Iteratioal Joural of achie Learig a Coutig, Vol., No., April 0 i WSNs [9. The first low-eergy aaptive clusterig hierarchy was LEACH, propose by Heizel

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1 Iteratioal Joural of achie Learig a Coutig, Vol., No., April 0 LEACH-GA: Geetic Algorithm-Base Eergy-Efficiet Aaptive Clusterig Protocol for Wireless Sesor Networs Je-Log Liu a Chiya V. Ravishaar, ember, IEEE Abstract This stuy proposes a geetic algorithm-base (GA-base) aaptive clusterig protocol with a imal probability preictio to achieve goo performace i terms of lifetime of etwor i wireless sesor etwors. The propose GA-base protocol is base o LEACH, calle LEACH-GA herei, which basically has set-up a steay-state phases for each rou i the protocol a a aitioal preparatio phase before the begiig of the first rou. I the perio of preparatio phase, all oes iitially perform cluster hea stio process a the se their messages with statuses of beig a caiate cluster hea or ot, oe IDs, a geographical positios to the base statio. As the base statio receive the messages from all oes, it the searches for a imal probability of oes beig cluster heas via a geetic algorithm by miimizig the total eergy cosutio require for coletig oe rou i the sesor fiel. Thereafter, the base statio broacasts a avertisemet message with the imal value of probability to the all oes i orer to form clusters i the followig set-up phase. The preparatio phase is performe oly oce before the set-up phase of the first rou. The processes of followig set-up a steay-state phases i every rou are the same as LEACH. Simulatio results show that the propose geetic-algorithm-base aaptive clusterig protocol effectively prouces imal eergy cosutio for the wireless sesor etwors, a resultig i a extesio of lifetime for the etwor. literature. I applicatios usig irect trasmissio (DT) protocols [6, sesor oes trasmit their sese ata irectly to a BS. Thus, the oes locate far from the BS will ie quicly sice they issipate much eergy i trasmittig ata pacets. DT protocols are iefficiet sice eergy levels of oes are raie rapily whe the BS is locate far. O the other ha, miimum trasmissio eergy (TE) protocols [7, 8 trasmit ata pacets to the BS by way of multi-hop relay. As a result, oes locate ear the BS ie quicly sice they e up relayig lots of ata o behalf of remote oes. The results of simulatios usig the DT a TE commuicatio protocols are show i Figs. (a)-(), with the BS locate at the poit with cooriate (50, 00). Clearly, DT a TE result i a poor istributio for eergy cosutio by oes. Sesor oes i some subregios have all ie out, but oes i other regios are still active. As a result, ata for a part of the sesor fiel may ot be etecte. (a) 0% oes ea (DT) (b) 50% oes ea (DT) Iex Terms Aaptive clusterig protocol, clusterig hea, geetic algorithm, imal probability, lifetime. I. INTRODUCTION Wireless sesor etwors (WSNs), which cosist of a umber of small battery-powere evices, are frequetly to obtai various sorts of useful ata from surrouigs. These evices sese physical properties, such as sou, humiity, pressure, lumiosity, teerature, or chemical cocetratio, a trasmit the gathere ata to a base statio (BS) for further aalysis a processig. WSNs have bee effectively eploye i tactical combat situatios, habitat moitorig, home security, a so o [-5. Sice WSNs cosist of may sesors with limite eergy, a eergy-efficiet etwor protocol is a iortat cosieratio i WSN applicatios. ay routig protocols for WSNs have appeare i the (c) 0% oes ea (TE) () 50% oes ea (TE) auscript receive arch 0, 0. This wor was supporte i part by Natioal Sciece Coucil of Republic of Chia uer Grat Number NSC 98--E--038-Y. Je-Log Liu is with the I-Shou Uiversity, Kaohsiug, 800 Taiwa (correspoig author to provie phoe: ext. 6579; fax: ; jlliu@isu.eu.tw). Chiya V. Ravishaar is with the Departmet of Couter Sciece & Egieerig, Riversie, CA 9507 USA ( ravi@cs.ucr.eu). Figure. Survival statuses of sesor oes usig DT ((a) a (b)) a TE ((c) a () ) protocols. Clusterig commuicatio protocols represet a superior approach, a result i more balace patters of eergy use 79

2 Iteratioal Joural of achie Learig a Coutig, Vol., No., April 0 i WSNs [9. The first low-eergy aaptive clusterig hierarchy was LEACH, propose by Heizelma et al. [0,. It showe how eergy loas coul be well amortize by yamically creatig a small umber of clusters base o a threshol fuctio T(s) with a priori probability p (say, 5%), i a set-up phase. The techique uses cluster heas (CHs) to meiate ata trasmissio. Simulatio results i [0, show that all oe te to issipate the same level of eergy over time sice the CH roles are rotate amog oes. Although LEACH clearly outperforms the DT a TE protocols, it retais several shortcomigs. Thus several ehace versios of LEACH have appeare i the literature [. LEACH uses a threshol fuctio parameterize by a probability p iput by user. However, the performace of sesor etwor is very sesitive to the value of p. Whe p is large, may clusters are forme a coul result i high eergy cosutio sice may CHs issipate eergy i trasmittig to the BS. O the other ha, whe p is small, oly a few clusters are forme, which may icrease eergy issipatio whe member oes trasmit to CHs. The literature suggests that the imal p value p, or the imal cluster umber, epes o parameters such as the total umber of oes istribute i the sesor fiel, the size of sesor fiel, the locatio of BS, a so o [3,. Our wor proposes a geetic algorithm-base (GA-base) aaptive clusterig protocol, terme LEACH-GA, to preict the imal values of probability effectively. II. ENERGY-EFFICIENT COUNICATION PROTOCOLS We ow briefly escribe the LEACH protocol, a the preset our geetic algorithm-base aaptive clusterig protocol. A. Clusterig Hierarchy i LEACH LEACH operates i several rous, each cosistig of a set-up a a steay-state phase. Each oe trasmits sese ata to its closest CH. The CH for each cluster receives a aggregates the ata from cluster members a the trasmits the aggregate ata to the BS through a sigle-hop relay (show i Fig. ). LEACH creates a set-up phase for CHs stio, a a steay-state phase for time slot scheulig a trasmissio. Each sesor oe s ecies iepeetly of other seor oes whether it will claim to be a CH or ot, by picig a raom r betwee 0 a a coarig r with a threshol T(s) base o a user-specifie probability p. The threshol is efie as follows [0: etwor. No-CH oes (or member oes) ecie to joi the cluster efie by the CH with the strogest receive sigal. Next, each o-ch ses a joi-request cotaiig their ID, to the closest CH usig CSA. Figure. The LEACH clusterig commuicatio hierarchy for WSNs. After the cluster-setup sub-phase, the CH recogizes the umber of member oes a IDs of the oes. Base o all joi-request messages receive withi the cluster, the CH creates a T scheule i aitio to a uique spreaig coe, a trasmits them to cluster members at the begiig of steay-state phase. Thereafter, all oes i the cluster trasmit their ata pacets to their CHs i the pre-specifie T time slot, usig this coe. As we ow that T-base protocols are aturally eergy preservig, because they have time slots built-i, a o ot suffer from collisios. Also, each member oe ca situate i a sleep moe at all times except urig its correspoig time slots i orer to ecrease oe s eergy issipatio. Whe the ata pacets set by a oe have bee receive by a CH, the CH aggregates a forwars them to the BS. These actios are repeate i each rou. The plots of simulatio results by LEACH are show i Figs. 3(a) a (b), for the BS locate at cooriate (50, 00). It is clearly show that the oes ea obtaie usig LEACH are more uiform tha that of DT a TE protocols. (a) 0% oes ea (b) 50% oes ea p T(s) p r mo ( ) p 0 if s G otherwise () Figure 3. Survival status of sesor oes uer LEACH. where G is the set of oes that have ot bee CHs i the last /p rous. Whe a oe ecies to be a CH, it broacasts a avertisemet message, with the oe s ID a a heaer, usig a o-persistet carrier-sese multiple access (CSA) AC protocol to esure the elimiatio of collisios, to the etire sesor fiel. The size of the message is small, so that it ca be efficietly broacaste to reach all of the oes i the B. Our Propose Geetic Algorithm-base Aaptive Clusterig Protocol Our wor itrouces a geetic algorithm-base variat of LEACH to etermie the imal value of p for various base statio placemets. The GA-base imizatio proceure is performe oly oce, before the set-up phase of the first 80

3 Iteratioal Joural of achie Learig a Coutig, Vol., No., April 0 rou. The pseuo-coe of the propose protocol is escribe as follows. Pseuo-coe of the Propose LEACH-GA Protocol: E Tx l E ( l, ) l E + l + l 0 0 () BEGIN : Specify the probability (p set ), umber of oes (); : E iit (s)=e 0, s=,,, ; (I) PREPARATION PHASE : if (E iit (s)>0 & rmo(/p set ) 0) the //p set ca set 0.5 : r raom(0,) a coute T(s); //give by () 3: if (r < T(s)) the : CCH{s}=TRUE; //oe s be a caiate CH 5: else 6: CCH{s}=FALSE; //oe s ot be a caiate CH 7: e if 8: e if 9: SeToBS(ID u, (x u,y u ), CCH(u)) All oes se messages to BS; 0: GAiBS(p ) Optimal probability is etermie; : BC (p ) BS broacasts a message bac to all oes; (II) SET-UP PHASE : o { //repeat for r rous : r raom(0,); 3: if (E iit (s)>0 & rmo(/p ) 0) the : coute T(s); //give by () 5: if (r < T(s)) the 6: CH{s}=TRUE; //oe s be a CH 7: else 8: CH{s}=FALSE; //oe s ot be a CH 9: e if 0: e if : if (CH{s}=TRUE) the : BC (ADV) broacast a avertisemet message; 3: Joi(ID i ); //o-cluster hea oe i joi ito the closest CH : Cluster(c); //form a cluster c; 5: e if (III) STEADY-STATE PHASE : If (CH(s)=TRUE) the : Receive(ID i, DataPCK) //receive ata from members; 3: Aggregate(ID i, DataPCK) //aggregate receive ata; : TasToBS(ID i, DataPCK); //trasmit receive ata; 5: else 6: If (ytimeslot=true) the 7: TasToCH(ID i, DataPCK); //trasmit sese ata; 8: else 9: Sleepoe(i)=TRUE; //oe i at a sleep state 0: e if : e if : } // oe rou is colete END III. OPTIAL CLUSTERING ANALYSIS We evaluate our protocol usig the first-orer raio moel of [0. The parameter settigs use i the simulatio for the moel are liste i TABLE I. Accorig to the raio eergy issipatio moel of Fig., the eergy require by the trasmit alifier E Tx (l,) to trasmit a l-bit message over a istace betwee a trasmitter a receiver is where 0 = / eotes the threshol istace, E represets the eergy cosutio i the troics for seig or receivig oe bit, a a represet alifier eergy cosutios for a short- a log-istace trasmissios, respectively. To receive a l-bit message, the eergy E Rx (l) require by the receiver is give by TABLE I. Parameters Iitial eergy (E 0 ) E ( l) = l (3) Rx E Figure. First-orer raio moel. PARAETER SETTINGS OF THE FIRST-ORDER RADIO ODEL Trasmitter Electroics (E ) Receiver Electroics (E ) Data Pacet Size (l) Values 0.5 J/oe 50 J/bit 50 J/bit 000 bits Trasmitter Alifier ( ) 0 0 or 00 pj/bit/m Trasmitter Alifier ( ) pj/bit/m Let a total of sesor oes be istribute uiformly i the sesor fiel of size meters, a be groupe ito clusters. The eergy require per rou for a CH to receive ata pacets from member oes, a aggregate a forwar them a istace to the BS is E CH l E ( l, ) l E ( ) ( ) + + < 0 0 () where E represets the eergy issipatio for aggregatig ata. The eergy issipatio for a o-cluster hea oe is o CH ( l, ) = l E + l toch E (5) where toch represets the istace betwee a cluster member a its CH. Sice the oes are assume to be uiformly istribute i the sesor fiel, the expecte value of square istace from a member oes to its CH, which locate at the 8

4 Iteratioal Joural of achie Learig a Coutig, Vol., No., April 0 poit (a, b), is give by [ ( x a) + ( y b) E toch = xy A Assumig the shape of clusters is a circle, thus (6) becomes [ = E toch ( x A = π + y ) xy The value of toch i (7) is twice that of Heizelma et al., who assume that the CH is place at the ceter of cluster. oreover, the eergy issipate i a cluster is obtaie as E total = ECH + ( ) Eo CH ECH o CH (8) Thus, the total eergy issipatio for a rou is give by E Total l E l E π π (6) (7) < 0 0 (9) From (9), the aalytical imal solutios for a p are obtaie. a p = π π π π < 0 0 < 0 0 (0) () We assume the cooriates of the BS to be (0.5, 0.5+B), a calculate the values of E [ a E [ to be 7 = + B ; = + B + () B Therefore the values of a p are relate to the total umber of sesor oes, omai size of sesor fiel, a the locatio of BS. I aitio, Heizelma et al. assume the BS is far from the oes, so the eergy issipatio follows the multipath moel. Thus, their formula for is oly the lower part of (0). The origial formula, eote as origial form i this wor, for from Heizelma et al. is [ = (3) π Therefore, the p ca be formulate as p = = () π I this wor, (0) a () are use as the correcte forms of aalytical solutio for a p without assumig the positios of BS locate ear or far from the sesor fiel. IV. GENETIC ALGORITH-BASED CLUSTERING At the begiig of preparatio phase, each oe iitially etermies whether or ot it shoul be a caiate cluster hea (CCH), usig the followig cluster hea stio proceure. First, every sesor oe sts a raom umber r from the iterval [0,. If r is smaller tha T(s), base o a prescribe probability p set, the the oe is a CCH. The value of p set ca be a large value i our protocol, p set =0.5, say. Thereafter, each oe ses its ID, locatio iformatio, a whether or ot it is a CCH to the BS. As the BS receives messages set by all oes, it performs GA operatios to etermie the imal probability, p = /, by miimizig the total amout of eergy cosutio i each rou. Therefore, the objective fuctio use i the GA ca be formulate as r f ( x) = c= i= c= q ( E ( E + [ i, CCH ( c)) x + α α + [ CCH ( c), BS) x c c (5) r where x = [ x, x,..., x c,..., x. The values of x c are oe for our biary-ga whe it is a CCH, otherwise, it is zero. The parameters = a α= were use for 0 ; while, = a α= were set for 0. The symbol q represets the umber of member oes i a CCH. The imal probability p is etermie by the GA by searchig the solutio space through a evolutioary imizatio process icorporatig probabilistic trasitios a o-etermiistic rules, a applyig stio, crossover a mutatio operators. Oce the imal probability p is fou, the BS broacasts the value of p to all oes. The set-up a steay-state phases begi. The proceures of set-up a steay-state phase are the same as i LEACH. V. SIULATION RESULTS Our wor assumes that all sesor oes are homogeeous a istribute uiformly over the sesor fiel with limite eergy that the lis betwee oes are symmetric, a that messages from all oes ca reach the BS. The oes are istribute raomly i a square of size. Each 8

5 Iteratioal Joural of achie Learig a Coutig, Vol., No., April 0 simulatio is repeate for 30 iepeet rus. I aitio, cotrol pacet sizes for broacastig pacet a pacet heaer were 50 bits log, a the eergy issipatio for aggregatig ata was 5 a 0 J/bit/sigal. A. Coariso of Optimal Probability of Cluster Heas I this sectio, the eergy issipatio for aggregatig ata a the parameter were specifie as 5 J/bit/sigal a 0 pj/bit/m, respectively. The total umber of sesor oes was 00. Figures 5(a) a (b) show the coariso of imal probability obtaie from moel aalysis a GA-base coutatio for a variety of locatios of BS for the sesor fiels of 50m 50m a 00m 00m. The coariso of solutios epicts that the istributio of preset p quite agree with the correcte form usig our aalytical formulas of (), whereas Heizelma et al. s results isplaye a large iscrepacy whe coare to the ata by usig the GA a preset moifie aalytical formulas. oreover, the results show that the imal probability, p, is clearly affecte by the locatios of BS. Whe the BS is locate ear the sesor fiel, the values of p are large. O the cotrary, the values of imal probability ecrease as the BS moves farther from the sesor fiel. Whe the BS locate at the ceter of sesor fiel, the values of E [ is give by [5, 6 [ E a the form of p ca be silifie as = x + y A A (6) = p = (7) π are coucte usig =00 a =00 to stuy the effect of to the value of p. The simulatio results for =00 a =00 are isplaye i Figs. 6 a 7, respectively. Figures 6(a) a (b) show that the preicte istributios of imal probability by preset GA were as well as the preset correcte form govere by () for BS locate at ifferet positios. I these two figures, the values of imal probability at the ceter of sesor fiel were iepeet of the omai size of sesor fiel base o (7). This wor also performe the simulatio of the case with =00, a the results are show i Figs. 7(a) a (b). From the results show i Figs. 5 a 7, the values of imal probability at the ceter of sesor fiel for the case of =00 were equal to the half of that of the case for =00. (a) 50m 50m sesor fiel (b) 00m 00m sesor fiel (b) 00m 00m sesor fiel Figure 6. Coariso of imal probability betwee aalytical aalyses a geetic algorithm imzatio for the sesor fiels of (a) 50m 50m a (b) 00m 00m usig =0 pj/bit/m a =00.. (a) 50m 50m sesor fiel (b) 00m 00m sesor fiel (b) 00m 00m sesor fiel Equatio (7) states that the parameter p is just fuctio of the total umber of sesor oes oly whe the BS locate at the ceter of sesor fiel. Namely, the value of probability at the ceter of sesor fiel is iepeet of the omai size. (a) 50m 50m sesor fiel (b) 00m 00m sesor fiel (b) 00m 00m sesor fiel Figure 7. Coariso of imal probability betwee aalytical aalyses a geetic algorithm imzatio for the sesor fiels of (a) 50m 50m a (b) 00m 00m usig =0 pj/bit/m a =00. \ Figure 5. Coariso of imal probability betwee aalytical aalyses a geetic algorithm imzatio for the sesor fiels of (a) 50m 50m a (b) 00m 00m usig =0 pj/bit/m a =00. oreover, the values of p are clearly epeet of the total umber of sesor oes () from the expressio of (). Whe the umber of sesor oes icreases, the values of imal probability will ecrease base o (). Two cases B. Coariso of the Presete LEACH-GA a LEACH I this sectio, the oes with 00 are istribute raomly i the sesor fiel with 50m 50m. Each simulatio is also repeate for 30 iepeet rus, a solutios are obtaie from the average of the rus. I aitio, cotrol pacet sizes for broacastig pacet a pacet heaer were 50 bits legth for the preset coutatios, a the eergy issipatio for aggregatig ata a the parameter were specifie as 0 J/bit/sigal a 00 pj/bit/m [, respectively. Figure 8 is the solutio istributio of p preicte by usig the presete LACH-GA for BS locate at ifferet positios. The coariso of the values of p coute by LEACH-GA 83

6 Iteratioal Joural of achie Learig a Coutig, Vol., No., April 0 a correcte formula is agreeable, whereas, the ata usig Heizelma et al. s formula show i () were clearly iscrepat coare to LEACH-GA a our correcte form. Especially, there are large errors performe usig the origial form whe the BS locate ear to the ceter of sesor fiel. Figures 9(a) a (b) coare the performace of four protocols with the BS locate at two cooriates of (5, 50) a (5, 350), respectively. Our protocol clearly has excellet performace as coare with other protocols. Whe the locatio of BS is far from the sesor fiel, presete protocol prologs the lifetime of etwor sigificatly sice it uses a imal probability i formig clusters. The gais achieve are as high as 5% a 0%, coare to LEACH with the BS locate at (5, 50) a (5, 350), respectively. (a) Figure 8. Coariso of imal probability betwee aalytical aalyses a geetic algorithm imzatio.. TABLE II lists the simulatio results obtaie usig LEACH a presete LEACH-GA protocols for BS locate at ifferet positios. The iitial eergy for all oes was 0.5(J) a the probability p use i LEACH is 5%, same as the settigs i [0,. The umber of rous require whe the umber ea of oes is %, 0%, 50%, a 00% are recore urig simulatios. From our results, the values of p clearly epe o the positios of BS. The value of imal probability is the largest whe the BS is at the ceter of sesor fiel, a it ecreases whe the BS moves outwar. oreover, the propose LEACH-GA outperforms LEACH i terms of lifetime of etwor. (b) TABLE II. COPARISON OF NETWORK LIFETIES (NUBER OF ROUNDS) BETWEEN LEACH AND PROPOSED LEACH-GA PROTOCOLS BS (5, y) Noes Dea Protocol Prob. % 0% 50% 00% LEACH LEACH-GA LEACH LEACH-GA LEACH LEACH-GA LEACH LEACH-GA LEACH LEACH-GA LEACH LEACH-GA Figure 9. Performace coarisos of etwor lifetime for the BS locate at poits of (a) (5, 50) a (b) (5, 350). VI. CONCLUSIONS This wor propose a GA-base aaptive clusterig protocol to etermie the imal thresholig probability for cluster formatio i WSNs. The LEACH protocol requires the user to specify this probability for use with the threshol fuctio i etermiig whether a oe becomes a CH or ot. However, the etwor performace is extremely sesitive to this probability, a it is very har to obtai a imum settig from available prior owlege. Hece, our approach uses a preparatio phase prior to the set-up phase of the first rou to gather iformatio about oe status, IDs, a locatio a ses it to the BS, which etermies the imal probability to use i the CH stio mechaism. Our simulatio results show that the imum istributio of probability matche the aalytical results propose by our correcte formulas well. oreover, our propose LEACH-GA metho outperforms TE, DT, a LEACH i terms of etwor lifetime, sice the use of the imal probability yiels imal eergy-efficiet clusterig. 8

7 Iteratioal Joural of achie Learig a Coutig, Vol., No., April 0 ACKNOWLEDGENT The wor was supporte i part by Natioal Sciece Coucil of Republic of Chia uer Grat Number NSC 98--E--038-Y. REFERENCES [ I. Ayiliz, W. Su, Y. Saarasubramaiam, a E. Cayirci, A survey o sesor etwors, IEEE Commuicatios agazie, vol. 0, o. 8, Aug. 00, pp. 0. [ K. Aaya a. Youis, A survey o routig protocols for wireless sesor etwors, A Hoc Networs, vol. 3, ay 005, pp [3 A. A. Abbasi a. Youis, A survey o clusterig algorithms for wireless sesor etwors, Couter Commuicatios, vol. 30, Oct. 007, pp [ A. aiwarig, J. Polastre, R. Szewczy, D. Culler, a J. Aerso, Wireless sesor etwor for habitat moitorig, i AC WSNA 0, Atlata, Georgia, Sept. 00, pp [5 S. Zhu, W. Wag, a C. V., Ravishaar, PERT: A ew power-efficiet real-time pacet elivery scheme for sesor etwors, Iteratioal Joural of Sesor Networs, vol. 3, issue, Ju. 008, pp [6 C. Itaagowiwat., R. Govia, D. Estri, J. Heiema, a F. Silva, Directe iffusio for wireless sesor etworig, IEEE/AC Trasactios o Networig, vol., issue, Feb. 003, pp. -6. [7 T. Shepar, A Chael Access Scheme for Large Dese Pacet Raio Networs, AC SIGCO Couter Commuicatio Review, vol. 6, issue, Oct. 996, pp [8 B. Krishamachari, D. Estri, a S. Wicer, oelig ata-cetric routig i wireless sesor etwors, Wireless Commuicatios, vol., issue,, Oct. 00, pp [9 D. P. Agrawal a Q. A. Zeg, Itrouctio to Wireless a obile Systems, e., Broos/Cole Pacific Grove, CA, 003. [0 W. B. Heizelma, A. P. Charaasa, a H. Balarisha, Eergy-efficiet commuicatio protocol for wireless microsesor etwors, i Proceeigs of the 33r Aual Hawaii Iteratioal Coferece o System Sciece, aui, Hawaii, Ja. 000, pp. -0. [ W. B. Heizelma, A. P. Charaasa, a H. Balarisha, A applicatio-specific protocol architecture for wireless microsesor etwors, IEEE Trasactios o Wireless Commuicatios, vol., issue, Oct. 00, pp [ P.T.V. Bhuvaeswari a V. Vaiehi, Ehacemet techiques icorporate i LEACH- a survey, Iia Joural of Sciece a Techology, vol., o. 5, ay 009, pp [3 S. Bayopahyay a E.J. Coyle, A eergy efficiet hierarchical clusterig algorithm for wireless sesor etwor, i INFOCO 003, vol. 3, Sa Facisco, CA, ar. 003, pp [ K. Yag, Y. Wu, a H. Zhou, Research of imal eergy cosutio moel i wirelss sesor etwor, i 00 Iteratioal Coferece o Couter Egieerig a Techology, Chegu, Chia, Apr. 00, pp. V7- - V7-. [5 S. Bayopahyay a E. J. Coyle, A eergy efficiet hierarchical clusterig algorithm for wireless sesor etwors, IEEE INFOCO 003, Sa Fracisco, CA, Apr [6 G. Smaragais, I. atta, a A. Bestavros, SEP: A stable tio protocol for clustere heterogeeous wireless etwors, i Proceeigs of Seco Iteratioal Worshop o Sesor a Actor Networ Protocols a Applicatios (SANPA), Bosto, Sep. 00, pp