt to w, P (u) >P(v) is nssry. Othrwis, whn thr r intrmit nos t n x, thn P (t) >P(v) n P (x) >P(v) sin x is visit. () shows th irt rplmnt pth for g (v w). Inthis s, oth th intrmit gs ((v u) n (u x)) hv highr prioritis thn th g (v w). Sin g (x w) is visit, th g (v w) n unmrk. Th iffrn twn ynmi n stti no/g ovrg onitions is tht visit no/g hs highr priority no/g. Not tht th ynmi no/g ovrg onitions n h-hop informtion whih mns h-hop lol topology informtion n q-hop piggyk visit no/g informtion in h riv mssg. For xmpl, s in Figur (), if h =2, no knows ll th gs in th ntwork xpt th g twn nos n. Thorm : Givn irt grph G =(V,E), V n E gnrt y th ynmi no n g ovrg onitions in rost gurnt th full livry. Th proof of Thorm is in th Appnix. Th xmpl in Figur 3 shows sour-s () in sh nos (s is th sour), () is th rsult ftr pplying th ynmi no/g ovrg onition. Nos n r lso forwring nos. slts g ( ) s forwring g n slts gs ( ) n ( f). Th g ( ) n unmrk us rplmnt pth onnting to vi s xists, n s is visit no n (s ) is visit g. Thrfor, th prioritis of gs ( s) n (s ) r oth highr thn tht of ( ). Th sm is tru for g ( ). Thn if K is finit, only th stors tht ontin th ol rrows n to swith on for trnsmission, muh lik th gry stors in (). B. Effiint Brosting Using Ntwork Coing n Dirtionl Antnns () In this sustion, w omin th ntwork oing n irtionl ntnn pprohs into th rost pplition, xploiting th vntgs of oth of thm. Algorithm sris xut on no. Bfor th rost strts, h no xhngs Hllo informtion with nighors for h rouns to gt th h-hop lol topology informtion. Upon th rrivl of th first mssg, timr is stup n th piggyk informtion in h riv mssg is ror to upt th no prioritis. Whn th timr xpirs, for h riv mssg, th no/g ovrg onitions r ppli s on th topology n rost stt informtion (nw prioritis), n forwring sttus n gs of th no r trmin. W us th xmpl in Figur 4 to illustrt th prour. This is th sm xmpl s in Figur. () is th rsult of DD ftr stp 4 of Algorithm. No is th forwring no for mssgs A, B, C, n D from nos,,, n s on th ynmi no ovrg onition. Eg ( ) is forwring g for mssgs C n D. Eg ( ) is forwring g for mssg D. Eg ( ) is forwring g for mssg A. Eg ( ) is forwring g for mssg A n B. In stp 5, whn th timr xpirs, no irumgyrts its irtionl ntnns to lt th g of stor lign to h forwring g. Thr r t most f lyouts whn th numr of slt forwring gs is f. In h stor of h lyout, ntwork oing is ppli to trmin th finl trnsmissions. Th lyout with th fwst totl trnsmissions is thn slt for us. Th no thn xuts th forwring. In th lgorithm, w ssum tht stps 4, 5, n 6 n omplt for th rrivl of th nxt mssg. In, ntwork oing is ppli in h stor of lyout inst of th ntir no s in [6]. W us th XOR-s lgorithm from [6]. Assuming m,m 2,...,m l r mssgs riv in orr in this stor. P,P 2,...,P t r th finl forwr mssgs (originl or o). P = m... m i, P 2 = m i+... m i2,..., P t = m it+... m l, whr

5 Algorithm lgorithm t no v. Bfor rost:. Exhng Hllo mssgs to upt lol topology. Upon rption of th first mssg (for th timr stup): 2. Stup th timr. 3. Upt nighorhoo no prioritis s on h riv mssg. 4. Whn timr xpirs, pply ynmi no/g ovrg onitions for h mssg. 5. If v is forwring no for som mssgs, () lign th g of stor to h forwring g, (2) trmin o mssgs in h stor using oing, (3) slt th position with th fwst totl trnsmissions. 6. Forwr o mssgs. h nighor n o from P to P t to gt ny missing mssg from m to m l. A gry pproh n us. For th riv mssgs in quu, th lgorithm tris to hv th mximum numr of mssgs strting from m to rt P, thn to rt P 2 n so on. For xmpl, in Figur 4 (), ssuming tht th rost mssgs rriv in th orr of A, C, B, n D t no. P is A t first, thn tris to mk P = A C. No ns mssg C n nos n n mssg A. With P, ll of thm n o. Thrfor P = A C is orrt oing. Thn n try P = A C B. Sin no ns mssg B, n it nnot o P to gt B, this is not orrt oing. P rmins s A C. Using th sm prour, w n gt P 2 = B D. Figur 4 () is th rsult using only ntwork oing, whr is th forwring no n forwrs th omin mssg P (= A C) n P 2 (= B D) omniirtionlly. () is on lyout of using K =2. Thn ns to trnsmit C n D in th lft stor n A n B in th right stor. () is nothr lyout for K =2, whr trnsmits P n P 2 to th uppr stor n P 3 (= A D) to th lowr stor. () n (f) show th s whr K is 4 with iffrnt lyouts. If w ssum tht th trnsmission of on mssg in 9 stor osts on unit of nrgy, th nrgy onsumption in th figurs from () to (f) r 8, 8, 6, 6, n 5. W n s tht th omintion of ntwork oing n irtionl ntnns n improv rosting prformn signifintly in trms of nrgy onsumption. Not tht th forwring of no without ntwork oing or irtionl ntnns osts 6. Th ntir prour n lso illustrt using Figur 5 (), whr m to m 6 r riv mssgs n D to D 6 r th orrsponing forwring nos/gs isions for thm s on topology n priority informtion. U mns to upt th priority informtion s on th piggyk informtion in th riv mssg n D is th finl trnsmission ision for svrl riv mssgs using ntwork oing in vli timr. Not tht th uplit rption of pross mssg is simply isr suh s m 5 riv ftr it hs n pross n forwr. As shown in th figur, th rrivl of m 5 ftr timr 2 xpirs will not intrigu nw timr or nw upting uring th timr 3 prio. C D D C () D B A P P 2 P P 2 D () () A A A B P P 2 () P P 2 P 3 () P P P 2 P 2 P 3 Fig. 4. () DD, () oing, () n () K =2, () n (f) K =4. Th sour nos in th ntwork n simply us omniirtionl trnsmission to sn out th rost mssgs. In orr to furthr ru th totl nrgy onsumption, sour nos n only swith on stors in whih thr r nighors for trnsmission. In this s, th mssg n rriv t t lst on forwring no s wll s othr non-forwring nighors, whih hlps with th potntil ntwork oing onut ltr on. As shown in Figur 4 (f), sour nos,,, n slt som stors to swith on for trnsmission, shown in th light gry stors. IV. EXTENSIONS OF A. Stti vs. Dynmi Forwr No Sltion As mntion ov, in [6], Li t l. ppli ntwork oing to ynmi forwring no sltion pproh, th PDP-s pproh, n stt tht th oing n irtly ppli to othr loliz trministi pprohs for rosting. Th prviously propos lso uss ynmi forwring sttus pproh. Hr, w xtn th propos to stti forwring no sltion pproh to nlyz thir ovrll prformn. In th stti vrsion of, w pply th oing to th stti forwring no/g sltion, th no/g ovrg onitions in [8], s shown in Algorithm 2. W will ompr th prformn n troffs of ths two lgorithms in th simultion stion. As in Algorithm 2, in th initiliztion phs for th rost strts, lol informtion is ollt vi th xhng of Hllo mssgs. Thn th no trmins its forwring sttus. This sttus is for ll of th following riv mssgs. Thn timr is stup whn th (f)

6 m m2 m m3 m3 m4 m5 m5 m6 m5 Algorithm 2 Stti lgorithm t no v. tim tim Hllo Hllo timr timr 2 timr 3 U U U U U U U D/D2/D D3/D4/D5/D D6/D () Dynmi m m2 m m3 m3 m4 m5 m5 m6 m5 timr timr 2 timr 3 Bfor rost:. Stp of Algorithm. 2. Dtrmin forwring sttus. Exit if it is non-forwring. Upon rption of th first mssg (for stup th timr): 3. Stp 2 of Algorithm. 4. Whn timr xpirs, follow Stp 5 (), (2), n (3) of Algorithm. 5. Stp 6 of Algorithm. Fig. 5. Ds D D () Stti Illustrtion of xution prour of ynmi/stti. first mssg rrivs. Whn th timr xpirs, ntwork oing is ppli in h stor of h lyout, n th st on is slt for us. Th ntir prour is illustrt in Figur 5 (). Aftr th xhng of Hllo mssgs, D s trmins th sttus of th no n lso th slt forwring gs if it is forwring no for ll th following riv mssgs. Thn upon th rption of th first mssg, timr is stup. Whn th timr xpirs, oing is ppli to ll riv mssgs to trmin th finl o mssgs for trnsmission. Th siz of th forwring no st slt using ynmi mnnr is smllr thn or qul to th on y stti mnnr, sin in th formr on th informtion of visit nos hlps to inrs th proility of th no ing n non-forwring no. Howvr, runnt trnsmissions y th xtr forwring nos in th stti mnnr my hlp to inrs th potntil ntwork oing in th ltr phs n hn th ovrll prformn, whih will vrifi vi simultion. Th ovious vntg of th stti is lss ovrh. Th rost mssgs o not n to piggyk th rost stt informtion. Also, s shown in Figur 5 (), fwr forwring nos/gs isions n to m. B. Singl Sour/Singl Mssg Brost As mntion ov, rosting using th ntwork oing mtho [6] is sign for th pplition of multipl sours with multipl rost mssgs, whr forwring no hs th potntil of omining som of th mssgs to ru th numr of trnsmissions. In th pplition of singl sour, only whn th rt of th gnrtion of mssgs is lrg nough, th ntwork oing my work in nos rltivly fr wy from th sour no. W sign two pprohs for th singl sour/singl mssg rost issu. W ssum singl sour in th rost n th rt of th gnrtion of mssgs is lrg nough tht it n viw s singl mssg pplition. Th si i is to ivi th singl mssg into svrl sgmnts n trt h sgmnt s singl rost mssg. ) Piplin-Bs Approh (PB): Whn thr is only on sour no in th ntwork rosting on mssg, th D sour no ivis th mssg into k sgmnts n sns h sgmnt s singl rost mssg, n rosts thm on-y-on in th piplin mnnr. In this wy, th singl sour/singl mssg prolm turns into singl sour with multipl mssg rost. In th r nr th sour no, th fft of ntwork oing is not signifint sin ll th sgmnts tn to om from on irtion. Howvr, in th frthr r, th fft is xpt to signifint. As shown in Figur 6(),s ivis th rost mssg into k sgmnts n sns thm out vi k rosting. Thrfor, th nighors of sour no s gt th first rost mssg S, thn th son on S 2 in orr from s. 2) Spr-Out Approh (SO): In orr to nhn th fft of ntwork oing in th singl sour/multipl mssg rost using th mssg sgmnttion mtho, w n furthr pply th mssg spr mtho to first spr th sgmnts out into th ntir ntwork. Aftr th sour no ivis th outgoing mssg into k sgmnts, it uss rnom wlk to spr th k of ths sgmnts. Som kin of TTL ontrol n us to mk sur th sgmnts rnomly sttr out into th ntwork. Upon rriving t stintion, sgmnt is rost y th stintion no. Th sour itslf kps sgmnt for ltr rost. As shown in Figur 6 (), th k sgmnts r spr in th ntir ntwork. In this wy, th pplition turns into th multipl sour with multipl mssgs rost. Although th unist in th prprossing phs osts xtr ovrh, th trnsmission rution rn from ntwork oing in th ntir ntwork is xpt to mor signifint. Not tht th nos on th unist routs n mrk thmslvs s visit nos for th ypssing sgmnts, whih hlps to potntilly ru trnsmission. V. IMPLEMENTATION ISSUES In this stion, w isuss som implmnttion thniqus in th ov propos lgorithms. A. Nighorhoo n Piggyk Informtion Colltion Not tht no GPS ssistn is nssry in th propos lgorithm. In Algorithm, h no sns out Hllo mssgs K tims to th K irtions n omplishs th irtionl nighorhoo isovry. In this s, ftr h rouns of th mssg xhng, h no knows its h- hop nighorhoo informtion, whih inlus oth nighors n in whih stors r ths nighors. Aoring to this informtion, h no n rt th nighor rption tl.

7 Sk S3 S2 S S S2 S S2 S S S Numr of Trnsmissions Coing Numr of Trnsmissions Coing () Piplin-s pproh Fig. 6. S k () Spr-out pproh Singl sour/singl mssg rost. Aftr no trmins its sttus togthr with th forwring gs, it piggyks this informtion in th rost mssg s prt of th q most rntly visit no informtion. Th no tht rivs this rost mssg n xtrt th visit nos/gs informtion from it. B. Timr in A timr is st for h no to ollt svrl rost mssgs. In th stti vrsion of, it hlps with th potntil ntwork oing. In th ynmi vrsion, it lso hlps to ollt mor rost stt informtion piggyk y ths mssgs to trmin th sttus of th no. Th timr sltion prsnts th prformn troff twn nrgy onsumption n ly. Whn th timr is st to, th fft of ntwork oing lmost rus to. Whn th timr is lrg nough to ountrt th iffrn of initil tim mong th rost mssgs in th ntwork, th ntwork oing n utiliz thoroughly. Aftr th forwring, th timr is rst for th nxt sssion. Th vlu of th timr n st in oth protiv n rtiv wy. In th formr mtho, th timr of no n st s on th numr of nighors of this no n th imtr of th ntwork. In th lttr on, no n just th vlu of th timr on-th-fly oring to th mssg rrivl rt t this no. VI. SIMULATION In this stion, w vlut th prformn of th propos lgorithm, s rsult of th vrg of simultion trils, y ompring th totl nrgy onsumption in trms of th numr of mssg trnsmissions in th ntwork n lso th siz of stors tht th mssg ws trnsmitt. W ompr with two lgorithms. () th lgorithm without ntwork oing or irtionl ntnns (). W simply ll it lgorithm sin th forwring no st slt y this mtho is sour-s, whih mns togthr with th sour no, th forwring no st forms for th ntwork. W us ynmi no ovrg onition s us in our. (2) th lgorithm with ntwork oing ut without irtionl ntnns (Coing). This is th pproh propos in [6], ut in orr to mk fir omprison, th unrlying forwring no sltion pproh w us in Coing is lso th ynmi no ovrg onition. W lso ompr with th propos stti (S-) to hk th prformn vrition. Finlly, th prformn Fig () Dns ntwork ( =8) () Sprs ntwork ( =6) Comprison of, Coing, n in numr of trnsmissions. of th two pprohs for th singl sour/singl mssg rost pplition is vlut, th piplin-s pproh (PB) n th spr-out pproh (SO). A. Simultion Environmnt Th simultions r onut on ustom simultor. In th simultion, n nos r rnomly pl in rstrit r. Th tunl prmtrs in th simultion r s follows. () Th numr of nos n. W vry th numr of ploy nos from 2 to to hk th slility of th lgorithms. (2) Th vrg no gr whih rprsnts th nsity of th ntwork. W us 6 n 8 s th vlus of to gnrt sprs n ns ntworks. (3) Th numr of stors of th ntnn pttrn K. Wus4n6sth vlus of K. (4) Th numr of rost sssions, i.., th numr of gnrt rosting mssgs. hs fix vlu of 2 in th simultion. Thrfor, whn n is iffrnt, w n simult vrious t los in th ntwork. Th sour nos r rnomly slt. (5) Th numr of sgmnts k in th PB n SO xtnsions. k is n 2 in th ntwork. W o not onsir no moility n signl intrfrn in th following simultions. Th following mtris r ompr: () th numr of trnsmissions in th pplition. W ssum tht th trnsmission of mssg (originl or o) following trnsmission g is on trnsmission, n (2) th vrg nrgy onsumption for rost mssg. W ssum tht on trnsmission (of originl rost mssg or o mssg) in h stor onsums on unit of nrgy. B. Simultion Rsults Figur 7 is th omprison of, Coing, n in th numr of trnsmissions in oth ns n sprs ntworks. () is th ns ntwork whr th vrg no gr is 8. W n s tht Coing n ru th numr of mssg trnsmissions, n th rution rt is roun.2. n furthr ru it signifintly. Whn th numr of nos inrss, th numr of trnsmissions in tns to stl. () is whn th vrg no gr is 6. n still ru th numr of trnsmissions ompr with or Coing. But th rution rt is lowr thn tht in th ns ntwork. Figur 8 is th omprison of, Coing, n in trms of nrgy onsumption whn K is 4 n 6. () n () r in ns ntworks. W n s tht n

8 Numr of Stors Coing Numr of Stors Coing Numr of Forworing Nos S Numr of Forworing Nos S () Dns ntwork (K =4) () Dns ntwork (K =6) () Forwring nos ( =8) () Forwring nos ( =6) Numr of Stors Coing Numr of Stors Coing Numr of Trnsmissions S- Numr of Trnsmissions S () Sprs ntwork (K =4) () Sprs ntwork (K =6) () Numr of trnsmissions ( =8) () Numr of trnsmissions ( =6) Fig. 8. Comprison of, Coing, n in nrgy onsumption. Fig. 9. Comprison of n S-. furthr ru th numr of swith on stors ompr with n Coing in whih ll stors of forwring no n to swith on for trnsmission. Whn K is lrgr, th rution rt of ovr n Coing is mor signifint sin lrgr forwring r n prun. () n () r in th sprs ntworks. lso rus th numr of swith on stors signifintly. Th lrgr th vlu of K, th lrgr th rution rt. Figur 9 is th omprison of n S- in trms of th numr of forwring nos n trnsmissions in oth ns n sprs ntworks. W n s tht lthough th numr of forwring nos slt in th stti mtho shoul lrgr thn tht in th ynmi on, s shown in () n (), th finl numrs of trnsmissions in n S- r vry los, spilly whn th ntwork is rltivly ns. This is us mor forwring nos to forwr inrss th proility of ntwork oing, whih mks up for th lrgr forwring no st. Th forwring no st of S- is roun.3 tims lrgr thn tht of whil th finl numr of trnsmissions is.3 tims highr. Th vntg of S- is tht it only lults th sttus of h no on for ny rost mssg from ny sour. It is lso unnssry to piggyk th rost stt informtion. Thrfor, if th ntwork is ns, S- is prfrr sin th ovrh of it is smllr whil th prformn is omprtiv. Figur shows th prformn vlutions of th two xtnsions of, PB n SO with iffrnt sgmnt numrs k =, 2. W n s tht in () whn th ntwork is ns, whih mns th trnsmission rng is lrgr, SO hs ttr prformn thn PB. Smllr k mks th vntg of SO ovr PB mor signifint. Whn k is 2, SO is vry los to PB. Bus th numr of trnsmissions is lrgr with lrgr numr of sgmnts in th initil phs of SO. In (), th rsults in th sprs ntwork r shown. Whn k is, SO is ttr thn PB. Whn k is 2, PB is vn ttr thn SO. This is us th initil phs of SO osts lot of ovrh in th s of lrgr k n smllr trnsmission rng, whih ls to mor hops to spr out th sgmnts. Th simultion rsults n summriz s follows. ) hs signifint prformn improvmnt in trms of th numr of trnsmissions ompr with n Coing, spilly in rltivly ns ntworks. 2) hs ttr prformn thn n Coing in trms of th numr of swith on stors whih orrspons to th nrgy onsumption. Th lrgr th vlu of K, th lrgr th rution rt of ovr th othr two mthos. 3) S- hs vry los prformn to, spilly whn th ntwork is rltivly ns. Thrfor, u to its othr vntg, suh s lss ovrh, S- is nothr option. 4) SO hs ttr prformn thn PB whn th ntwork is rltivly ns n th numr of sgmnts mssg is ivi into is smll. Whn in sprs ntworks with lrg k, PB vn hs ttr prformn thn SO. VII. CONCLUSIONS Ntwork oing hs n xploit for ffiint rosting to furthr ru th numr of trnsmissions in th multipl sour rost pplition. In this ppr, w omin th ntwork oing-s rost pproh with rosting using irtionl ntnns for mor ffiint rost strtgy, vloping ffiint rosting using ntwork oing n irtionl ntnn lgorithm (). W xtn xisting rosting using th irtionl ntnn pproh to ynmi mo. Although th oing-s pproh is inpnnt of th unrlying forwring no sltion prour, w show tht iffrnt forwring no sltions

9 Numr of Trnsmissions PB(k=) SO(k=) PB(k=2) SO(k=2) Numr of Trnsmissions PB(k=) SO(k=) PB(k=2) SO(k=2) s f u u W u () Dns ntwork ( =8) () Sprs ntwork ( =6) Fig.. Comprison of PB n SO in numr of trnsmissions. Fig.. Proof of ynmi no/g ovrg onitions. fft th ovrll prformn signifintly. W lso isuss th singl sour/singl mssg pplition n sign two pprohs s th xtnsion of th propos lgorithm for it. Prformn nlysis is onut through simultions. Th propos pproh hs ttr prformn thn tritionl -s rost n th xisting ntwork oing-s rost in trms of nrgy onsumption. Also, th stti vrsion of hs omprtiv prformn in nrgy onsrvtion with smllr ovrh. In th futur, w will improv th roustnss for moility n MAC lyr intrfrn of th propos pprohs n prform mor omprhnsiv simultion onsiring moil nvironmnt. ACKNOWLEDGEMENT This work ws support in prt y NSF grnts CCR 32974, CNS , CNS , CNS 534, CCF , n CNS Emil: ji@s.fu.u. REFERENCES [] R. Ahlsw, N. Ci, S. R. Li, n R. W. Yung. Ntwork informtion flow. IEEE Trnstions on Informtion Thory, (4):24 26, 2. [2] F. Di n J. Wu. Effiint rosting in ho wirlss ntworks using irtionl ntnns. IEEE Trnstions on Prlll n Distriut Systms, (4): 3, 26. [3] C. Frgouli, J. Wimr, n J.-Y L. Bou. A ntwork oing pproh to nrgy ffiint rosting: from thory to prti. In Pro. of IEEE INFOCOM, 26. [4] C. Hu, Y. Hong, n J. Hou. On mitigting th rost storm prolm with irtionl ntnns. In Pro. of IEEE ICC, 23. [5] S. Ktti, D. Kti, W. Hu, H. Rhul, n M. Mr. Th importn of ing opportunisti: Prtil ntwork oing for wirlss nvironmnts. In Pro. of ACM SIGCOMM, 26. [6] L. Li, R. Rmj, M. Buhikot, n S. Millr. Ntwork oing-s rost in moil ho ntworks. In Pro. of IEEE INFOCOM, 27. [7] W. Lou n J. Wu. On ruing rost runny in ho wirlss ntworks. IEEE Trnstions on Moil Computing, (2): 22, 22. [8] W. Png n X. Lu. On th rution of rost runny in moil ho ntworks. In Pro. of ACM MoiHo, 2. [9] S. Plish, M. Blkrishnn, K. Birmn, n R. Rnss. MISTRAL: Effiint flooing in moil -ho ntworks. In Pro. of ACM MoiHo, 26. [] A. Qyyum, L. Vinnot, n A. Louiti. Multipoint rlying for flooing rost mssg in moil wirlss ntworks. In Pro. of 35th Hwii Int l Conf. on Systm Sins (HICSS-35), 22. [] C. C. Shn, Z. Hung, n C. Jiko. Dirtionl rost for ho ntworks with proltion thory, Thnil rport, Computr n Informtion Sins, Univrsity of Dlwr. 24. [2] D. Simplot-Ryl, J. Crtigny, n I. Stojmnovi. An ptiv loliz shm for nrgy ffiint rosting in ho ntworks with irtionl ntnns. In Pro. of 9th IFIP PWC, 24. [3] I. Stojmnovi, M. Sigh, n J. Zuni. Dominting sts n nighor limintion s rosting lgorithms in wirlss ntworks. IEEE Trnstions on Prlll n Distriut Systms, ():4C25, 22. [4] J. Su n I. Mrsi. An ffiint istriut ntwork-wi rost lgorithm for moil ho ntworks. In CAIP Thnil Rport 248, 2. [5] Y. C. Tsng, S. Y. Ni, Y. S. Chn, n J. P. Shu. Th rost storm prolm in moil ho ntwork. Wirlss Ntworks, (2-3):53C67, 22. [6] J. Wu n F. Di. A gnri istriut rost shm in ho wirlss ntworks. IEEE Trnstions on Computrs, (): , 24. [7] J. Wu n H. Li. On lulting onnt ominting sts for ffiint routing in ho wirlss ntworks. In Pro. of ACM DIALM, 999. [8] S. Yng, J. Wu, n F. Di. Effiint kon onstrution mthos in MANETs using irtionl ntnns. In Pro. of IEEE ICDCS, 27. VIII. APPENDIX Proof of Thorm. If w n prov tht, givn sour no s, for ny no in th ntwork, thr is pth with ll intrmit nos n gs signt to forwr, w prov tht full livry is hiv. W ssum tht ll of s nighors form ring r s n outr rim of no, lik thgryrw in Figur. Not tht W is not mpty. W ssum tht no u is of th highst priority in r W.Ifw n prov tht ithr u is forwring no n (u ) is forwring g, or on of s nighors is visit no n it forwrs th mssg to, w ontrit th ssumption tht nnot rh from s. W mk th two ssumptions tht ithr u is not forwring no or u is forwring no ut g (u ) is not forwring g. W fin ontritions for ths two ss. Cs : u is not forwring no. Thrfor, for nighor f of u, oring to th ynmi no ovrg onition, ithr () thr is rplmnt pth onnting f to with t lst on intrmit no on it, u,or()f irtly onnts to, n th priority of f is highr thn tht of u. u nnot hv highr priority thn u sin u is th nighor of with th highst priority. If u is visit no, n ovr y u. For, iff is lso nighor of, it nnot hv highr priority thn u. Cs 2: u is forwring no ut g (u ) is not forwring g (n is on th g). A pth onnting u to must xist, with ll th gs with highr prioritis thn (u ) or visit. Sin u is th highst priority no, u on th pth nnot highr n hs to visit no with forwring outgoing g onnting to. In tht s, n ovr. All of th ontritions ov show tht n rh from th sour no s.