A Data Aggregation Algorithm Based on Splay Tree for Wireless Sensor Networks

Transcription

1 49 JOURNAL OF COMPUERS, VOL. 5, NO. 4, APRIL 010 A Dt Aggregton Algorthm Bsed on Sply ree for Wreless Sensor Networks ZHANG Shu-Ku * 1,, CUI Zh-Mng 1,,GONG Sheng-Rong 1, LIU Qun 1,FAN Jn-X 1 1 School of Computer Scence nd echnology, Soochow Unversty, Suzhou, Chn,15006 JngSu Provnce Support Softwre Engneerng R&D Center for Modern Informton echnology Applcton n Enterprse, Suzhou, Chn, Eml: {zhngsk, szzmcu, shrgong, luqun, jxfn }@sud.edu.cn Abstrct-Detectng the regon of emergent events s n mportnt pplcton of wreless sensor networks (WSN). One of the key chllenges n detectng event n WSN s how to detect t ccurtely whle trnsmttng mnmum nformton to provde suffcent detls bout the event. In ths pper, n ggregton lgorthm bsed on sply tree s proposed to cheve the followng gols: montorng dt of ny porton of the regon cn be obtned t one tme by queryng the root nsted of floodng those regons, thus ncurrng sgnfcnt energy svngs. he performnce nd cost of the lgorthm re nlyzed nd evluted. he results show the proposed lgorthm s effcent nd effectve n delng wth dt ggregton. Keywords: Wreless sensor network, sply ree, dt ggregton, polynoml regresson. I. INRODUCION Dt ggregton s common operton n sensor networks. rdtonlly, nformton smpled t the sensor nodes needs to be conveyed to centrl bse stton for further processng, nlyss, nd vsulzton by the network users. Dt ggregton n ths context cn refer to the computton of sttstcl mens nd moments, s well s other cumultve qunttes tht summrze the dt obtned by the network. Such ccumulton s mportnt for dt nlyss nd for obtnng deeper understndng of the sgnl lndscpes observed by the network. he exstng reserches hve nlyzed the ggregton lgorthm for the pplcton of the sensor network [1],[],[3].kng the memory ccess of ggregton lgorthm nd other fctors nto ccount, n optmzed ggregton lgorthm [4] ws proposed, but there s no consderton of dt multple-hop trnsmsson. Dt compresson lgorthms bsed on wvelet trnsformng for sensor networks were proposed n Lterture [5]. It cn reduce the energy cost of nodes n dt trnsferrng effcently for sensor networks, so, t cn prolong the lfetme of the whole networks to greter degree. But t hd not consdered the lgorthm processng energy consumpton nd mult-hop pth. Ltertures [6], [7] consder the energy optmzton seprtely from the ngle of the pth trnsmsson qulty nd the pth energy consumpton to extend the lfetme, but they hve not consdered the dt ggregton. * Correspondng uthor: S.-K Zhng, el.: , E-ml ddress:zhngsk@sud.edu.cn, Postl ddress: No 1 Shzh Street Suzhou Chn Anlyss of dt ggregton lgorthm ndctes tht [1] seekng for the optml ggregton tree on the condton of complete ggregton equtes to solvng NP-Complete problem of the mnmum Stener tree. Accordng to ths NP-Complete problem, lterture [8] hs consdered the blnce of the computton processng energy consumpton nd the trnsmsson energy consumpton, nd the cse wthout complete ggregton, but t does not nvolve the overll mult-hop energy consumpton nd by ths constructng ggregton tree. Moreover, consderng the computton of mesure ws done by the snk node. Lterture [9] proposed the shortest pth tree lgorthm, nd n ths lgorthm ech source node trnsmts dt long the shortest pth to the gtherng node. If these pths overlp wth ech other, nd crry on dt ggregton lterntely n the overlp secton, ths lgorthm s less complex nd wth less dely of network tme. But ts energy svng effect ws gretly ffected by the network topology nd cnnot wn gret stsfcton n most cses. hrough constructng the coverge lke the Vorono, nd choosng the pproprte quntty nd the poston to optmze the dt ggregton, t my reduce the dt quntty trnsmttng to the Snk node [10],[11],[1]. Lterture [10] proposed the lgorthm of the greedy ggregton tree. Its shortest pth ws constructed between the frst source node the Snk node rrves nd the nerest source node of the tree fterwrd. However, usng ths method, Snk cn not lern the sensed vlue but through hgh cost floodng n the gven scope, nd once the grdent vector ws estblshed, t wll not chnge n the mplementton. In LEACH [1], node set ws chosen ccordng to clusters, whch clusters ech node wll jon to rely on the node nd the clusters communcton cost. However, s only very few nodes ct s the role of clusters, from whch the pproprte Snk node s fr wy, clusters wll consume excessve energes s result of the trnsmsson dt to the bse stton. In lterture [11], boundry node possbly belongs to more thn one vorono unt; n ths cse, f Snk sends out the relted dt nqury n the nterest regon, f necessry, ths boundry node must route enqury request, whch wll form the bottleneck. he dstrbutonl nucleus regresson [13] shre smlr spects wth ths pper s lgorthm, but there re gret dfferences. As for the former, every node hs ts pproxmte coeffcent n ts locl regon scope, thus t cnnot reply to the nqury correctly whch nvolves outsde ts locl regon. But n the lgorthm of ths pper, do: /jcp

2 JOURNAL OF COMPUERS, VOL. 5, NO. 4, APRIL the coeffcent s trnsmtted upwrd fter the chld node s compressed nd ggregted. herefore, the root node of sply tree obtns the fnl dt set of pproxmte coeffcent bout ts entre covered regon. Now, Snk obtns montor vlue of ny nterested regon poston through the drect nqury to the root node, nd ech node sends nformton contnng vector, whch s used to descrbe the coverge of ts locl re; the sze of ths vector ncreses wth mssve neghbor nodes whch shre the nucler vrble long wth t. However, n ths pper, n vew of dt ggregton lgorthm of event trggerng drvng bsed on sply tree, the quntty of the dt pcket whch trnsmts through ech node s constnt, nd the demnd bout the node functon s smple. It works only f we gurntee tht the node cn correspond wth the constnt power n smll scope, nd t hs certn memory functon. here s no need to dd the specl functon node n the sensor network. II. NEWORK MODEL In ths pper, suppose N sttc sensor nodes wth resources lmted rndomly re deployed n montorng re R = ( r r), denoted by set S=(s 1, s,, s N ), where s represents the frst sensor node, s llustrted n Fg. 1. Ech node hs ts locton nformton through trngulton [14], nd the locton of the sensor, s s represented by (x, y ), nd ech node hs ts unque ID, the sme cpcty of clculton communcton nd energy resources. he node cheves the loose tme synchronsm through me Synchronzton Servce [15], the communcton ccess reduces the chnnel conflct v CSMA/CA. he gol of ths pper s to construct the Aggregton ree (A) n ths N nodes network, where A s conssted of Nt nodes clled ree Node, whch s used to receve nd ggregte dt, the other (N - N t ) nodes re referred to s non-tree (N) nodes. Ech N node senses ts envronmentl prmeter(s) nd reports t to ts nerest tree node. he A s well spred over the entre WSN so tht N t tree nodes re unformly dstrbuted n the network. In ths wy, t ensures tht the ttrbute redngs sent by N nodes to the correspondng tree node ncur smller hop count, nd thereby prolongs the overll lfetme of the N nodes. For smplcty, we use P event (denoted by the dshed rectngle n Fg.1) to represent n event nd the event regon s denoted by the re, R event where R event R.he norml phenomenon s ssumed to hve lredy been sensed n the network by the entre A. R s defned s the porton of R not occuped by ny event, R = R - R event.. Fg. 1 Network model III. GENERAION OF AGGREGAION REE he lgorthm proposed n ths pper s tht deployng Decde_Root lgorthm frst to determne some nodes s tree root, then cllng A_FORM lgorthm to form the sply tree bsed on the sensor node. Once node receves the nformton of ts chld nodes, t wll trnsmt n ggregton pckge. he root node only trnsmts the fnl nformton ncludng the sensed ttrbute. In the followng prt we wll gve concrete descrpton of the lgorthm. A. Choose of Root Node Generlly spekng, the occurrence of some events s thought to be the unusul chnge of the envronment condton (e.g. temperture, humdty, pressure nd so on), whch possbly ppers n mny wys, such s unusul chnge of sudden sensed prmeter or contnul chnges wth the tme pssng by. At the sme tme, mny event ttrbutes hve the chrcterstc of tme-spce correlton nd contnuous grdul vrton n the two-dmensonl Euclden spce [1]. Wth the lpse of tme, f the sensor s redng mntns stedy, we wll suppose tht these ttrbutes re the tme-spce correlton to the sensor montor, nd these sensors hve close relton wth redngs of other sensors locted n the sme regon. Obvously, the occurrence of some event cn trgger prtl nodes n the WSN. It mght be only one nmed the solted spot or mny, mong whch spot closest relted wth ths event from those trggered nodes s nmed the event spot, nd whch be tken s the root to construct ggregton tree expndng to the entre regon. Algorthm Decde_Root s to fnd the event spot C to hve the regon event selected, nd to tke t s root node to construct ggregton tree. Let trggered nodes set conssted of pex set V (G) of dgrm G, one-hop neghbor set of the node v s N v.dhops neghbor set s N.ree generted by N nodes of d v connected grph G need N-1 sdes [4]. It s not dffcult to see tht the tme spent on the ggregton s closely relted to the dstnce from the Snk node to the frthest node. When the regon of the event s lrger, t wll possbly cuse bgger tme dely. Let MVV() = mx{ d(, j )} denoted the mxmum dstnce from to j ny node. If pex x of grph G, stsfed MVV(x) ={mn{ d (, j )}, x s the event spot,.e. the event spot s the nerest pex dstnt from the mxmum pex [4]. After node s s trggered, t brodcsts ts own d mmedtely. Node s j whch hs not been trggered receves d from node s, nd dscrds t. rggered node s k receves d from node s, nd reds t n the buffer, menwhle renews to hop number of node s. If node s hs not receved ny node ID sendng out ID brodcst n g seconds, then node s s the solted node, nd the dt trnsmsson strts. Otherwse, when the buffer content of trggered node s non-null, brodcst ts buffer content, when node s receves brodcst buffer, dd one to hop number wth the Dfferent cluse d correspondence; f s buffer doesn t hve ths cluse d, dd one to hop number

3 494 JOURNAL OF COMPUERS, VOL. 5, NO. 4, APRIL 010 of ths cluse nd red nto t the buffer; f the buffer hs ths cluse d, nd hops vlue of ths cluse whch dd one s bgger thn or s equl to hops vlue of the orgnl cluse n the brodcst nformton, then do not renew ths cluse; otherwse renew ths cluse by ddng one to hops vlue of ths cluse n the brodcst nformton. Untl no more renewls of ny node buffer,then ths node stted tht t s the event spot, nd brodcsts the stop pckge, whose content ncludes tme lbel, node d, wtng tme threshold wc nd declne prmeters of threshold tme nd so on. Seekng for event pont lgorthm Decde_Root: 1 At the orgnl stte the node buffer s null, node d cn be dstngushed n the locl rnge; Whle ( node s be trggered s.tme<meout) { 3 s brodcstngidbr (); 4 f (node s j be trggered nd recevngidbr () { 3. wrte ID to buffer nd [hop]=1; // trggered node s j receves IDbr of node s, reds d n the buffer, hops number from s j to s s 1 4. If ( node s j not be trggered nd recevng IDbr ) { 5. dump IDbr ; // dscrd receved IDbr 6. } 7. If (s.tme>= meout) { 8. s s solted pont ; // s s solted pont 9. dt trnsmtted; 10. ext(); 11. } 1. Whle(node s be trggered nd not buffer empty) { 13. s. brodcstng BUbr (); // 14. If (s.recevng BUbr() nd (!s.hs(bubr)) { 15. s.dd(); // hops number of ths cluse dds 1 n the Brodcst nformton 16. } 17. Else f(s.dfferent()) { 18. updt s ; // Renew ths node buffer 19. s. brodcstng BUbr(); 0. } Else not updt; // Does not renew ths node buffer 1. }. End Whle 3. s.sy(); // s declres tht t s the event spot; 4. } 5. End Whle 6. s.brodcstng SOP();//brodcst the stop pckge, ncludng tme lbel, node d, wtng tme threshold wc nd threshold tme declne prmeters nd so on. After the lgorthm executon fnshes, the event spot C of the regon event wll be found. Before the node brodcsts the buffer content ech tme, t needs very lttle tme dely. Its purpose s to keep enough tme for the node to receve the stop pckge, nd to vod the phenomenon tht mny nodes successvely stte for n event spot. Suppose tht there re N nodes n grph G, the number of hops from event spot to the frthest pex s h. In grph G ll nodes fnshng brodcst one tme s clled one round. hrough brodcstng buffer nformton, hops number of the frthest neghbor tht ll nodes cn sense dds one t ech round process. At the h th round, t lest one node hs lredy ntegrted ll nodes to ts own sensed re n grph G, nd not renew neghbor scope of these spots t the (h+1)th round ny longer, by ths stge lgorthm termntes. herefore, the number of sendng probe pckets Probe ltogether s: [NUM] cen =N(h+1) (1) B. Constructon of ree In order to gurntee tht A dffuse to the entre network, the sensor node trnsmts the sensed vlue to the correspondng tree node by smll hops, holdng the topologcl stblty of dsperson node s fr s possble, to mntn the orgnl good sensed coverge re, we ntroduce the grph Vorono s well s the Deluny trngle network relted to descrbe the sensor network topology, nd bsed on the defnton of Deluny trngle, sply tree s constructed n Wreless Sensor Networks by tkng the centrl node s the root. he sply tree s one knd of bnry tree, nd ts superorty les n tht t does not need to record the redundnt nformton used n the blnced tree. Let e s spot of plne, then n ' ' ' VR( e) = { p R d( p, e) d( p, e ), e e, e E} () s clled the polygon Vorono. hen grph Vorono s defned s VD( E) = VR( e ) (3).e. set of ll polygons Vorono n plne, but the trngulr Deluny network s formed by the polygon orgnc center for connectng ll neghborng V-. he trngulr net Deluny hs mny mportnt propertes [14], t cn obtn the neghborng nodes nformton through the Deluny expresson, Furthermore, nd t cn be used n serchng for the closest node. Bsed on Deluny descrpton n the sensor network, we cn construct the sply tree tkng the node whch s defnte by the Decde_Root s the root. Let the trget sector s A, senston node collecton n the regon s S = { s ( x, y ) s A} (4) Where, (x,y ) s the poston coordnte of the known node s. In ddton, let the weghted grph correspondent by the node collecton S network s G n the regon, dstnce of neghbor nodes s the weght of ech sde correspondng. And Let externl memory of the sensed regon s n ponts set K={k (x,y ) k A}, then tke node s n the trget sector s the center regrdng the set of ponts K node extenson tree s defnte s, hs ( s > K ) = pth( s k ), k K > (5) Where, p th ( s > k ) s the gretest spn pth from node s to node k n grph G, ts length s l [15]. In ths pth, the mnmum dstnce between ech node s bgger or equl to the mnmum dstnce n ny other pth from s to k nd the node number s the smllest n grph G. he gretest spn pth hd reflected n extenson crcut between two nodes. Wht needs to be ponted out here s tht n specfc undrected grph G, the gretest spn pth between two spots s not unque, possbly hs multstrps. But for the dfferent extrterrtorl node set, the sply tree of tkng the root node s the center correspondng s lso not unque. Let the depth of the tree be p, nd the tree node sves the ttrbute of the sme type. Such tree ws consdered blnced, whch reduced dt loss nd ncresed ccurcy of dt ggregton [15]. Algorthm Form_A constructs sply tree wth gven depth nd ech root node constructs

4 JOURNAL OF COMPUERS, VOL. 5, NO. 4, APRIL sply tree of ggregton nodes by runnng ths lgorthm. When node chooses ts two chldren, t wll choose the two bggest spn nodes, ensurng tht the tree covers more sensed regons s fr s possble when dffuson. In the process of the multple regressons, t cn cheve the hgh ccurcy, nd my reduce the redundncy of the dssemnton montor vlue. After the sply tree s formed, n ech sub-domns ll surplus nodes send dt to the nerest tree-node wy from themselves. In ths pper, construct tree through three knds of nformton: Becon, Probe nd JOIN. Fg. descrbed the process bout the exchnge of dfferent sgnls to construct the query tree. sector's re s regon: Recevng NM u Hop+1< Hop u,v π r, the number of nodes n the Intlzton u dded N v d ; Intlzton tmer; Hop++; Hop v,v = Hop; f Hop<d,brodcst NM u ; lsten wt; Recevng one or mny nform messge, NM u= =Mn(Hop) mer out Ext Fg.3.he processng procedure of Becon on v (1) Becon Messge In the dscovery process of d-hop neghbors, ech node u brodcsts Becon news NM u = {ADV_dscovery,u,Hop} n d-hop scopes, where, Messge s the type of nformton, hop felds s the count of the nformton hop, whose ntl s 0, nd u s the node ID. he v-node whch receved NM u dds u to ts own d-hop neghbor lst N d v. For receved one or more redundnt NM u, v chooses Hop vlue of the mnmum NM u, ts Hop feld plus 1 nd updte Hop u,v =Hop, f Hop <d contnues to brodcst to the neghbors, nd then v enters wtng stte. When V n the wtng stte,lstenng to the Hop+1<Hop u,v, the NM u of v,then record the nformton nd Hop feld dds 1, repet the process; otherwse v does not mke ny ctons untl the tmer tme-out. Here the tmer Length cn be set s long s the network ntlzton phse. From dfferent nodes of the Becon, the recevng node v runs the sme process. Fg. 3 s the utomton representton of Becon messge process. hrough the Becon news brodcstng ech node v cn obtn node set n the d-hop scope, d N = { u Hop d} Hop u,v denotes the pproxmte v Fg. Exchnge of sgnls to construct the ggregton tree. u, v most short-pth hops between the node v nd u whch obtns by renewng the brodcst retrnsmt process wth hops. Snce the sttc deployment of sensor networks, for ech node u, d N s stble. hs u d N s set of u ll possble tree node members. n the lyer J, ech node brodcsts Becon pckge to ll ts neghbors of the next hop, thus, the nodes of level j+1 receve mny Becon pckges from level j, nd stochstclly selects node wth probblty vlue p' > p ' 's ther fther node, nd trnsmts Probe pckge to t. We cn see from Fg., node d receves Becon from A nd B, p ( nput of ths lgorthm) s optmzed by the followng method. Set tht the fther node brodcsts ts Becon news wth correspond rdus r to fn-shped regons wth the center of crcle ngle 10 0 C, nd ths 10 n π r p r = (6) 360 Followng the bnoml dstrbuton, to choose the regon probblty p'' for the two nodes s ther fther nodes. p n n r r '' = C 0.5 (1 105) If nodes receve number of Becons from the expected fther node, then ther IDs wll be kept by the prent node of the new choce, n order to resume quckly when the node fls. (). Probe Messge he Selected fther node wts to receve Probe the pckge from ts chld node, fterwrd, decdes whch two to tke s ts chld nodes. Once t receves messge of ll the nodes n ts next-hop j +1, t wll choose two frthest nodes wy from t s ts chldren. hose nodes tht hve not been chosen by ny fther node wll no longer choose to become member of the A nd trnsform nto the offcl sensor nodes, n ths wy, the sze of the tree (becuse the cost of the sensor communctons s fr greter thn of the cost of storge) cn be reduced pproprtely. As cn be seen from fg., node d chooses B s ts prent node, to whch t sends pcket probe, then, the node A sends becon to node, b, c nd d, but only node, b nd c receve probe pckges. (3). Jon Messge Fther nodes n the selecton of chldren send them jon messge, nd nnounces tht they wll jon the tree. Fg. shows, A choce of nodes nd c for ther chldren, nd the dstnce from nd c to A s further thn tht of ether from to b or from b to c. he pseudo-code of lgorthm s n the followng form. Constructon of sply trees lgorthm Form_A(p,p") Input: the depth nd the b-vlue. Output: bnry tree c rooted t r of depth t most p nd unque 1. Begn ID ssgned to ech node of c.. For ech level j from 0 to p- l /* l s the lrgest spn pth length of nter-node */ For ech node from l to j

5 496 JOURNAL OF COMPUERS, VOL. 5, NO. 4, APRIL M s node t level j + l 4. n s node t level j 5. n sends Becon pcket contnng n s ID n to M Where dstnce between n nd M < r /* r s the correspondence rdus */ 6. M chooses n s ts prent wth probblty > p" 7. M sends Probe pcket to n 8. n wts NWAI tme ( whch s suffcently loog fxed tme perod) to receve Probe pcket from ech M who selected n s prent 9. End 10. End he sensor network, the node n the pth of the lrgest spn hs good dsperson, reduced the nfluence of cpcty of network-sense due to the overlppng coverge, therefore these dspersve good nodes need to mntn. hrough the defnton of the sply tree, determned nodes set needs to be mntned n the sensor network. IV. DAA AGGREGAIONS he mn de of tree bsed dt ggregton lgorthm s to use the trnsmsson model M beng ble to ft more montor dt nsted of the montor dt of trnsmsson nodes, to reduce the cpcty of dt trnsmsson, thus sves the energy of the sensor node. herefore t needs to consder the reltons between the cost of the return model nd dt quntty t my ft. he smller the cost of trnsmsson model, the more dt t cn express, the more energy-svng. Becuse the montor vlue of node s often subject to mny fctors, we expect to ft the most dt wth the mnmum cost mode, nd the multple lner regresson models s exctly n lne wth ths gol. In sply tree ech node receves nd stores dt reported by the recent non-tree node cyclclly to t, nmely the N node s responsble for the senston, but A node s responsble to store, here, the vlue sved n A node s regrded s the functon vlue of the x-y coordnte. hs process descrbes by three-topple (f, x, y),.e. f s the ttrbute vlue trnsmtted by node locted t (x, y). Dt tuple of node stored n A produces the pproch functon f (x, y), nd the progressve functon f (x, y) by the nput of the three vrbles (z, x, y) forms the mplementton of mult-polynoml functons, dt n such tree node my denotes by multple regresson polynoml functon. he followng s to dscuss the process of crryng out the dt ggregton through the polynoml regresson on the sply tree. In generl, the form of mult-dmensonl lner regresson functon s s follows [16] : m y = f ( x, x,..., x ) = 1 m 0 + x k k (7) k = 1 where x 1,x,,x m s ndependent vrble of the forecst model, y s the smple vlue wth n dmensonl vector, whch denotes from specfc level x k to estmted the vlue of node, nd s (m+1) l dmensonl vector estmted vlue of. Usng the lest squre crteron, cuses the qudrtc dfference to be smllest. F( ) = ( X y) ( X y) (8) where = [ 1,,, n ] (9) he essentl condton of exstence mnmum s the F( ) prtl dervtve s zero, then F( ) = ( X y) ( X y) = 0 gn y 1 1 x11 xm 1 y y = X = 1 x1 n x y n mn ( X y) ( X y) = ( ( X y)) ( X y) + ( ( X y)) ( X y) = X ( X y ) = X X X y = 0 (10) hen: X X = X y (11) If X X s rreversble, there s soluton. In the 1 equton (11) on both sdes s multpled by ( X X ), hs 1 ( = X X ) X y. Usng the polynoml regresson, we cn obtn the followng equton. where, 1 y y1 x1 x1 y1 x1 y1 x1 x1 y1 x1 y y y x x y x y x x y x y X = 1 y n y n y n y n y n y n Z z1 z, z n, [ ] =,, β = β1, β,, β n. 1 β= ( X X) XY p( x, y) = β + β y + β y + β x + β xy β xy + β x + β x y + β x y (1) (13) From the equton (1), we cn compute β wth gven locton (x, y), nd obtn the vlue of z = p (x, y) s property vlue of (x, y) nodes. Set β s (m+1) l - vector, then X X certnly s the m+1 [15] step nonsngulr. In other words, n>>m+1nd X cnnot denote for weghted lner combnton of ny other row set. In ths pper, the dt ggregton lgorthm ccordng to the nput of the wdth prorty, ech tree node hs coeffcent from the formul (1) nd sends the coeffcent set to ts prent node. Nodes of ech level use the coeffcent whch obtns from ts chld to renew sensor ttrbute vlue, nd these dt combne the detecton vlue of node tself to clcult the new coeffcent set, nd then trnsfer to hgher level. In the process, to dentfy the even ttrbute vlue n the regon s the crux of the mtter, becuse they hve drect berng on the ccurcy of the ggregton, nd through the upper nd lower bounds the of coordntes of the

6 JOURNAL OF COMPUERS, VOL. 5, NO. 4, APRIL { x mn,y mn,x mx,y mx } to dentfy of the regon, where the mnmum nd mxmum vlue from the son of the fther of the current node n the tree under ll the sensor nodes. As n fg. 4, set s the current ggregton node, nd dt vlue n the regon updtes through. he scope of the regon defnes by the subtree of to whch pssed through the smllest nd lrgest coordntes of the sensor nodes. hus, node gets the border coordntes of the regon from ts chld. hrough bsed on constructon of the sply tree nd the bove descrpton bout the process of regresson, nswer queres every specfed tme, such s "SELEC temperture FROM sensors WHERE locton = (x, y)", or the hghest temperture n trget scope of ssues. In the ltter cse, generte set of (x, y) coordntes n the desgnted re, Snk frstly nformed of the ttrbute vlue of ech pont locton to clculte the mxmum vlue. When Snk needs to know the dt of (x, y), t wll send ths nqury to the root, the nqury by the A spredng down untl the lef nodes of the lst lyer. A dt ggregton lgorthm bsed on sply tree SPA(p,n s ),n s s the verge number of sensor nodes reportng to the tree node. 1: Begn : For ech of lef node of the tree fle node dt s red multvrte polynoml regresson s performed on ech dt fle nd the coeffcents re stored n the ech of the rrys β 0,β 1,,β 8 ech of sze N End For 3: Intlze level to p Whle p s greter thn 0 1 sum = level + p ;k = level Whle k < sum 4: for ech of the non lef nodes k of the tree computes rndom x-y ponts for ech of ts chldren nd (+l) where (x mn,y mn) nd (x mx,y mx) re the coordntes of the leftmost nd down most node nd rghtmost nd top most node respectvely reportng to the node nd +l. End For 5: Usng (β 0,β 1,,β 8) nd (β (+1)0,,β (+1)1,,β (+1)8) new ttrbute vlues re clculted nd ppended to node k.dt.node k then clls the regresson functon to clculte (β k0,,,β k8) nd psses t to ts prent. 6: End Whle 7: Level = sum 8: End Whle 9: End Compred to the energy consumpton nd dely of trnsmsson sngle dt to correspondng locton, t s more effectve the dt s reported by the process of SPA ggregton. In A, compresson rto s defned s the byte number sent fter the compresson of the orgnl dt. Set tht the depth of A to p nd A hs ( p + 1) totl of t = 1 lef nodes, ech pcket sze of w - byte ncludes sensor redngs nd the locton coordntes correspondng to the redngs. In ths wy, the sze of byte number whch enters to every lef node s n s w, where ns s the totl number of sensor nodes sent to ech tree node. herefore, byte number trnsferred to the lef nodes s = n w p. l s In ddton to redng the ttrbute vlue from the sensor nodes, ech non-lef node gets vlue for nput from ts two chldren, to updte the coeffcent nd the x- y vlue of the regon border. herefore, the totl byte number nputtng to non-lef node nl s: n w +, p 1 p nl = ( w + w + w )) ( 1 ) s x y c get the output pcket of byte whose sze s ( w + w + w ) from the tree node (ncludng x y c coeffcents nd the scope of the x-y). he totl byte number output from ll nodes s = ( w + w + w ), nd then the p 1 ( 1) 0 x y c compresson rto s: 0 C. R = + l nl Fg. 4 node clculte the boundry of the regon for dt regenerton ( w + w + w ) t x y c = (14) ( n w t + ( w + w + w )( t 1)) s x y c l Where, t s the totl number of tree nodes, tl s the number of lef nodes. V. SIMULAION RESULS AND DISCUSSION In ths pper, dscrete event smulton pltform NS ws employed to conduct smulton tests; the smulton prmeters re shown n tble 1 nd the focus s to mke performnce evluton of the dt ggregton lgorthm n the followng spects: (1) ccurcy of sensor ttrbutes of the whole coverge regon, ncludng the bsolute vlue nd error percentge, ()compresson rto, (3) comprson between the szes of the ggregted pckets nd non-grregted pckets n the root. ble 1 Vlues of smulton prmeters used Prmeter Vrton A R 40m D 1630 A/D A s P" 0.33 p 4 n s 1 he defnton of the vrbles ws shown n tble 1. Supposng the totl number of node n regon A s D, then the densty of nodes ρ=d/a, A s s the sub-regon ncludng the sngle ggregton tree c, so the verge number U of node s determned by A s n the sub-regon.

7 498 JOURNAL OF COMPUERS, VOL. 5, NO. 4, APRIL 010 For complete bnry tree, the totl number of nodes s t, hs: ( p + 1) t = 1 (15) In ddton, n s set by the front, tht s, the verge number of sensor nodes reportng to the tree node, n the subregon the upper bound of node number U [16] s: U = n t + t s or t = U ( n + 1) s, replcement of t usng formul (15), results n n optml soluton wth the depth U of A: p = ln( + 1) 1,set D=1630, A= n + 1 s ρ = = 0.005, = hen the verge A s number of nodes n the regon s U = =408. Set the depth of the tree p=4, nodes number c = t= (4+1) -1=31,n s =1. he totl number of sensor nodes n ths regon =31 1=37. In fct, the totl number of nodes n the regon U = = 403 <408. herefore, the bove defnton of prmeters s effectve. (1).Erro Rte When the pproxmton of the ctul vlue, the error rte E= ( z z z) 100 εth,where ε th =6% s the error threshold, z, z re respectvely the pproxmte dt nd the ctul dt. Fg. 5 hs demonstrted the depth of the ggregton tree nd reltons of the error rte. We cn see tht wth the ncrese of the ggregton tree depth, the scope of the tree node coverge wll be greter; so s to mke the whole regon cn be better montored, t the sme tme, the verge error nd the error rte of smlr dt fll stedly, tht s exctly wht we expected. When the depth of the tree s 1, the error rte wll rech the mxmum, becuse the tree hs only three nodes (n the regon the mjorty of the sensor node dspersed, not n the tree node, nd cn not be sent to A) to montor the scope of the regon. Percentge Error Fg. 7 shows the dt trffc fter dt ggregton though SPA lgorthm n the root, s well s the root receves dt non-ggregton nd the norml one-tomny communcton. hough the depth of the sply tree s dfferent, when ll the nodes of the sply tree mplement dt compresson, the sze of pcket sent from root to the Snk s constnt, tht s, fxed ( w + w + w ) bytes. he pcket sze sent from one x y c tree to nother tree node by node s lmost constnt, nd t s nothng to do wth the sze of the network, whch mkes the totl energy of dt kept wthn resonble bounds. hs confrms the bove ssumptons, tht s, ech tree node sends the pcket whch only contns coeffcents nd x-y coordntes to ts prent node, nd the sze of the pcket s ndependent of the number of nodes n the tree. In the trdtonl mny-to-one communctons, ll of the leves must send dt to the root node, so tht when the network node ncreses, the sze of dt pcket trnsmsson growth through the root node wth no lmts. hrough the mplementton of ths lgorthm for dt compresson, the lrgest Dt communctons reduce by the mount of 85% n comprson wth [17]. Compresson rto (C.R.) Sze of the fnl dt pcket t the root Depth of A(p) Fg.6. Dependence of compresson rto Depth of A Fg. 5. Vrton of percentge error wth depth (). Compresson Rto Fg. 6 shows the compresson rto chnges wth the depth of the tree, s expected, lmost constnt for 0.0. he declne of the curve shows tht wth the depth ncreses, the compresson rto reduces. he deeper the depth of the tree s, the better the degree of compresson turns, nd the less the output becomes. he hgh compresson rto reduced the whole nformton content nd thus hs sved the correspondence bnd wdth nd the totl energy. (3). Sze of Root Output Pcket Depth of A(p) Fg. 7 Dependence of sze of dt pcket (t root node) VI. CONCLUSION In ths pper, we proposed novel dt ggregton lgorthm through the constructon of the sply tree, nd ths lgorthm wll lso be ble to detect the event ttrbute vlue n the postons where the sensor nodes re lcked. In the constructon phse of the tree, the root choce s dstrbutonl. It elmnted the request for the overll stuton root postonl nformton by snk. By lmtng the number of communctons, fxed-sze nformton nd wthout tkng the depth of the ggregton tree nto ccount, ts percentge of error cn

8 JOURNAL OF COMPUERS, VOL. 5, NO. 4, APRIL be controlled wthn n cceptble rnge when dt compresson rto remns constnt. Smulton results show tht the lgorthm cn effectvely mprove the percepton cpcty of the overll network nd reduce the energy consumpton. ACKNOWLEDGMEN Supported by the the Ntonl Nturl Scence oundton of Chn ( , , ); Nturl Scence Foundton of Jngsu Provnce of Chn(BK008161, BK008154, BK009116); he Key Progrms of Mnstry of Educton of Chn (07040); Jngsu Provncl Mjor Progrm of Scence echnque support nd ndependent nnovton Foundton (BE008044); Funded by Prereserch Project of Soochow Unversty; he Openng Project of Jngsu Provnce Support Softwre Engneerng R&D Center for Modern Informton echnology Applcton n Enterprse (SX00903); he Hgher Educton Grdute Reserch Innovton Progrm of Jngsu Provnce n 009. REFERENCES [1] L JZ, L JB, Sh SF. Concepts, ssues nd dvnce of sensor networks nd dt mngement of sensor networks.journl of Softwre,003,14(10): [] Ren FY, Hung HN, Ln C. Wreless sensor networks.journl of Softwre,003,14(7): [3] Noto Kmur,Shhrm Ltf.A survey on dt compresson n wrless sensor networks,in proc of the Int'l conf on Informton echnology:codng nd Computng.Los CA:005,:8-13 [4] Kenneth B,krste A.Energy wre lossless dt compresson,acm rnsoncoputer Systems,006,4(3):50-91 [5] XIE Zh-Jun, WANG Le, LIN Y-Png,et l.an Algorthm of Dt Aggregton Bsed on Dt Compresson for Sensor Networks, Journl of Softwre,006,17(4): [6] Olg Sukh,Pedro Jose,Andres Lchenmnn,et l.generc routng metrc nd polces for WSNs,In Proc of 3th Europen Workshop on wrless sensor networks.berln,006, [7] Noseong Prk,Deyoung Km,Yoonmee Doh,et l.n optml nd lghtweght routng for mnmum energy consumpton n wrless sensor networks,in Proc of the 11th IEEE Int'l Conf on Embedded nd Rel_tme Computng Systems nd pplctons.new York,005, [8] I Kdyf,M Kndemr.unng n-sensor dt flterng to reduce energy consumpton n wrless sensor networks, In Proc of Desgn,Automton And est In Europe Conference And Exhbton.Los Almtos,CA,004, [9] Dntu,R.AbbsK O'Nell, el l.dt Centrc Modelng of Envronmentl Sensor Networks[C],Globl elecommunctons Conference Workshops, GlobeCom Workshops [10] Intngonwwt, Estrn, Govndn.Impct of network densty on dt ggregton n wreless sensor networks,.proc Of the th Interntonl Conference on Dstrbuted Computng Systems, July 00, [11] Henry Dubos Ferrere, Deborh Estrn.Effcent nd Prctcl Query Scopng n Sensor Networks. IEEE Interntonl Conference on Moble Ad-hoc nd Sensor Systems, Los Angeles, USA, Aprl [1] W. Henzelmn, A. Chndrksn,H Blkrshnn.Energy- Effcent Communcton Protocol for Wreless Mcrosensor Networks, Proc of the 33th Interntonl Conference on System Scences, Hw,Jnury 000 [13] Guestrn C,Bodk P,hbux R,et l.dstrbuted Regresson:n Effcent Frmework for Modelng Sensor Network Dt,.3th Interntonl Symposum on Informton Processng n Sensor Networks (IPSN' 04).New York, [14] Koushnfr F, Potkonjk M, Sngovnn-Vncentell A. Error models for lght sensors by sttstcl nlyss of rw sensor mesurements, In: Proc of the IEEE Sensors, 004.3: [15] Ignco Sols, Kt Obrczk, In-Network Aggregton rdeoffs for Dt Collecton n Wreless Sensor Networks,INRG echncl Report 10, 003 [16] Vurn MC,Akn OB,Akyldz IF. Spto-emporl correlton:heory nd pplcton for wreless sensor networks. Computer Networks, 004,45: [17] lmn Wolf, Sum Y. Cho.Aggregted Herrchcl Multcst for Actve Networks, IEEE Mltry Communctons Conference,001,: ZHANG Shu-Ku s currently n ssocte professor n the Insttute of Computer Scence nd technology t Soochow Unversty, Chn. Hs reserch res nclude d-hoc nd wreless sensor networks, moble computng, dstrbutng computng, ntellgent nformton processng, prllel nd dstrbuted systems etc. CUI Zh-Mng He s professor nd doctorl supervsor t the Insttute of Computer Scence nd technology, Soochow Unversty nd CCF senor member. Hs reserches res re ntellgent nformton processng, dstrbutng computng, Deep Web dt mnng etc. GONG Sheng-Rong s professor of Insttute of Computer Scence nd technology n Soochow Unversty, Chn. He receved hs the PhD n Computer Scence from Bejng Unversty of Aeronutcs & Astronutcs of Chn n 001.Hs reserch res re vdeo processng nd communctons nd computer vson. LIU Qun s professor nd doctorl supervsor t the Insttute of Computer Scence nd technology, Soochow Unversty nd CCF senor member. Hs reserches res re ntellgent nformton processng, dstrbutng computng, utomted resonng nd GIS etc. FAN Jn-X receved the BS, MS, nd PhD degrees n computer scence from Shndong Norml Unversty, Shndong Unversty,nd Cty Unversty of Hong Kong, Chn, n 1988, 1991, nd 006, respectvely. He s currently professor of computer scence n the School of Computer Scence nd echnology t Soochow Unversty, Chn.Hs reserch nterests nclude prllel nd dstrbuted systems, nterconnecton rchtectures, desgn nd nlyss of lgorthms.