Hole Detection for Increasing Coverage in Wireless Sensor Network Using Triangular Structure
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1 IJCSI International Journal of Computer Science Iue, Vol. 9, Iue, No, January 0 ISSN (Online): Hole Detection for Increaing Coverage in Wirele Senor Network Uing Triangular Structure Saram Babaie an Seye Saja Pirae Department of Computer engineering, Tabriz-Branc, Ilamic Aza Univerity, Tabriz, Iran Department of Computer engineering, Tabriz-Branc, Ilamic Aza Univerity, Tabriz, Iran Abtract Te emerging tecnology of wirele enor network (WSN) i expecte to provie a broa range of application, uc a battlefiel urveillance, environmental monitoring, mart pace an o on. Te coverage problem i a funamental iue in WSN, wic mainly concern wit a funamental quetion: How well a enor fiel i oberve by te eploye enor? Mobility i exploite to improve area coverage in a kin of ybri enor network. Te main objective for uing mobile enor noe i to eal coverage ole after te initial network eployment, wen eigning a ole ealing algoritm, te following iue nee to be aree. Firt, ow to ecie te exitence of a coverage ole an ow to etimate te ize of a ole. Secon, wat are te bet target location to relocate mobile noe to repair coverage ole? We ue te triangular oriente iagram (HSTT) for aim to goal were it imple,ave low calculation among contruction an it i great to calculate te ize of ole exactly. Keywor: Wirele Senor network; Area Coverage; ole etection; ize calculation; target location; Coverage.. Introuction ecent avance in micro-electro-mecanical ytem, embee proceor, an wirele communication ave le to te emergence of Wirele enor network (WSN), wic conit of a large number of ening evice eac capable of ening, proceing an tranmitting environmental information. Application of WSN inclue battlefiel urveillance, environmental monitoring, biological etection, mart pace, inutrial iagnotic, an o on []. A funamental iue in WSN i te coverage problem [, 3]. Te coverage problem i eavily epenent on te coverage moel of iniviual enor an te location of te eploye enor noe. Senor coverage moel can be coniere a a meaure of te quality of ervice of enor ening function an i ubject to a wie range of interpretation ue to a large variety of enor an application. In te literature, a wiely ue enor coverage moel i te ening ik moel were a enor can cover a ik centere at itelf wit a raiu equal to a fixe ening range. Network ening coverage on te oter an can be coniere a a collective meaure of te quality of ervice provie by enor noe at ifferent geograpical location. In many cae, we may interpret te coverage concept a a non-negative mapping between te pace point (of a enor fiel) an te enor noe (of a eploye enor network). For example, given te ening ik moel, te area (pace point) covere by a et of enor i te union of teir ening ik. Wirele enor can be eiter eterminitic place or ranomly eploye in a enor fiel. Determinitic enor placement can be applie to a mall to meium enor network in a frien environment. Wen te network ize i large or te enor fiel i remote an otile, ranom enor eployment migt be te only coice, e.g., cattere from an aircraft. It a been own tat a critical enor enity exit beyon wic a enor fiel can be completely covere almot urely in every ranom eployment [4, 5]. To guarantee complete coverage in one ranom eployment, it i often aume tat te number of cattere enor i more tan tat require by te critical enor enity. However, ti normally require a great number of enor noe to be eploye anoter way to improve network coverage i to leverage mobile enor noe. Mobile enor noe are equippe wit locomotive platform an can move aroun after initial eployment, for example, te mobile enor noe obomote [6] an imoue [7]. Altoug in general a mobile enor noe i more expenive tan it tationary compeer, it can erve muc functionality uc a a ata relay or collector, an can greatly improve many network performance uc a enancing timeline of ata report. In ti article, our focu i to ealing coverage ole uing genetic algoritm wit minimize total movement of mobile enor.. ELATED WOK Bang Wang, Hock Beng Lim, Di Ma wit article [] propoe: Copyrigt (c) 0 International Journal of Computer Science Iue. All igt eerve.
2 IJCSI International Journal of Computer Science Iue, Vol. 9, Iue, No, January 0 ISSN (Online): Hole etection an ole ize etimation Voronoi iagram can be ue to etect a coverage ole an calculate te ize of a coverage ole [8, 9]. A Voronoi iagram for N enor,,, N in a plane i efine a te ubiviion of te plane into N cell eac for one enor, uc tat te itance between any point in a cell an te enor of te cell i cloer tan tat itance between ti point an any oter enor. Two Voronoi cell meet along a Voronoi ege an a enor i a Voronoi neigbor of anoter enor if tey are a Voronoi ege. We refer te reaer to [0] for more icuion on Voronoi iagram an it application. A Voronoi iagram i firt contructe for all tationary enor noe, auming tat eac noe know it own an it neigbor coorinate. Wang et al. [9] propoe a localize contruction algoritm to contruct a local Voronoi iagram: Eac noe contruct it own Voronoi cell by only coniering it -op neigbor. After te local Voronoi iagram contruction, te enor fiel i ivie into ub region of Voronoi cell an eac tationary noe i witin a Voronoi cell. A noe i a Voronoi neigbor of anoter one if tey are a Voronoi ege. Fig. illutrate a Voronoi iagram in a boune enor fiel, were te bounarie of te enor fiel alo contribute to a Voronoi cell. Accoring to te property of a Voronoi iagram, all te point witin a Voronoi cell are cloet to only one noe tat lie witin ti cell. Terefore, if ome point of a Voronoi cell are not covere by it generating noe, tee point will not be covere by any oter enor an contribute to coverage ole. If a enor cover all of it Voronoi cell vertice, ten tere are no uncovere point witin it Voronoi cell; oterwie, uncovere point exit witin it Voronoi cell. coverage ole witin te Voronoi cell i larger tan a treol. Wang et al. [3] convert te enor movement problem into a maximum weigt maximum-matcing problem to ecie wic mobile noe oul move to wic target location. 3. OU WOK We aume tere i an environment like fig. Tat fill wit tationary enor at te firt fore implement. In our iagram (HSTT) we connect te center of enor ening to gater wit conition of mae a triangular every tree ajacent enor. Our iagram can be ue to etect a coverage ole an calculate te ize of a coverage ole Fig. Initial eployment. Fig. Illutration of uing Voronoi iagram to etect a coverage ole an ecie te ole ize.. Detination election After eciing te exitence of a coverage ole an it ize, a tationary noe nee to ecie te number of mobile noe an te target location of tee mobile noe to eal it ole. Go [8] propoe tat for eac Voronoi vertex, one mobile noe oul be ue to eal te coverage ole aroun ti Voronoi vertex, if te ize of it Fig.3 Contraction te triangular oreinte tructure. Copyrigt (c) 0 International Journal of Computer Science Iue. All igt eerve.
3 IJCSI International Journal of Computer Science Iue, Vol. 9, Iue, No, January 0 ISSN (Online): = ( a)( b)( c) () (a) (b) Were a b c i te emi perimeter. (c) () Fig.5 Interection between two circle (e) (f) Let two circle of raii an r an centere at (0,0) an (,0) interect in a region ape like an aymmetric len. Te equation of te two circle are x y () ( x ) y r (3) Combining () an () give (g) () ( x ) ) ( x r (4) Multiplying troug an rearranging give x x x r (5) Solving for x reult in Fig.4 Te total poible ate wit tree enor. elation to area of te triangle. Let A be te triangle area an let a, b an c, be te lengt of it ie. By Heron formula, te area of te triangle i area A 4 ( a b c )( (i) a b c )( b c a )( c a b ) x r (6) Te cor connecting te cup of te len terefore a alf-lengt y given by plugging x back in to obtain y x r ( ) 4 ( r ) (7) Solving for y an plugging back in to give te entire cor lengt a= ten give Copyrigt (c) 0 International Journal of Computer Science Iue. All igt eerve.
4 IJCSI International Journal of Computer Science Iue, Vol. 9, Iue, No, January 0 ISSN (Online): a 4 ( r ) (8) ( r )( r )( r )( r ) Ti ame formulation applie irectly to te perepere interection problem To fin te area of te aymmetric "len" in wic te circle interect, imply ue te formula for te circular egment of raiu an triangular eigt A(, ) co ( ) twice, one for eac alf of te "len." Noting tat te eigt of te two egment triangle are x x Te reult i r r A A, ) A( r ) () (, r r r co ( ) co ( ) r ( r )( r )( r )( r ) Now we calculate te area fig 3. (9) (0) () (4) ( a b c)( a b c)( b c a)( c a b) 3.b If a=b=c= Te area of ole calculate like ection 3.a. 3.c If a=b or a=c or b=c Te area of ole calculate like ection 3.a. 3. ( 3) int er ect Accoring to equation an By aume r= we ave (5) int er ec t 3.e co ( ) co ( ) ( 3) int er ect int er ect co ( ) int er ec t co ( ) int er ec t ( ) ( ) ( ) ( ) ( ) ( ) (6) 3.a If a, b, c> ( ) 3 We know te total angular of triangular i: ˆ ˆ ˆ 80 So ( 3) (3) Accoring to equation we ave 3.f It i obviouly tat tere i not ole. 3.g It calculate like.. 3. It calculate like.a 3.i In ti tate we ave tree interection region o we ave (7) Copyrigt (c) 0 International Journal of Computer Science Iue. All igt eerve.
5 IJCSI International Journal of Computer Science Iue, Vol. 9, Iue, No, January 0 ISSN (Online): ( int er ect3 ) 3 int er ect int er ect co ( ) ( ) ( ) int er ec t incenter i te point of concurrence of te triangle angle biector. In aition, te point M A, M B an M C of interection of te incircle wit te ie of ABC are te polygon vertice of te peal triangle taking te incenter a te peal point (c.f. tangential triangle). Ti triangle i calle te contact triangle. It ow in fig 7. int er ec t co ( ) ( ) ( ) 3 co ( ) int er ec t3 3 ( ) ( ) In all of tate if 0 ten we conclue we ave a ole. 4. Detination election In our propoe iagram (HSTT) After eciing te exitence of a coverage ole an it ize, a tationary noe nee to ecie te number of mobile noe an te target location of tee mobile noe to eal it ole.we want to aim maximum coverage o after calculate te area of ole we coice one of te circumcircle or incircle type. If te area i le tan mobile enor ening region we ue te circumcircle center for target location, if area of ole i larger tan enor ening reign we ue te incircle center for target location to aim maximum coverage. Te circumcenter of a triangle can be foun a te interection of te tree perpenicular biector. (A perpenicular biector i a line tat form a rigt angle wit one of te triangle ie an interect tat ie at it mipoint.) Ti i becaue te circumcenter i equiitant from any pair of te triangle point, an all point on te perpenicular biector are equiitant from toe point of te triangle. It ow in Fig 6. Fig.6 Contruction of te circumcircle (re) an te circumcenter (re ot). Te incircle i te incribe circle of a triangle ABC i.e., te unique circle tat i tangent to eac of te triangle tree ie. Te center of te incircle i calle te incenter, an te raiu of te circle i calle te in raiu. Te Fig.7 Contruction of te incircle. 5. Concluion In ti paper, we propoe a triangular oriente iagram (HSTT) tat etect of ole an calculate it ize. Alo for maximum coverage we etermine te target localization for mobile enor for ealing of coverage ole. All of tem caue to along wirele network life time an optimization. In propoe iagram we ue circumcircle an incircle to aim ti goal. Our iagram compare wit Voronoi iagram ave ome avantage uc a. It i imple for contruction.. It a lower tan Voronoi iagram calculation for contruction. 3. We get exact area of ole no etimation of it. 6. Future Work We can emerge ome ajacent triangular in our propoe iagram for ue te low number of mobile enor to ealing coverage ole. Alo we can ue te ierarcical meto accoring to ize of ole to get maximum coverage by minimum mobile enor. at te future we work to aim ti goal. eference [] I. Akyiliz, W. Su, Y. Sankaraubramaniam, E. Cayirci, Wirele enor network: a urvey, Computer Network 39 (4) (00) [] C.-F. Huang, Y.-C. Teng, A urvey of olution to te coverage problem in wirele enor network, Journal of Internet Tecnology 6 () (005) 8. [3] M. Carei, J. Wu, Energy-efficient coverage problem in wirele a oc enor network, Computer Communication 9 (4) (006) [4] H. Zang, J. Hou, On eriving te upper boun of a- lifetime for large enor network, in: ACM International Sympoium on Mobile A Hoc Networking an Computing (MobiHoc), 004, pp. 3. Copyrigt (c) 0 International Journal of Computer Science Iue. All igt eerve.
6 IJCSI International Journal of Computer Science Iue, Vol. 9, Iue, No, January 0 ISSN (Online): [5] S. Kumar, T.H. Lai, J. Balog, On k-coverage in a motly leeping enor etwork, in: ACM International Conference on Mobile Computing an etworking (Mobicom), 004, pp [6] G.T. Sibley, M.H. aimi, G.S. Sukatme, obomote: a tiny mobile robot latform for large-cale a-oc enor network, in: IEEE International onference on obotic an Automation, 00, pp [7] Y.-C. Teng, Y.-C. Wang, K.-Y. Ceng, Y.-Y. Hie, imoue: an integrate mobile. [8] A. Go, Etimating coverage ole an enancing coverage in mixe enor etwork, in: IEEE International Conference on Local Computer Network, 004, pp [9] G. Wang, G. Cao, P. Berman, T.F.L. Porta, Biing protocol for eploying mobile enor, IEEE Tranaction on Mobile Computing 6 (5) (007) [0] F. Aurenammer, Voronoi iagram, a urvey of a funamental geometric ata tructure, ACM Computing Survey 3 (4) (99) [] G. Wang, G. Cao, T. LaPorta, Proxy-bae enor eployment for mobile enor network, in: IEEE International Conference on Mobile A-oc an Senor Sytem (MASS), 004, pp [] Bang Wang, Hock Beng Lim, Di Ma, "A urvey of movement trategie for improving network coverage in wirele enor network", Computer Communication 3 (009) , Elevier. Copyrigt (c) 0 International Journal of Computer Science Iue. All igt eerve.
![bley, M.H. aimi, G.S. Sukatme, obomote: a tiny mobile robot latform for large-cale a-oc enor network, in: IEEE International onference on obotic an Automation, 00, pp. 43 48. [7] Y.-C. Teng, Y.-C. Wang, K.](/docs-images/44/15281442/images/page_6.jpg "-Y. Ceng, Y.-Y. Hie, imoue: an integrate mobile. [8] A. Go, Etimating coverage ole an enancing coverage in mixe enor etwork, in: IEEE International Conference on Local Computer Network, 004, pp.")
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