Proceedngs of he 2010 IEEE Inernaonal Conference on Informaon and Auomaon June 20-23, Harbn, Chna SkyCube Compuaon over Wreless Sensor Neworks Based on Exended Skylnes Zhqong Wang 1, Zhyue Wang 2, Junchang Xn 3, Man Wang 3 and Qanx L 1 1 Sno-Duch Bomedcal and Informaon Engneerng School 2 School of Elecroncs and Informaon Engneerng 3 College of Informaon Scence & Engneerng Norheasern Unversy Harbn Insue of Technology Norheasern Unversy Shenyang, Laonng, P.R.C. Harbn, Helongang, P.R.C. Shenyang, Laonng, P.R.C. wangzq@bme.neu.edu.cn Absrac - Wh he wde applcaon of wreless sensor nework n many domans of he naonal economy, more and more researchers pay aenons o daa managemen of wreless sensor nework. As he man means of mul-decson and daa mnng, skylne query n wreless sensor nework gradually becomes a focus of he researches. In recen years, skycube query has been deeply dscussed, bu due o he specal properes of wreless sensor nework, exsng approaches could no be drecly appled no he sensor envronmen, so n hs paper, skycube query n wreless sensor nework s furher researched and a new skycube query algorhm based on exended skylne (SCAES) s proposed, oo. SCAES exracs he necessary daa from he nework hrough exended skylne and flers hese daa ha do no belong o he skycubes, by he correspondng properes, whn he nework. And hen he daa ransmsson s reduced. The expermen resuls show ha SCAES could grealy reduce he daa ransmsson, whle calculang he skycube of he nework, and exend he lfe-span of he nework. Index Terms - wreless sensor nework; skylne; skycube; exended skylne I. INTRODUCTION Wh he rapd developmen of wreless neworks, low-power embedded echnology and mcroelecronc echnology, wreless sensor nework (WSN) has been wdely appled n varous felds. The energy sored n sensor nodes s lmed because he energy s ofen provded by baeres and he baeres replacemen or chargng up s dffcul snce he sensor neworks are ofen naccessble (hgh-rsk area, ec.). Therefore, how o energy-effcenly manage large amouns of daa colleced by WSNs has recenly become a hospo. As an mporan ool of mul-obecve decson-makng, skylne query plays an mporan role n many sensor applcaons. For example, n raffc monorng applcaons, he narrower he road s and he greaer he raffc flow s, he raffc ams, or even car accdens are more lkely o occur. Therefore, WSN can be used n he road nework o connuously monor he dangerous area. In hs way, raffc pressure n he relevan areas can be releved o some exen by akng measures n advance and he rsk of raffc ams and accdens can hus be reduced. The daa pons n he daa se T ha are no domnaed by any oher daa pon form he skylne of T. When a daa pon n he daa se T s no worse han anoher daa pon n all dmensons, and s beer han a leas n one dmenson, s sad ha domnaes. In praccal applcaons, snce requremens dffer from user o user, her concern of skylnes n dfferen dmensons also dffers accordngly. Therefore, he conceps of subspace and skycube are nroduced. Alhough skycube query has been wdely used n he radonal daabases feld, snce he spaal characerscs of sensor nodes, such as energy-consraned and wreless mul-hop communcaons, are no consdered, can no be appled drecly o he feld of WSNs. In hs paper, characerscs of skycube query are analyzed n deal. And hen a new skycube query algorhm based on exended skylne (SCAES) s proposed o solve he problems abou skycubes n WSNs. The man conrbuons of hs paper are summarzed as follows: 1. Skycube query algorhm based on exended skylne (SCAES) are presened o solve he problems abou skycubes n WSNs. 2. The characers of skylne query n subspace are analyzed and a new mehod whch adops n-nework fler s pu forward o mprove he performance of SCAES. 3. Performance evaluaon expermens are desgned, whose resuls shows ha daa ransmsson n WSNs can be reduced effecvely by adopng SCAES algorhm. The organzaon of hs paper s as follows: he relaed work are nroduced n Secon II; The deals of SCAES algorhm and s opmzed algorhm are presened n Secon III; Expermen resuls and analyss showng he effecveness of he proposed approaches are repored n Secon IV; Fnally, we conclude hs paper n Secon V. II. RELATED WORK 978-1-4244-5704-5/10/$26.00 2010 IEEE 1572
Wh he wde applcaon of WSN, daabase managemen n sensor neworks has aroused grea aenon from he specalss and scholars. Leraure [1, 2] dealed he sensor nework-relaed ssues. A seres of research resuls have been obaned from sensor daa managemen echnology n recen years. TnyDB [3] and COUGAR [4] are wo ypcal percepual daa managemen sysem. They mplemen a ype of SQL nerface o complee he smple aggregaon query, such as MAX, MIN, AVERAGE, SUM, COUNT. Skylne query was frs nroduced o daabase leraures n 2001 by Borzsony e al. [5], and gradually araced exensve aenon. In recen years, skylne query has also go more and more aenon n wreless sensor neworks. Chen e al. [6] suded he ssues of skylne monorng n WSN, and proposed a hreshold based herarchy fler algorhm MINMAX o reduce nework daa ransmsson. Xn e al. [7, 8] suded he sldng wndow skylne query n he WSN and, respecvely, proposed flerng based and mappng based mehods o effecvely reduce he daa ransmsson a sensor nodes, hereby reducng he overall nework energy consumpon. Skycube query has gradually receved more aenon. Yuan e al. pu forward he boom-up and op-down algorhms o calculae he SKYCUBE whch conans all he subspace skylnes. Pe e al. presened he concep ha he subspace s deermned by he skylne se and proposed he correspondng algorhm o solve he skylnes. In leraure [11], Pe e al. gave an n-deph analyss of he characerscs of he skylne se and he decson-makng subspace, and effecvely solved he skylne se and he decson-makng subspace based on he skylne n he whole space. We can neher apply oher query algorhm n he wreless sensor neworks drecly o he skylne query nor ransplan skylne query algorhms n he cenralzed envronmen o WSN envronmen, us because here are paral order of domnan relaons n skylne query, furhermore, he energy and compuaonal ably are lmed n WSNs. III. SKYCUBE QUERY ALGORITHM BASED ON EXTENDED SKYLINE (SCAES) A. Basc SCAES Algorhm One of he basc algorhms o solve skycube n WSNs s TAG, whch calculaes he skycubes a he sensor nodes and hen adops n-nework aggregaon mehod o reduce he nework daa ransmsson of he nermedae resuls. However, snce skycube calculaon s que complex and compuaonal ably s lmed and such algorhm requres los of calculaons a he sensor nodes, long query response delay, whch can no be oleraed by he users, wll be caused. Meanwhle, los of nersecons exs beween he subspace skylne and s paren pace skylne, whch wll cause repea daa ransmsson and a grea wase of energy n neworks. Analyss reveals ha n WSNs, he base saon has sronger compuaonal ably and can acheve real-me skycube calculaon. Moreover, some basc calculaon can be done by he sensor noes whn a shor me whch wll reduce unnecessary daa ransmsson. In hs way, daa ransmsson s reduced and a he same me, he skycube query response me s also shorened. The process of skycube calculaon n WSNs can be summarzed as Algorhm 1. Algorhm. 1 Skycube calculaon n WSNs Inpu: skycube query; Oupu: skycube n WSNs; 1:The base saon sends a skycube query o he neworks; 2:The sensor node exracs he necessary daa from he neworks followng he rules; 3:sends he necessary daa o he base saon; 4:The base saon collecs all he daa sen back by sensor nodes; 5:The base saon adops he skycube algorhm n he cenralzed envronmen o compue he skycubes n WSNs; 6:Reurn; How o acheve he skycube calculaon wh fewes daa exraced from he neworks becomes he key. Before he nroducon of specfc algorhm, heorec analyss of he relaons beween subspace and s paren space s presened. Lemma 1. A subspace daa pon eher s a paren space skylne pon, or has he same value wh any paren space skylne pon n he subspace. The characersc of subspace skylne s nroduced n Lemma 1, accordng o whch he followng concluson can be made. Theorem 1. A non-global daa pon belongs o he subspace skylne se only when has he same value wh a global daa pon n ha subspace. Proof. Usng reducon o absurdy. Assumng ha wo daa pons and do no have he same value n he subspace, bu boh belong o he skylne of ha subspace. Accordng o Lemma 1, mus be a non-global daa pon, whch s conrary o he assumpon. 1573
Accordngly, a non-global daa pon belongs o he subspace only when has he same value wh a global daa pon n ha space. Accordng o Theorem 1, f he global skylnes and all he oher daa whch share he same values wh he skylnes n ceran spaces can be exraced from WSNs, he skycube mus be ncluded. Ths s he concep of exended skylne. Nex, he relevan defnons and characerscs presened by leraure[12] are nroduced. Defnon 1. The daa pon n he daa se T s srcly domnaed by only when s beer han n all dmensons. Defnon 2. Daa pons n daa se T whch are no domnaed by any oher pons forms he exended skylne of T. Lemma 2. If daa pon s srcly domnaed by he daa pon n daa space S, s domnaed by. Theorem 2. Skylne s he subse of he correspondng exended skylne. Boh he skylne and daa whch have he same value wh he skylne n he subspace are ncluded n he exended skylne. Does all he daa belongng o he skycube are ncluded n hose daa? Furher dscussons are presened. Lemma 3. If he daa pon s srcly domnaed by n he daa space S, n any subspace of S, s also srcly domnaed by. Proof. Accordng o Defnon 1, he lemma can be go ncdenally. Theorem 3. Daa whch are srcly domnaed do no belong o he skylne of any subspace. Proof. Accordng o Lemma 3, f daa pon s srcly domnaed by n all he daa spaces, s domnaed by n any subspaces. Accordng o Defnon 2, does no belong o he exended skylne of any subspace. Moreover, accordng o Theorem 2, we know skylne s he subse of he correspondng exended skylne. Therefore, does no belong o he skylne of any subspace. Theorem 4. All he daa of skycube are ncluded n he exended skylne. Proof. Accordng o Theorem 3, any daa pon ha dose no belong o he skylne n any subspace does no belong o he skycube. Therefore, Theorem 4 can be proved. Accordng o Theorem 4, f exended skylne query s execued n he neworks, he base saon can calculae he skycube n he WSNs precsely by usng he resuls of exended skylnes. In hs way, he exracon of any oher daa wll no be necessary. The execung algorhm of he calculaon of exended skylne by he sensor nodes are shown n Algorhm 2. Algorhm. 2 calculaon of exended skylne Inpu: local daa and receved exended skylnes; Oupu: resuls of local exended skylne; 1: Sensor node merges he receved from he chldnodes; 2: The colleced daa are added no he emporary daa se; 3: The exended skylne of he emporary daa se s calculaed; 4: The are submed o he paren node; 5: Reurn; The algorhm a base saon s shown n Algorhm 3. Algorhm. 3 Skycube calculaon n WSNs Inpu: all receved exended skylnes; Oupu: resuls of skycube n WSNs; 1: The base saon merges he local exended skylne nformaon receved from he chldnodes; 2: The exended skylne of he emporary daa se s calculaed; 3: The skycube n WSNs s calculaed; 4: The resul of skycube s submed o he user; 5: Reurn; B. SCAES algorhm based on n-nework fler I should be noced ha here s no need o collec he nformaon sored a he base saon because no all he exended skylne pons belong o he skycube. In order o propose a reasonable flerng soluon, he followng secons dealed he analyss of s characerscs. Theorem 5. If daa pon s domnaed by n he daa space S and s srcly domnaed n he space S, where S S, hen n any subspace S, when S S, does no belong o he skylne of S. Proof. If daa pon s domnaed by n he daa space S, are no worse han n all he dmensons of S. Therefore, are no worse han n any dmenson of S. Because s srcly domnaed by n he daa space S S, s beer han n all he dmensons of S. Moreover, snce S S, n he space S, here exss one dmenson where s beer han. In oher words, n he space S, s domnaed by and does no belong o he skylne of S. 1574
If he daa pon s domnaed by anoher pon n he global daa space, s srcly domnaed by n he subspace S 1. The larges space n whch may be he skylne of s S S1. Meanwhle, f anoher daa pon k domnaes n he space S S1 and srcly domnaes n S where 2 S2 S S1, he larges space n whch may be he skylne of wll be narrowed o S S1 S2. Analogcally, once he space se are found o be empy, shows ha he daa pon neher belongs o he skylne of any subspace, nor o he skycube. Therefore, can be dscarded a he nermedae nodes, whch wll reduce unnecessary daa ransmsson when calculang he exended skylne. A hs pon, he purpose of daa flerng can be fulflled by udgng he daa of he exended skylne one by one. In order o accelerae he speed, he daa can be organzed no R-ree. Because he amoun of expended skylne resul daa s no large, me and space consumpon wll no be overszed. Therefore, he demand can be me by sensor nodes. IV. PERFORMANCE VERTIFICATION In hs secon, we presen our smulaon resuls evaluang he performance of SCAES-basc agans SCAES-fler under number of sensor nodes, daa dmensonaly, change of daa repeon rae. All algorhms are C++ mplemened, and adop synhess daa n [1] ncludng ndependen and ancorrelaed, whch are he common benchmarks for skylne query. We smulae sensor nework by equably placng n sensors nodes n an area of uns, he average area ha each node s n s one square un. The communcaon radus of each sensor node s se o 2 2 and he maxmum packe of ransmsson s 48 byes. The man parameers of he expermens are gven n Table I. For each expermen, he value of one parameer wll be changed, whereas oher parameers are se o defaul values. TABLE I PARAMETERS IN EXPERIMENT Parameers Defaul value Varaon range Nodes number 300 100, 200, 300, 400, 500 Daa dmenson 4 2, 3, 4, 5, 6 Daa repeon rae 15 5, 10, 15, 20, 25 Fg.1 ndcaes ha when he number of nodes ncreases, he communcaon cos ncreases correspondngly. I s because he ncrease of sensor nodes means ha more daa are nvolved n he calculaon. Therefore, he resuls of he skylne ncrease. Meanwhle, SCAES-fler s superor o SCAES-basc, because a flerng mechansm s adoped by SCAES-fler, whch reduces unnecessary daa ransmsson. Fg.2 ndcaes ha wh he ncrease of daa dmensons, he communcaon cos of boh SCAES-basc and SCAESfler ncreased dramacally. I s because he ncrease of dmensonaly makes he probably of daa beng domnaed decreases and accordngly he probably of daa becomng he subspace skylne ncreases. Therefore, communcaon cos ncreases dramacally. Meanwhle, for he same reason as llusraed n he las paragraph, SCAES-fler s beer han SCAES-basc. (a) Independen (b) An-correlaed Fg. 1 The nfluence of by he sensor nodes number Fg.3 ndcaes ha wh he ncrease of daa repeon rae, he communcaon cos of SCAES-basc algorhm ncreases slowly. I s because he ncrease of daa repeon rae leads o he ncrease of he number of daa whch have he same value, accordngly he probably of daa beng subspace skylne. Therefore, communcaon cos also ncreases. Snce SCAES-fler adops he n-nework fler sraegy o avod unnecessary daa ransmsson, he negave effec caused by he ncreased number of exended skylne resuls s avoded. From he above expermen, can be concluded ha SCAES-fler algorhm s always much beer han SCAESbasc, wh he changes of he number of nodes, daa dmensonaly and daa repeon rae. I grealy reduces he daa raffc among sensor nodes. Therefore, can be sad ha 1575
SCAES-fler algorhm s an effcen skycube calculang algorhm n WSNs. (a) Independen (b) An-correlaed Fg. 2 The nfluence of daa dmensons (a) Independen V. CONCLUSION Because energy n sensor nodes s mosly consumed by wreless communcaons, he key problem of sensor daa managemen n WSNs s how o mnmze daa ransmsson n WSNs. Based on he n-deph analyss of he characerscs of skylne query, SCAES algorhm, n whch exended skylne s used o calculae he skycube n WSNs, s proposed. Moreover, an opmzed algorhm of SCAES, whch adops he flerng sraegy, s presened. Ths algorhm furher mproves he performance of SCAES and also reduces daa ransmsson. The expermen resuls show ha SCAES algorhm can effecvely reduce he communcaon cos among nework sensor nodes, hereby exendng he lfe span of WSNs. Acknowledgemen. Ths research s suppored by he Scence Foundaon of Laonng Provnce Chna (Gran NO. 20082033). REFERENCES [1] REN Feng-Yuan,HUANG Ha-Nng,LIN Chuang. Wreless Sensor Neworks. Journal of Sofware, 2003, 14(2): 1148-1157. [2] LI Jan-Zhong,LI Jn-Bao,SHI Sheng-Fe. Conceps, Issues and Advance of Sensor Neworks and Daa Managemen of Sensor Neworks. Journal of Sofware, 2003, 14(10): 17171727. [3] S Madden, R Szewczyk, M J Frankln e al. TAG: A Tny AGgregaon Servce for Ad-Hoc Sensor Neworks. In: Proc. of OSDI. New York: ACM Press, 2002, 131-146. [4] Y Yao, J Gehrke. The cougar approach o n nework query processng n sensor neworks. SIGMOD Record, 2002, 31(3): 9-18. [5] S Borzsony, K Socker, D Kossmann. The skylne operaor. In: Proc. of ICDE, Los Alamos, USA: IEEE Compuer Press, 2003, 717-719. [6] H Chen, S Zhou, J Guan. Towards Energy Effcen Skylne Monorng n Wreless Sensor Neworks. In: Proc. of EWSN, Hedelberg: Sprnger- Verlag, 2007, 101-116. [7] J Xn, G Wang, L Chen e al. Connuously Mananng Sldng Wndow Skylnes n a Sensor Nework. In: Proc. of DASFAA, Hedelberg: Sprnger-Verlag, 2007, 509-521. [8] J Xn, G Wang, X Zhang. Energy Effcen Skylne Queres over Sensor Nework Usng Mapped Skylne Flers. In: Proc. of APWeb/ WAIM, Hedelberg: Sprnger-Verlag, 2007, 144-156. [9] Y Yuan, X Ln, Q Lu, eal. Effcen compuaon of he skylne cube. In Proc. of VLDB, New York: ACM Press, 2005, 253--264. [10] J Pe, W Jn, M Eser, Y Tao. Cachng he bes vews of skylne: A semanc approach based on decsve subspacese. In Proc. Of VLDB, New York: ACM Press, 2005, 241--252. [11] J Pe, Y Yuan, X Ln, e al. Towards muldmensonal subspace skylne analyss effcen compuaon of he skylne cube. ACM Transacon on Daabase Sysem, 2006, 31(4):1335-1381. [12] A Vlachou, C Doulkerds, Y Kods, M Vazrguanns. Skypeer: Effcen subspace skylne compuaon over dsrbued daa. In Proc. of ICDE, Los Alamos, USA: IEEE Compuer Press, 2007, 416-425. (b) An-correlaed Fg. 3 The nfluence of daa repeon rae 1576