Effective Coverage and Connectivity Preserving in Wireless Sensor Networks

Transcription

1 Effectve Coverage and Connectvty Preervng n Wrele Senor Network Nurcan Tezcan Wenye Wang Department of Electrcal and Computer Engneerng North Carolna State Unverty Emal: {ntezcan,wwang}@eo.ncu.edu Abtract In th paper, we addre the problem of fndng an optmal coverage et by effectvely elmnatng redundant node wth guaranteed connectvty wthout ung centralzed control and accurate locaton nformaton. Ung a fully dtrbuted approach, we propoe an effectve redundant node elmnaton method that conder even the mallet overlappng regon to etablh a coverage et. Further, an extenon cheme preented that fnd the mnmum number of enor among the coverage et, where the network connectvty guaranteed. We preent the mulaton reult to llutrate achevable coverage et whle preervng connectvty, and energy avng to verfy our approache. I. INTRODUCTION In recent year, wrele enor network (WSN) have been ued n many event-crtcal applcaton, uch a habtat montorng, health applcaton, battlefeld montorng, wld anmal protecton. To upport uch applcaton, an mportant problem that hould be addreed how well a gven area can be montored to catch all the event by the WSN - an ue often related to QoS, and known a coverage [11], [18]. On the other hand, enor have very lmted energy upply. They are uually hard to recharge ther battere after deployment, ether becaue of the number of node too large, or becaue the deployment area hotle. Hence, prevou tude [1], [15] [17] focued on the problem of fndng an optmal et of enor mantanng the coverage and connectvty of the network to acheve energy-effcent communcaton. By th way, only a group of enor actvely work for event detecton, data tranmon or aggregaton, where redundant node ave energy for the next round that make network lfetme prolonged n an effcent way. In partcular, fndng an optmal coverage or connectvty et can be mplemented ung ether centralzed [1], [5], [15] or dtrbuted algorthm [4], [8], [14], [16], [17]. Centralzed oluton bacally organze enor to preerve the enng coverage wthout leavng blnd pont n the enng feld by ue of a central authorty (the nk) and global locaton nformaton of enor. Even though they fnd near-optmal oluton, they can not be appled to hgh-dene enor network wth large number of enor node due to the communcaton expene of havng global nformaton at the nk. Therefore, many dtrbuted oluton have been propoed [4], [8], [14], [16], [17] where coverage acheved by formng connected et-cover n a dtrbuted manner for each query [8]. In [5], rather than enng feld, a et of target wth known locaton are necearly covered by each et cover. Therefore, only actve node n the et-cover end and receve data. On the other hand, n [16], a dtrbuted chedulng algorthm ha been propoed where each node turn telf off ung local neghbor nformaton where all node have dentcal enng range that the ame a ther tranmon range. However, the enng range of a enor node mght be approxmately n between 1-3 m, wherea the tranmon range of that enor mght be n between 5-3 m [18]. In th paper, we focu on the problem of dtrbuted calculaton of coverage of each ndvdual enor to effectvely elmnate redundant node ung relatve locaton nformaton,.e., vrtual coordnate. Although, locaton nformaton can be readly obtaned by GPS-upported enor or localzaton cheme propoed for enor network [6], [9], t uually cotly and mght be qute mleadng n ome cae. For example, even though two node are geographcally cloe to each other, gnal trength may not be trong due to the obtacle between them. Thu, rather than exact locaton nformaton of enor, we ue receved gnal trength (RSS) meaurement-baed vrtual coordnate and vrtual dtance between enor node whle determnng ther coverage boundare [13]. In partcular, obtacle may caue neffectve detecton of event [7]. Therefore, ung vrtual dtance may alo help u to reduce the effect of rregularty n enng range due to obtacle, uch a buldng, and tree. We ummarze the contrbuton of th paper are a follow. Frt, we preent a dtrbuted coverage calculaton algorthm that fnd overlappng enng regon to effectvely dcover redundant enor node ung vrtual coordnate. After dcoverng the poble redundant node, an energyaware algorthm ued to contruct optmal-coverage et whch can be ued for node chedulng, topology control, etc. Thrd, an extenve method propoed to fnd mnmum number of domnatng enor among the coverage et, where the network connectvty guaranteed. In th ene, the routng problem multaneouly olved wth the connected domnatng et whch form a connected backbone to carry out the data traffc to the nk, thu no extra routng protocol are needed. Fnally, we carry out performance evaluaton and demontrate the mulaton reult to llutrate achevable et of enor for coverage whle preervng connectvty. The ret of paper organzed a follow. In Secton II, we explan the network model and ome aumpton and term that wll be ued n the paper. We decrbe the dtrbuted

2 coverage calculaton algorthm and redundant node dcovery n Secton III. Ung th algorthm, effectve coverage and connectvty et contructon are preented n Secton IV. Followng, mulaton reult are preented n Secton V. Fnally, Secton VI conclude the paper. II. PRELIMINARIES Let S = { 1, 2, 3,..., N } be the fnte et of enor, dtrbuted randomly n a two-dmenonal area A, where there are uffcent enor to montor the feld. Each enor ha a unque dentfer (uch a MAC addre). All enor node know ther enng range, denoted by r, whch aumed to be dentcal for all enor, and ther tranmon range, t. In th paper, we aume that tranmon range greater or equal to the enng range,.e., r t [18]. We ue vrtual coordnate and vrtual dtance gven n [13]. A enor dcover t neghbor n t tranmon range by perodcally ent hello meage and collect receved gnal trength (RSS) meaurement of t neghbor. By th way, each enor place t one-hop neghbor to a vrtual coordnate ytem centered at telf [13] and calculate the vrtual dtance. The followng notaton wll be ued n the paper: 1) S, the enng regon of a node a crcular area centered at (vx, vy ) and radu of r, where (vx, vy ) the vrtual coordnate of. 2) T, tranmon neghbor of enor wth whch can communcate drectly. 3) C, coverage neghbor of enor whch have a common enng area wth. We clafy the coverage neghbor of a enor a 1-hop and 2-hop baed on vrtual dtance. 4) For each enor par and j that have common enng area, we aocate a trple (Pj 1, P j 2, j) where (Pj 1, P j 2 ) are the two nterecton between and j arranged n the counterclockwe order, and the effectve angle. Let u denote the vrtual dtance between and j by vd(, j),.e., vd(, j) = (vx vx j ) 2 + (vy vy j ) 2. If vd(, j) < r, then enor record the enor j a t 1-hop coverage neghbor, whch mean the j nde t enng range, j C 1 Negh. If vd(, j) < 2r, then enor take the enor j a t 2-hop coverage neghbor, that not n t enng range but hare a enng area n common, then, j C 2 Negh, where C 1 Negh C 2 Negh = C T. Defnton 1: Let S be the enng regon of enor. If S j C S S j, we call enor a redundant enor, nce t enng regon can be covered by t coverage neghbor, C. A ubet of enor, C S called a coverage et f the unon of the enng regon of the C cover the entre feld A, that A S C. We conder a enor node to be an eental node (E-node) n C f C. Otherwe, t a redundant node (R-node). Our goal to contruct a coverage et havng mnmum number of E-node. After contructng the coverage et, we fnd a ubet of the coverage et, called domnatng coverage et, D, uch that each E-node (C/D) can drectly communcate wth one of π r P 2 P 1 π 2π π Fg. 1. (a) r π j 2π 2 A 2 B2 A C 2 A 2 C1 B 1 A1 B 2 B1 C2 4 2 (b) Illutraton of dtrbuted coverage problem. the enor n D. We conder a enor to be an eental domnatng (ED) node f D. Next, we preent the dtrbuted coverage calculaton and redundant node dcovery algorthm to contruct the coverage and domnatng coverage et. III. COVERAGE CALCULATION AND DISCOVERY OF REDUNDANT NODES One of the man challenge n dtrbuted coverage calculaton to determne whether the enor redundant ung t 1-hop and 2-hop coverage neghbor. In th context, we ue the term of coverage calculaton to calculate whether a enng regon S of a enor fully covered. To the bet of our knowledge, extng coverage method [4], [17] only condered 1-hop coverage neghbor,.e., neghbor nde the enng range. In th paper, we alo take nto account the 2-hop neghbor that hare area n common a well to decreae the lower bound for the number of coverage neghbor whle effectvely elmnatng redundant node. Next, we wll how propoed coverage calculaton tep that conder both 1-hop and 2-hop coverage neghbor. The frt tep, called permeter-tet, check whether there are enough coverage neghbor uch that all pont n the permeter hould be wthn a enng range of a coverage neghbor. Th a neceary condton baed on the aumpton of denely deployed node [11]. The econd tep called center-tet n whch t examned whether the center of a enor coverage can be covered by at leat one of t neghbor. The thrd tep called dtance tet, thoe coverage neghbor mut be cloe enough to the enor, o that there may not be uncovered area nde the enng regon. Here, we explan thee three condton n detal a follow: Permeter-tet: A enor frt determne whether the permeter of t enng regon covered. By examnng each 1-hop and 2-hop coverage neghbor, a enor can determne f nterected arc n total are uffcent to encloe t permeter from to 2π [11]. If the permeter encloed, we refer that permeter-tet paed. To do th, we mply determne the nterecton pont of the arc and can the permeter a llutrated n Fg. 1 (a). C1 A2 4

3 We how an example of the permeter-tet n Fg. 1 (b), where enor ha 4 coverage neghbor. Ung ther vrtual coordnate, enor can fnd the nterecton pont of the arc [2]. Let the lne egment from to 2π n Fg. 1 (b) denote the permeter of. After we lt the arc and then can the permeter n a hown n Fg. 1 (b), we can ee that the entre permeter encloed by [A 2 C 1 ] (node 3 ), [C 1 C 2 ] (node 4 ), [B 1 B 2 ] (node 1 ) and [A 1 A 2 ] (node 2 ). Although, permeter-tet enure that a enor ha uffcent number of coverage neghbor, th doe not guarantee the full coverage of the enng regon. There may have ome uncovered area n the mddle of the regon. Thu, we propoe a center-tet and a dtance-tet, o that a enor enure that neghbor are cloe enough to the center and provde full coverage. Lemma 1: S j C S S j f and only f any pont P on the permeter of covered by an arc P j 1 P j 2, where j C. Proof: Snce the permeter crcle that urround the enng regon S alo n S, any arc P j 1 P j 2 on th permeter crcle mut alo be covered by one or more enor n C. Center-tet: When a enor pae the permeter-tet, t ha neceary number of coverage neghbor. However, th not uffcent to clam that the enng regon fully covered. For ntance, there are two example n Fg. 2 (a) and (b), where permeter-tet ha been paed. In Fg. 2 (a), neghbor of are uccefully cover the enng regon. However, n Fg. 2 (a), even there are 5 coverage neghbor, there an uncovered area n the mddle of the regon. Therefore, the motvaton of the center-tet to enure that the center of a enng regon can be covered by at leat one of a node neghbor. In th tep, enor chooe one of t coverage neghbor j a prmary neghbor whch atfe d(, j) r, where d(, j) the dtance between and j. One ntutve neceary condton that there hould be at leat one prmary neghbor to cover the center pont of a enng regon. If there no prmary neghbor a n Fg. 2 (a),.e., dtance between all coverage neghbor of the are greater than r, then neghbor are not uffcent to acheve full coverage. Therefore, center-tet a neceary condton n fndng a coverage et. In Fg. 2 (b), the prmary neghbor of 4, where d(, 4) = OP r. In cae there are multple enor atfyng d(, j) r, we elect the one havng the mnmum dtance a the prmary neghbor. Corollary 1: For each, S j C S S j f and only f 1 C C1 hop. Proof: Conder a enor havng coverage neghbor C. Let all coverage neghbor are 2-hop neghbor,.e., j C, j C 2 hop. In th cae, all coverage neghbor hould be outde t enng range, where j C, vd(, j ) > r. If all j C are more than r away from the enor telf, there a gap n the nner regon where enor located that cannot be covered by any neghbor. By th contradcton, we how f there no 1-hop coverage neghbor of, S can 2 3 (a) Dtance tet: fal O 4 (b) Dtance tet: pa. Fg. 2. Two example where permeter-tet paed for enor. not be covered. Dtance-tet: When a enor pae the permeter-tet, and center-tet, t tll poble that there are uncovered area of a enor coverage. The motvaton of dtance-tet to verfy that coverage neghbor are cloe enough to the center and atfy full coverage, whch baed on the electon of prmary neghbor n the center-tet. Let p () be the prmary neghbor of. In th tet, we check f for all j C Negh, the followng condton atfe: d(, j) r + d(, p). (1) In Fg. 2 (b), to llutrate the dtance between and neghbor clearly, we draw an extended coverage range of node, where the center and the radu R = OB = r + OP. We called the orgnal enng range of a R and the extended range a R n the Fg. 2 (b). The condton n (1) can be verfed by two extreme cae: for d(, p) =, that, node p and node are n the ame locaton, then the radu of the extended coverage, R = r, whch exactly the ame a, that, there no extenon of coverage from node p ; for d(, p) = r, that, node p on the permeter of node, then R = r + r = 2r, whch mean that the extended coverage enlarged one tme. Therefore, the extended coverage how the maxmum dtance that the prmary neghbor can reach. If all enor n the coverage neghborhood of are cloer than r + d(, p), then we ay that full coverage acheved and dtance-tet paed. Therefore, the frt condton, permeter-tet a neceary condton to cover the permeter; and the econd condton, center-tet alo a neceary condton to cover the center. The thrd condton, dtance-tet very effectve for the full coverage after many tet, though t an approxmate condton for coverage calculaton. Therefore, enor that have paed the permeter, center, and dtance-tet, are marked a R-node and wll be elmnated to fnd an optmal coverage et whch wll be explaned n the next ecton. Lemma 2: Let, j C S S j S, where C the ubet of coverage neghbor that uffcent for permetertet, then f j C, d(, j) < r + d(, p)1. 1 We omt ncluon of the proof of th lemma due to pace retrcton. P 3 B

4 Ung the propoed method, a enor can be covered by at leat three coverage neghbor. If only 1-hop coverage neghbor are condered then all three neghbor are needed to be cloer than r mlar to the coverage calculaton method n [4], [17]. On the other hand, f we alo conder 2-hop coverage neghbor, then only a ngle 1-hop coverage neghbor together wth two 2-hop coverage neghbor can be uffcent to cover S. Note that two enor can not be at the ame locaton. Lemma 3: If j C S S j = S, then there mut be a ubet of C, denoted by C, uch that j C S S j = S. So, we can wrte 3 C, where C atfe ether 1 C C1 Negh and 2 C C2 Negh, or C C1 Negh. Proof: From Corollary 1, we know that at leat one enor n C 1 Negh needed for full coverage. The angle of the arc that not covered by any enor j, j C 1 Negh, atfe > π. Snce all arc that contute the 2π permeter mut be covered for full coverage (ee Lemma 1), the uncovered arc can be covered by enor n C 2 Negh. However, the angle β of the arc covered by any enor k, k C 2 Negh, atfe β < 2π 3. Hence for full coverage, at leat two enor n C 2 Negh are needed. Now let u conder the econd cae where only 1-hop coverage neghbor are ued. The angle α of the arc covered by any enor m, m C 1 Negh, atfe α < π. Smlar to the frt cae, each enor n C 1 Negh can only cover le than π, therefore at leat three enor are needed n for full coverage. C 1 Negh IV. CONSTRUCTING COVERAGE AND DOMINATING COVERAGE SETS In th ecton, we wll explan how coverage and connected domnatng et are contructed n a dtrbuted fahon. Frt tep to dcover the poble redundant node, whch explaned n the prevou ecton. However, each redundant node can not be removed from the coverage et unle t neceary coverage neghbor are n the coverage et. Therefore, we ue an energy-aware redundant elmnaton method, where enor calculate ther beneft of beng n the coverage et n term of energy and then tart endng announcement meage to bult the coverage et. After coverage et etablhed, domnatng coverage dynamcally contructed tartng from the nk. Here, we gve the detal of the tep that each enor follow. A. Contructng Coverage Set To contruct the coverage et, we frt need to determne eental node to preerve coverage and elmnate the redundant one. If enor calculate that t coverage neghbor, C, are not uffcent to montor t enng regon, then t mandatory member of the coverage et,.e., f S j C S S j, then C. In th cae, a enor broadcat an I-AM-ESSENTIAL meage and become a member of coverage et. Otherwe, t a canddate of beng redundant node and follow the beneft calculaton tep that determne t beneft to be n the coverage et. Any enor that not a mandatory E-node ha to calculate t beneft. Our goal to chooe the coverage et of enor to maxmze the beneft n term of coverage and the redual energy,.e., the larget uncovered enng regon covered wth the leat enor havng maxmum redual energy. Conder the enor wth enng regon S. If S fully covered by the current E-node,.e., S j C S E S j, then enor end an I-AM-REDUNDANT meage and go to leep mode. Otherwe, t calculate and broadcat t beneft, whch : beneft(, t) = e (t) S S C E, (2) where S C E the total regon covered by the mandatory E-node neghbor of enor, and e (t) [, 1] the redual energy level. Node havng hgher redual energy, and maller covered area wll have a better chance of beng n coverage et wherea other wll be elmnated a redundant node. In th tep, mandatory node have already announced and each node aware of t beneft and t neghbor beneft. Then, node tart to broadcat I-AM-ESSENTIAL meage after a hort back-off tme, denoted by T back off, where < T back off CB MAX. CB MAX denote the maxmum back-off and determned baed on the average one-hop latency durng neghbor dcovery. We aume that enor have globally ynchronzed clock [12]. A enor determne t back-off tme baed on t beneft,.e., a node havng the maxmum beneft wll have the hortet back-off tme, thu announcng the I-AM-ESSENTIAL meage earler. When a enor receve I-AM-ESSENTIAL meage from t coverage neghbor, t hould update t beneft nce t covered regon, S S C E, mght ncreae by newly announced E-node neghbor. If S S C E S, enor reet t backoff tmer, end an I-AM-REDUNDANT meage and go to leep. Otherwe, the beneft wll decreae proportonal to the covered area whch may alo prolong the back-off tme. Coverage ter etablhed at the end of CB MAX. Next, we wll dcu how the domnatng coverage etablhed to preerve connectvty ung mnmum number of node. In harp contrat to earler tude [8], [17], we decompoe the coverage and connectvty feature of the WSN n th work. After etablhng the optmal coverage et, all E- node are not necearly be actve all the tme. Only a mall number of E-node can work a a backbone to forward the data traffc and delvery tak ent by the nk. To acheve th, we etablh a domnatng coverage et among coverage et where an E-node ether a domnatng node or a drect (one-hop) neghbor of a domnatng node. The domnatng node alway tay actve to preerve the connectvty of the network and forward the data traffc to/from the nk. E-node can communcate at leat wth one ED-node and end/receve ther meaurement/query va ther neghborng ED-node. B. Contructng Connected Domnatng Set Followng, we need to contruct a domnatng et among the node n the coverage et. We ue a greedy approach m-

5 lar to the centralzed algorthm,.e., enor are removed one by one a long a the remanng et connected. However, when uch a greedy approach run by enor, a dtrbuted algorthm, e.g., dtrbuted breadth-frt earch, neceary to enure that the remanng network connected n each teraton. In a large-cale enor network, dtrbuted breadthfrt earch may ncur hgh overhead due to t computatonal complexty,.e., O(Dlog 3 N), where D the dameter of the network [3]. Therefore, we propoe a dynamc domnatng et contructon approach trggered by the nk. Durng domnatng et contructon, enor broadcat three type of meage. JOIN-Backbone: It ndcate that there no domnator n the neghborhood, thu enor may become a domnatng node. CANDIDATE-Backbone: A enor broadcat th meage after recevng JOIN-Backbone. NOT-IN-Backbone: Th meage ent by enor whch are already connected to a domnatng node and they decde not to be domnatng node Fg. 3. Gven enor 1, 2, 3, 4, 5 C, where 1 receve Jon- BACKBONE meage and broadcat to t neghbor, thu become an EDnode. Our domnatng et contructon tart from the nk by endng a broadcat JOIN-Backbone meage. The dea that enor whch wll forward the meage, are ncluded to the connectvty et a a domnator. In the frt tep, JOIN- Backbone meage receved by the neghbor of the nk, whch are called canddate domnator. A canddate domnator, agan et a back-off tme [, DB MAX ] to forward the meage, where DB MAX denote the maxmum backoff whle etablhng connectvty-ter and determned baed average one-hop latency, and the node denty. Backoff tme wll be nverely proportonal to redual energy level and the degree of connectvty. In th context, degree of connectvty the number of neghbor whch have not ent a JOIN-Backbone or NOT-IN-Backbone meage. For example, enor ha 4 neghbor among whch two of them have ent a NOT-IN-Backbone meage, wherea the other neghbor ha ent a JOIN-Backbone meage. Th mple that two neghbor are connected to ED-node and one neghbor ha already become an ED-node. In th cae, degree of connectvty of 1 n calculatng t beneft. Smlar to the prevou tep, a node havng greater beneft ha horter back-off tme, thu forwardng JOIN-Backbone meage earler to be an ED-node. When a node receve a JOIN-Backbone meage, t () update t t connectvty decreaed; becaue one of t neghbor become a domnator; () et/update t CANDIDATE Backbone 1 2 CANDIDATE Backbone CANDIDATE BackboneCANDIDATE Backbone NOT IN Backbone NOT IN Backbone CANDIDATE Backbone Fg. 4. Sgnalng dagram howng the meage whle contructng domnatng coverage et for the example enor gven n Fg. 3. back-off tme baed on newly calculated beneft; and () broadcat a CANDIDATE-Backbone meage. By recevng CANDIDATE-Backbone meage durng the back-off tme, canddate domnator can be notced f ther neghbor are alo canddate. If all neghbor of a canddate node ether domnator or canddate domnator, t can afely gve up of beng domnator, nce all t neghbor are already receved a CANDIDATE-Backbone meage. In th cae, a enor node end a NOT-IN-Backbone meage ndcatng that t wll not be an element of domnatng coverage. At the end of a back-off perod, a canddate whch ha not been elf-removed, forward JOIN-Backbone meage and become an ED-node. Followng the forwarded JOIN-Backbone meage, new canddate appear and end CANDIDATE-Backbone meage. Th proce contnue untl all node have receved at leat one JOIN-Backbone meage. Note that, a enor update t beneft after recevng JOIN-Backbone or NOT-IN-Backbone meage. The energy conumpton of ED-node may be hgher than the E-node; and R-node may have the lowet energy conumpton due to contnuou leep. Thu, to acqure a far energy conumpton among enor, coverage and connectvty et hould be updated throughout the lfetme of the network. In th paper, we make ue of global update where all E- node and ED-node are re-elected ndependent from the current et. In partcular, global update the proce of repeatng algorthm wth latet redual energy level of enor. By th way, enor that have overlappng regon and were E-Node n the prevou round mght be R-node n the next update becaue more energy ha been conumed when they were E-node before. V. PERFORMANCE EVALUATION The performance of our approach evaluated ung mulaton that are performed n an 25 m x 25 m area contng of dfferent number of enor dtrbuted randomly. In the bac cenaro, 1 fxed enor node havng tranmon range of 1 m and enng range vary from 15 m to 4 m are ued. We ue the rado power conumpton parameter n [1]. The energy conumpton of turnng the rado on/off neglgble. The buffer ze of enor node choen a 5 and the packet length 1 byte. In the frt experment we nvetgate the performance of our coverage calculaton under three metrc: the total number 4

6 Sze of coverage and domnatng et E node ED node Poble redundant node Number of Node Number of redundant and E node N=2 redundant node N=2 E node N=1 redundany node N=1 E node Average enng range (m) Network Lfetme (ec) actve coverage et actve allnode N = 1 N = 3 N = 5 Node Denty (a) (b) (c) Fg. 5. Performance of the redundant dcovery and elmnaton algorthm. of locally detected redundant enor, the total number of node for coverage (E-node), and the total number of node to preerve connectvty (ED-node). To cover a 25 m x 25 m area wth enng range of 3 m on average, we ue random placement of 1 to 3 node. From Fg. 5 (a), we can oberve that among thee fve cenaro, the network havng 3 node ha the hghet number of locally detected redundant node, wherea the number of E-node and E-node do not gnfcantly change wth node denty. A hown n Fg. 5 (a), even n the low denty, E-node rato above 5%, whch how that only 5% of the node are necearly be actve when the propoed method ued. Moreover, we evaluate the number of redundant and E-node of hgher enng range. When the rato of enng range ncreaed, the number of redundant node ncreaed up to 7% where the number of E-node and ED-node reman the ame. Fgure 5 (b) how the number of node n a low dene network (N=1) and hgher denty wth N=2. Fnally, we evaluate the poble energy avng when the coverage et ued, where R-node are cheduled to leep to ave energy and only E-node and ED-node are actve. In Fg. 5 (c), we demontrate the network lfetme compared to the cheme when all node are actve. We conder a WSN a alve when the enng feld fully covered. In other word, a network alve when every pont n A covered by at leat one enor. Accordng to th, we oberve that network lfetme prolonged gnfcantly when R-node are cheduled to leep whle preervng coverage and connectvty, epecally n hgh denty network. Even n low denty network wth 1 node, network lfetme prolonged up to 28% whch how the effectve energy avng of ung coverage and domnatng coverage et. VI. CONCLUSIONS In th paper, we focu on the problem of fndng an optmal coverage and domnatng coverage et that can be ued for energy-effcent communcaton n large cale enor network. We preent a dtrbuted algorthm that effectvely elmnate redundant node wth guaranteed connectvty for heterogeneou enor havng dfferent enng range. Further, an extenon cheme preented that fnd the mnmum number of domnatng enor among the coverage et whch can alo be ued n effectve node chedulng and topology control. REFERENCES [1] Z. Abram, A. Goel, and S. Plotkn. Set K-Cover Algorthm for Energy Effcent Montorng n Wrele Senor Network. In Proc. of Int. Conference on Informaton Proceng n Senor Network, Berkeley, Calforna, USA, Aprl 24. [2] D. Arganbrght. Practcal Handbook of Spreadheet Curve and Geometrc Contructon/Book and Dk. CRC Pre, [3] S. Butenko, X. Cheng, C. 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