Optimized Query Planning of Continuous Aggregation Queries in Dynamic Data Dissemination Networks

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1 WWW 007 / Trac: Performance and Scalablty Sesson: Scalable Systems for Dynamc Content Otmzed Query Plannng of Contnuous Aggregaton Queres n Dynamc Data Dssemnaton Networs Rajeev Guta IBM Inda Research Lab New Delh, Inda grajeev@n.bm.com Krth Ramamrtham Indan Insttute of Technology Mumba, Inda rth@cse.tb.ac.n ABSTRACT Contnuous ueres are used to montor changes to tme varyng data and to rovde results useful for onlne decson mang. Tycally a user desres to obtan the value of some aggregaton functon over dstrbuted data tems, for examle, to now (a) the average of temeratures sensed by a set of sensors (b) the value of ndex of md-ca stocs. In these ueres a clent secfes a coherency reurement as art of the uery. In ths aer we resent a low-cost, scalable technue to answer contnuous aggregaton ueres usng a content dstrbuton networ of dynamc data tems. In such a networ of data aggregators, each data aggregator serves a set of data tems at secfc coherences. Just as varous fragments of a dynamc web-age are served by one or more nodes of a content dstrbuton networ, our technue nvolves decomosng a clent uery nto sub-ueres and executng sub-ueres on judcously chosen data aggregators wth ther ndvdual sub-uery ncoherency bounds. We rovde a technue of gettng the otmal uery lan (.e., set of subueres and ther chosen data aggregators) whch satsfes clent uery s coherency reurement wth least cost, measured n terms of the number of refresh messages sent from aggregators to the clent. For estmatng uery executon cost, we buld a contnuous uery cost model whch can be used to estmate the number of messages reured to satsfy the clent secfed ncoherency bound. Performance results usng real-world traces show that our cost based uery lannng leads to ueres beng executed usng less than one thrd the number of messages reured by exstng schemes. Categores and Subject Descrtors H.3.5 [Onlne Informaton Servces]: Web Based Servces General Terms Algorthms, Management, Measurement, Performance, Desgn. Keywords Content dstrbuton networs, Dynamc data, contnuous aggregaton ueres, data coherency, uery dssemnaton cost. 1. INTRODUCTION Many data ntensve alcatons delvered over the Web suffer from erformance and scalablty ssues. Content dstrbuton networs (CDNs) solved the roblem for statc content usng Coyrght s held by the Internatonal World Wde Web Conference Commttee (IW3C). Dstrbuton of these aers s lmted to classroom use and ersonal use by others. WWW 007, May 8 1, 007, Banff, Alberta, Canada. ACM /07/0005. caches at the edge nodes of the networs. CDNs contnue to evolve to serve more and more dynamc alcatons [1, ]. A dynamcally generated web age s usually assembled usng a number of statc or dynamcally generated fragments. The statc fragments are served from the local caches whereas dynamc fragments are created ether by usng the cached data or by fetchng the data tems from the orgn data sources. One mortant ueston for satsfyng clent reuests through a networ of nodes s how to select the best node(s) to satsfy the reuest. For statc ages content reuested, roxmty to the clent and load on the nodes are the arameters generally used to select the arorate node [3, 4]. In dynamc CDNs, whle selectng the node(s) to satsfy the clent reuest, the central ste (to-level CDN node) has to ensure that age/data served meets clent s coherency reurements also. Technues to effcently serve fast changng data tems wth guaranteed ncoherency bounds have been roosed n the lterature [5, 6]. Such dynamc data dssemnaton networs can be used to dssemnate data such as stoc uotes, temerature data from sensors, traffc nformaton, and networ montorng data. In ths aer we roose a method to effcently answer aggregaton ueres nvolvng such data tems. In data dssemnaton schemes roosed n lterature [5, 6], a herarchcal networ of data aggregators s emloyed such that each data aggregator serves the data tem at some guaranteed ncoherency bound. Incoherency of a data tem at a gven node s defned as the dfference n value of the data tem at the data source and the value at that node. Although CDNs use ageurge [8] based coherency management, we assume that n dynamc data dssemnaton networs, these messages carry the new data values thereby an nvaldaton message becomes a refresh message. For mantanng a certan ncoherency bound, a data aggregator gets data udates from the data source or some hgher level data aggregator so that the data ncoherency s not more than the data ncoherency bound. In a herarchcal data dssemnaton networ a hgher level aggregator guarantees a tghter ncoherency bound comared to a lower level aggregator. Thus data refreshes are ushed from the data sources to the clents through the networ of aggregators. Dssemnaton networs for varous data tems (ossbly from dfferent data sources) can be overlad over a sngle networ of data aggregators as shown n Fgure 1. Thus, from a data dssemnaton caablty ont of vew, each data aggregator (DA) s characterzed by a set of (s, c ) ars, where s s the data tem whch the DA can dssemnate at an ncoherency bound c. Examle 1: In a networ of data aggregators managng data tems S 1 -S 4, varous aggregators can be characterzed as- D1: {(S 1, 0.5), (S 3, 0.)} D: {(S 1, 1.0), (S, 0.1), (S 4, 0.)} 31

2 WWW 007 / Trac: Performance and Scalablty Aggregator D1 can serve values of S 1 wth an ncoherency bound greater than or eual to 0.5 whereas D can dssemnate the same data tem at a looser ncoherency bound of 1.0 or more. Usually, clent s nterested n an aggregaton of these dynamc data tems at a certan ncoherency bound. These contnuous ueres are used to montor changes n dynamc data and rovde results useful for onlne decson mang. For generatng the result of a uery, data from multle sources s reured. As a result, the uery has to be evaluated ether at data aggregators [9] or at the clent. In ths aer we assume exstence of data dssemnaton networ of multle data tems to answer a class of ueres termed, contnuous ncoherency bounded weghted aggregaton ueres, whch are formally defned next. 1.1 Contnuous Incoherency-Bounded Weghted Aggregaton Queres A contnuous weghted aggregaton uery can be formally wrtten as: V s ( t) n = = s = 1 ( t) w V s s the value of a clent uery nvolvng n data tems wth the weght of the th data tem beng w, 1 n. s (t) s the value of the th data tem at the data source at tme t. Such a uery encomasses SQL aggregaton oerators SUM and AVG besdes general weghted aggregaton ueres such as ortfolo ueres, nvolvng aggregaton of stoc rces, weghted wth number of shares of stocs n the ortfolo. Due to sace lmtatons we are not resentng executon schemes for other aggregaton ueres such as MIN/MAX. Interested readers are referred to [10] for the extended verson of ths aer. Let the value of th data tem, n Euaton (1), nown to the clent/da be d (t). Then the data ncoherency s gven by s (t)- d (t). For a data tem whch needs to be dssemnated at an ncoherency bound C the data refresh s sent to the clent or lower level DA, f the s (t)-d (t) s more than C. If user secfed ncoherency bound for the uery s C, then the dssemnaton networ has to ensure that: n (1) ( s ( t) d ( t)) w C () = 1 Whenever data values at sources change such that uery ncoherency bound s volated, the udated value(s) s dssemnated to the clent. If the networ of aggregators can ensure that the th data tem has ncoherency bound C then the followng condton ensures that the uery ncoherency bound C s satsfed: n C w = 1 C A clent secfed uery ncoherency bound needs to be translated nto ncoherency bounds for ndvdual data tems or sub-ueres such that Euaton (3) s satsfed. It should be noted that Euaton (3) s suffcent condton for satsfyng the uery ncoherency bound but not the necessary. Ths way of translatng the uery ncoherency bound nto the sub-uery ncoherency bounds s reured f data s transferred between varous nodes usng only ush based mechansm. Such a translaton s not reured n ether a ull based mechansm as shown n our earler aer [9] or combnatons of ush and ull. In ths aer we (3) Sesson: Scalable Systems for Dynamc Content consder only ush based data dssemnaton among servers, DAs and clents. Next we resent the summary of our aroach towards executng the contnuous mult-data weghted addtve aggregaton uery wth the objectve of mnmzaton of number of refreshes from data aggregators to the clent. Our technue can be used for varous oular alcatons where dfferent clents reure aggregaton of multle data tems at ther ndvdual ncoherency bounds. Montorng stoc ortfolos s one such oular alcaton whch we use for erformance measurements. Sources Networ of data aggregators Clents Fgure 1: Data dssemnaton networ for multle data tems 1. Summary of Aroach and Contrbutons Consder a clent uery Q1=50 S S S 3 wth a reured ncoherency bound of 80 (n a stoc ortfolo S 1, S, S 3 can be dfferent stocs and ncoherency bound can be $80).We want to execute ths uery over data aggregators gven n Examle1 mnmzng number of refreshes. There are varous otons for the clent to get the data tems: The clent may get the data tems S 1, S and S 3 searately. The uery ncoherency bounds can be dvded among data tems n varous ways whle satsfyng Euaton 3. In ths aer, we show that gettng data tems ndeendently s a costly oton. Ths strategy gnores facts that the clent s nterested only n the aggregated value of the data tems and varous aggregators can dssemnate more than one data tem. If a sngle DA can dssemnate all three data tems reured to answer the clent uery, the DA can construct a comoste data tem corresondng to the clent uery (S =50 S S S 3 ) and dssemnate the result to the clent so that the uery ncoherency bound s not volated. It s obvous that f we get the uery result from a sngle DA, the number of refreshes wll be mnmum (as n ths case data tem udates may cancel out each other, thereby eeng the uery result wthn the ncoherency bound). As dfferent data aggregators dssemnate dfferent subsets of data tems, no data aggregator may have all the data tems reured to execute the clent uery whch s ndeed the case n Examle1. Further, even f an aggregator can dssemnate all the data tems, t may not be able to satsfy the uery coherency reurements. In such cases the uery has to be executed wth data from multle aggregators. Another oton s to dvde the uery nto a number of subueres and get ther values from ndvdual DAs. In that case, the clent uery result s obtaned by combnng the results of 3

3 WWW 007 / Trac: Performance and Scalablty more than one sub-uery. For the DAs gven n Examle1, the uery Q1 can be dvded n two alternatve ways: lan1: D1 {50 S S 3 }; D {S } lan: D1 {S 3 }; D {50 S 1, + 00 S }.e., n lan1 result of sub-uery 50 S S 3 s dssemnated by D1 and that of S (or 00 S ) by D. Combnng them at the clent gves the uery result. Selectng the otmal lan among varous otons s not-trval. As a thumb-rule, we should be selectng the lan wth lesser number of sub-ueres. But that s not guaranteed to be the lan wth the least number of messages. Further, we should select the sub-ueres such that udates to varous data tems aearng n a sub-uery have more chances of cancelng each other as that wll reduce the need for refresh to the clent (Euaton ). In the above examle, f udates to S 1 and S 3 are such that when S 1 ncreases, S 3 decreases, and vce-versa, then selectng lan1 may be benefcal. We gve an algorthm to select the uery lan based on these observatons. Whle solvng the above roblem of selectng the otmal lan we ensure that each data tem for a clent uery s dssemnated by one and only one data aggregator. Although a uery can be dvded n such a way that a sngle data tem s served by multle DAs (e.g., 50 S S S 3 s dvded nto two sub-ueres 50 S S and 70 S S 3 ); but n dong so the same data tem needs to be rocessed at multle aggregators, ncreasng the unnecessary rocessng load. By dvdng the clent uery nto dsjont sub-ueres we ensure that a data tem udate s rocessed only once for each uery (For examle, n case of ad data subscrtons t s not rudent to get the same data tem from the multle sources). The uery ncoherency bound needs to be dvded among subuery ncoherency bounds such that, besdes satsfyng the clent coherency reurements, the chosen DA (where the subuery s to be executed) s caable of satsfyng the allocated sub-uery ncoherency bound. For examle, n lan1 allocated ncoherency bound to the sub-uery 50S S 3 should be greater than 55 (=50* *0.) as that s the tghtest ncoherency bound whch the aggregator D1 can satsfy. We rove that the number of refreshes deends on the dvson of the uery ncoherency bounds among sub-uery ncoherency bounds. Smlar result was roved for data ncoherency bounds n [11]. Thus, what we need s a method of (a) otmally dvdng clent uery nto sub-ueres and (b) assgnng ncoherency bounds to them; such that (c) selected sub-ueres can be executed at chosen DAs and (d) total uery executon cost, n terms of number of refreshes, s mnmzed. We rove that the roblem of choosng sub-ueres whle mnmzng uery executon cost s an NPhard roblem. We gve effcent aroxmaton algorthms to choose the set of sub-ueres and ther corresondng ncoherency bounds for a gven clent uery. In contrast, all related wor n ths area [11, 1] roose gettng ndvdual data tems from the aggregators whch, as we show n ths aer, leads to large number of refreshes. For solvng the above roblem of otmally dvdng the clent uery nto sub-ueres, we frst need a method to estmate uery executon cost for varous alternatve otons. A method for estmatng the uery executon cost s another mortant contrbuton of ths aer. As we dvde the clent uery nto sub-ueres such that each sub-uery gets Sesson: Scalable Systems for Dynamc Content executed at dfferent aggregator nodes, the uery executon cost (.e., number of refreshes) s the sum of the executon costs of ts consttuent sub-ueres. We model the sub-uery executon cost as a functon of followng arameters: (a) Dssemnaton costs of the ndvdual data tems nvolved. The data dssemnaton cost s deendent on data dynamcs and ncoherency bound assocated wth the data. We model the data dynamcs usng a data synoss model, and the effect of the ncoherency bound usng an ncoherency bound model. These two models are combned to get the estmate of the data dssemnaton cost. (b) A correlaton measure of data dynamcs, uantfyng the chance that the udates of two data tems wll cancel each other out such that a sub-uery of ther sum wll ncur less refreshes than dssemnatng the ndvdual data changes. We use cosne smlarty between data tems for ths urose. Ths arameter s wdely used n nformaton retreval doman [0]. Through extensve smulatons we show that: Our method of dvdng uery nto sub-ueres and executng them at ndvdual DAs reures less than one thrd of the number of refreshes reured n the exstng schemes. For effcent executon, more dynamc data tem should be art of sub-uery nvolvng larger number of data tems. Our method of executng ueres over dynamc data dssemnaton networ s ractcal snce t can be mlemented usng a mechansm smlar to URL-rewrtng [4] n CDNs. Just le n a CDN, the clent sends ts uery to the central ste. For gettng arorate aggregators (edge nodes) to answer the clent uery (web age), the central ste has to frst determne whch data aggregators have the data tems reured for the clent uery. If the clent uery can not be answered by a sngle data aggregator, the uery s dvded nto sub-ueres (fragments) and each subuery s assgned to a sngle data aggregator. In case of a CDN, web age s dvson nto fragments s a age desgn ssue, whereas, for contnuous aggregaton ueres, ths ssue has to be handled on er-uery bass by consderng data dssemnaton caabltes of data aggregators as reresented n Examle Outlne of the Paer We gve a formal mathematcal defnton of the uery lan selecton roblem n Secton. Query cost model for a mult-data ncoherency bounded aggregaton uery s develoed n Secton 3. The uery cost model uses the data dssemnaton model resented n Secton 3.1 and cosne smlarty measure whch s exlaned n Secton 3.. In Secton 4, we frst rove that the otmzaton roblem resented n Secton s NP-hard then we gve aroxmate algorthms for the roblem. In Secton 5, erformance evaluaton done usng real-world traces s resented to show that our sub-uery based uery evaluaton scheme executes the clent uery at less than one thrd cost comared to other nown schemes. Related wor s resented n Secton 6 and the aer concludes n Secton 7.. QUERY PLAN SELECTION PROBLEM In ths secton, we gve a formal defnton of the otmzaton roblem descrbed n the revous secton. We are gven a set D of data aggregators, set S of data tems and one-to-many mang f: D(S, C) where C s a sub-set of real number reresentng ncoherency bounds for varous data tems (n the set S ) at 33

4 WWW 007 / Trac: Performance and Scalablty aggregators n D. Each ncomng clent uery over the data tems set S S has corresondng weghts gven as a set W. Thus the uery can be reresented as set of tules of data_tem, weght,.e., = {s, w } wth the uery ncoherency bound C. We need to erform the followng two tass such that the number of refreshes to the clent s mnmum: Tas1: Dvde the clent uery = {s, w } nto sub-ueres = { s, w } so that =.e., although dfferent sub-ueres may be executed at dfferent aggregators, combnng ther results gves the value of the clent uery. Tas: Allocate each sub-uery, wth ts ncoherency bound C, to data aggregators. Whle fulfllng the followng condtons: Condton1: Query ncoherency bound s satsfed,.e., C C. The sub-uery should be assgned to a data aggregator d D ff: Condton: The chosen aggregator should have all the data tems aearng n the sub-uery.e. S ( ) S ( f ( d )). Here ndcates roject oerator n relatonal algebra. Condton3: Data ncoherency bounds at the selected data aggregator c j = C ( σ ( f ( d )) s= s ( j) should be such that C X where s (j) s the j th data tem aearng n the subuery and X s the tghtest ncoherency bound the aggregator can ensure for the gven sub-uery. X can be calculated as: X =c j w j. Here ndcates select oerator n relatonal algebra. 3. QUERY COST MODEL Before develong the uery cost model we frst summarze the model to estmate the number of refreshes reured to dssemnate a data tem at certan ncoherency bound. For smulaton exerments we use data tems from sensor networ and stoc data domans as exlaned n our revous wor [9]. Stoc traces of 45 stocs were obtaned by erodcally ollng htt://fnance.yahoo.com. Sensor networ data used were temerature and wnd sensor data from Georges Ban Cruses Albatross Shboard [13]. Due to aucty of sace we resent results usng stoc data only but smlar results were obtaned for sensor data as well [14]. For detaled analyss and smulaton results, readers can refer to the extended verson of the aer [10]. 3.1 Data Dssemnaton Cost Cost of dssemnatng a data tem at a certan gven ncoherency bound C can be estmated by combnng two models: Incoherency bound model s used for estmatng deendency of data dssemnaton cost over the desred ncoherency bound. As er ths model, we have shown n [10] that the number of data refreshes s nversely roortonal to the suare of the ncoherency bound (1/C ). Smlar result was earler reorted n [5] where the data dynamcs was modeled as a randomwal rocess. Data dssemnaton cost 1/C (4) Sesson: Scalable Systems for Dynamc Content Data Synoss Model s used for estmatng the effect of data dynamcs on number of data refreshes. We defne a data dynamcs measure called, sumdff, to obtan a synoss of the data for redctng the dssemnaton cost. The number of udate messages for a data tem s lely to be hgher f the data tem changes more n a gven tme wndow. Thus we hyothesze that cost of data dssemnaton for a data tem wll be roortonal to sumdff, defned as: R s = s s 1 (5) where s and s -1 are the samled values of the data tem at th and (-1) th tme nstances (consecutve tcs). In [10] we corroborate the above hyothess usng smulaton over a large number of data tems. Pearson roduct moment correlaton coeffcent (PPMCC) [19] values, used for uantfyng lnearty between data sumdff and number of refreshes reured to mantan a fxed ncoherency bound, were found to be between 0.90 and 0.96 for varous values of ncoherency bounds. Sumdff value for a data tem can be calculated at the data source by tang runnng average of dfference between data values at the consecutve tcs. A data aggregator can also estmate the sumdff value by nterolatng the dssemnated values. Thus, the estmated dssemnaton cost for data tem S, dssemnated wth an ncoherency bound C, s roortonal to R s /C. Next we use ths result for develong the uery cost model. 3. Query Dssemnaton Cost Consder a case where a uery conssts of two data tems P and Q wth weghts w and w resectvely; and we want to estmate ts dssemnaton cost. If data tems are dssemnated searately, the uery sumdff wll be: R w R + w R = w + w (6) data = 1 1 Instead, f the aggregator uses the nformaton that clent s nterested n a uery over P and Q (rather than ther ndvdual values), t maes a comoste data tem w +w and dssemnates that data tem then the uery sumdff wll be: Ruery = w ( 1 ) + w ( 1 ) R uery s clearly less than or eual comared to R data. Thus we need to estmate the sumdff of an aggregaton uery (.e., R uery ) gven the sumdff values of ndvdual data tems (.e., R and R ). Only data aggregators are n oston to calculate R uery as dfferent data tems may be from dfferent sources. We develo the uery dssemnaton model n two stages Quantfyng correlaton between dynamcs of data From Euatons (6) and (7) we can see that f two data tems are correlated such that f value of one data tem ncreases, that of the other data tem also ncreases, then R uery wll be closer to R data whereas f the data tems are nversely correlated then R uery wll be less comared to R data. Thus, ntutvely, we can reresent the relatonsh between R uery and sumdff values of the ndvdual data tems usng a correlaton measure assocated wth the ar of data tems. Secfcally, f s the correlaton measure then R uery can be wrtten as: R uery (7) ( w R + w R + ρw R w R ) (8) 34

5 WWW 007 / Trac: Performance and Scalablty The correlaton measure s defned such that 1 +1, so, R uery wll always be less than w R +w R (as exlaned earler) and always be more than w R w R. The correlaton measure can be nterreted as cosne smlarty [0] between two streams reresented by data tems P and Q. Cosne smlarty s a wdely used measure n nformaton retreval doman where documents are reresented usng a vector-sace model and document smlarty s measured usng cosne of angle between two document reresentatons. For data streams P and Q, can be calculated as: ( 1)( 1) ρ = (9) ( ) ( ) Query normalzaton Suose we want to comare the cost of two ueres: a SUM uery nvolvng two data tems and an AVG uery nvolvng the same data tems. Let the uery ncoherency bound for the SUM and the AVG ueres be C 1 =C and C =C, resectvely. From Euaton (8), sumdff of the SUM uery wll be double that of the AVG uery (as the weght of each data tem n the SUM uery s double of that n the AVG uery). Hence, uery evaluaton cost (as er R /C ) of the SUM uery wll be half that of the AVG uery (as SUM uery ncoherency bound s double). But, ntutvely, dssemnatng the SUM of two data tems, at double the ncoherency bound should reure the same number of messages as ther AVG. Thus, there s a need to normalze uery costs. From a uery executon cost ont of vew, a uery wth weghts w and ncoherency bound C s same as uery wth weghts w and ncoherency bound.c. So, whle normalzng we need to ensure that both, uery weghts and ncoherency bounds, are multled by the same factor. Normalzed uery sumdff s gven by: R uery ( w R + wr + ρw RwR ) = (10) ( w + w + ρw w ).e., the value of the normalzng factor should be 1/ w + w + ρw w. The value of the ncoherency bound has to be adjusted by the same factor. Normalzaton ensures that ueres wth arbtrary values of weghts can be comared for executon cost estmates. From Euatons (9 and 10) the value of uery sumdff can be estmated at a data aggregator node f t has all the reured data tems dssemnated to t. An aggregator can use nterolated values of data tems to estmate as t s not (always) lely to have all the data udates. In the extended verson of the aer [10] we resent an effcent method (usng [1]) to calculate whch can also be used when the corresondng data tems are not beng dssemnated by the same data aggregator. Euaton (10) can be extended to get uery sumdff for any general weghted aggregaton uery gven by Euaton (1) as: R Q n w R + ρjww jr R = 1 = 1 j = 1, j = n n n w + ρ w w = 1 = 1 j = 1, j n n j j j (11) Sesson: Scalable Systems for Dynamc Content 3..3 Valdatng the uery cost model To valdate the uery cost model we erformed smulatons by constructng more than 50 weghted aggregaton ueres usng the stoc data wth each uery consstng of 3-7 data tems wth data weghts unformly dstrbuted between 1 and 10. For each uery the number of refreshes was counted for varous normalzed ncoherency bounds between 0.01 and 0.5. Fgure shows that the number of messages s roortonal to the normalzed uery sumdff as calculated usng Euaton (11) f ther normalzed ncoherency bounds are same. In ths case PPMCC value s found to be 95%. Smlarly, Fgure 3 shows the deendence of the number of refreshes on 1/C to rove that the relatonsh that holds between them for sngle data tem also holds for a uery wth multle data tems. The uery cost model can be used n varous alcatons of uery assgnment, load balancng, otmal order of rocessng, etc. In the next secton, we use ths uery cost model for our uery lan roblem to otmally dvde a clent uery nto sub-ueres and execute t over a networ of data aggregators so that the number of refreshes can be mnmzed Fgure : Varaton of uery cost wth uery sumdff (Normalzed C=0.3) Fgure 3: Number of refreshes for varyng uery ncoherency bounds 4. EXCEUCTING QUERIES USING SUB- QUERIES For executng an ncoherency bounded contnuous uery, a uery lan s reured whch ncludes the set of sub-ueres, ther ndvdual ncoherency bounds and data aggregators whch can execute these sub-ueres. We need to fnd the otmal uery executon lan whch satsfes clent coherency reurement wth the least number of refreshes. As exlaned n Secton 1, what we need s a mechansm to: Tas 1: Dvde the aggregaton uery nto sub-ueres; and 35

6 WWW 007 / Trac: Performance and Scalablty Tas : Allocate the uery ncoherency bound among them. whle satsfyng the followng condtons dentfed n Secton : condton 1. Query ncoherency bound s satsfed. condton. The chosen DA should be able to rovde all the data tems aearng n the sub-uery assgned to t. condton 3. Data ncoherency bounds at the chosen DA should be such that the sub-uery ncoherency bound can be satsfed at the chosen DA. Objectve : Number of refreshes should be mnmzed. Let the clent uery be dvded nto N sub-ueres { : 1N}; wth R beng sumdff of th sub-uery and C beng ncoherency bound assgned to t. As gven s Secton 3, the dssemnaton cost of a sub-uery s estmated to be roortonal to R /C. Thus uery cost estmate s gven by: N Z = ( R / C (1) = 1 Whle allocatng sub-uery ncoherency bounds we need to ensure that the uery coherency reurement C s satsfed (condton1);.e., N C C = 1 ) (13) For satsfyng condton, sub-ueres should be such that all ts data tems can be dssemnated by the chosen DA. Let X be the tghtest ncoherency bound (defned n Secton ) the chosen DA can satsfy for. For the condton3, we have to ensure that C X for each sub-uery and ts assgned data aggregator. Z needs to be mnmzed for mnmzng the number of refreshes as er the objectve. Before attemtng the hard roblem of otmzng Z, let us frst consder a smler roblem where values of C are gven. In ths smler roblem we dvde the clent uery nto sub-ueres to mnmze the estmated executon cost (Z) wthout consderng the otmal dvson of the uery ncoherency bound nto sub-uery ncoherency bounds. Besdes worng as a ste towards a soluton for the whole roblem ths case can also be used where allocaton of ncoherency bounds to sub-ueres s done ndeendent of the data dynamcs. For examle, t may be re-decded that ncoherency bounds for all data tems wll be the same. Thus, for a gven uery and ts ncoherency bounds, the sub-uery ncoherency bounds can be obtaned. Next we rove that ths smler verson of the roblem s NP-hard. 4.1 Fndng Otmal Query Plan s NP-hard For rovng that the roblem s NP-hard, we use reducton from 3-dmensonal matchng (3DM) roblem. For a gven clent uery and DA, let us frst defne maxmal sub-uery as the largest art of the uery whch can be dssemnated by the DA (.e., the maxmal sub-uery has all the uery data tems whch the DA can dssemnate at the reured ncoherency bound). For examle, for a clent uery 0S 1 +5S +35S 3 wth ncoherency bound 80; let the re-decded ncoherency bound for each data tem be 1. For the data aggregators D1 and D gven n Examle 1, the maxmal sub-uery for D1 wll be 1 =0S 1 +35S 3, whereas for D t wll be =0 S 1 + 5S. 3DM Problem: Gven three sets X, Y and Z, each wth N elements, and a set M X Y Z, s there a subset M1M such that M1 =N and no two elements of M1 agree n any coordnate? We use a slghtly dfferent (decson) verson of the otmzaton roblem to reduce the 3DM roblem. To solve the 3DM roblem we reduce t to a SUM uery of 3N tems: N The SUM uery: ( x + y + z ) for x X, y Y, z Z. Sesson: Scalable Systems for Dynamc Content = 1 We assume that all the data tems have the same sumdff values of 1; cosne smlarty between all the data tems s 0; and all data tems are allocated an ncoherency bound of 1. For each element (x, y j, z ) M, we assume the exstence of a data aggregator dssemnatng these three data tems only. In the decson verson of otmal lan roblem we as whether there exsts a uery lan wth uery cost estmate value N/3. If a uery lan wth cost estmate value N/3 exsts; t mles that the uery lan has N ueres wth 3 tems each (that wll lead to uery cost value of 1/3 er sub-uery as er Euaton (11) whereas any other combnaton of sub-ueres wll lead to more cost). Three data tems from each chosen data aggregators form a trlet for the set M1 whch solves 3DM. Because of sace constrants we are not gvng the comlete roof of NPhardness of the orgnal roblem. In general, there s no nown aroxmate algorthm for such a roblem. It should be noted that erformng Tas1 for achevng the objectve s NP-hard, so we gve two greedy heurstcs n next two sub-sectons; whereas Tas can be erformed otmally wth condtons1-3 whle achevng the objectve. In our aroach, we frst try to erform Tas1, whle satsfyng as many condtons as ossble, and then otmally erform Tas whle satsfyng all the condtons. 4. Mnmum Cost Heurstc Fgure 4 shows the outlne of greedy heurstcs where dfferent crtera () can be used to select sub-ueres. In ths secton we descrbe the case where the estmate of uery executon cost s mnmzed n each ste of the algorthm (mn-cost) whereas n the next secton we resent the case where gan due to executng a uery usng sub-ueres s maxmzed (max-gan) Query Plan wth Pre-decded Incoherency Bound Allocaton For the gven clent uery () and mang between data aggregators and the corresondng {data-tem, data ncoherency bound} ars (f: D(S, C)) maxmal sub-ueres can be obtaned for each data aggregator. Let A be the set of such maxmal subueres. In ths set, each uery a A can be dssemnated by a desgnated data aggregator at the assgned ncoherency bound. For each sub-uery a A, ts Sumdff R a s calculated usng Euaton 11. Usng the set A and sub-uery sumdffs, we use the algorthm outlned n Fgure 4 to get the set of sub-ueres mnmzng the uery cost. In ths Fgure each sub-uery a A s reresented by the set of data tems covered by t. As we need to mnmze the uery cost, a sub-uery wth mnmum cost er data tem s chosen n each teraton of the algorthm.e., crtera mnmze (R a /C a a ). All data tems covered by the selected subuery are removed from all the remanng sub-ueres n A before erformng the next teraton. 36

7 WWW 007 / Trac: Performance and Scalablty Result whle A choose a sub-uery a A wth crtera Result Result a A A-{a} for each data element e a for each b A b b-{e} f b = A A-{b} else calculate sumdff for modfed b return Result Fgure 4: Greedy algorthm for uery lan selecton 4.. Otmzng uery executon cost Now we consder the overall roblem to select the otmal set of sub-ueres whle smultaneously dvdng the uery ncoherency bound among them. In ths case we get the set of maxmal ueres (A) wthout consderng the mnmum ncoherency bounds that the data aggregators can satsfy (.e., condton3). In ths algorthm we frst get the otmal set of sub-ures wthout consderng the condton3 and then allocate ncoherency bound among them usng condton1 (Euaton (13)) and condton3. Lagrange multler scheme can be used to solve for ncoherency bounds (from Euatons 1 & 13) so that Z s mnmzed: C = R N = 1 C /( R ) (14).e., wthout the constrants of condton3, sub-uery ncoherency bounds should be allocated n roorton to R. Usng Euatons (1) and (14) we get: Z N 1/ 3 1 R / 3 = 1 = C (15) From Euaton (15), t s clear that for mnmzng the uery executon cost we should select the set of sub-ueres so that 3 R s mnmzed. We can do that by usng crtera 1/ mnmze ( R a / a ) n the algorthm descrbed n Fgure 4. Once we get the otmal set of sub-ueres we can use the Euaton (13) and condton3 (C X ) to otmally allocate the uery ncoherency bound among them. Ths allocaton roblem can be solved by varous convex otmzaton technues avalable n the lterature such as gradent descent method, barrer method etc. We used gradent descent method (fmncon functon n MATLAB) to solve ths non-lnear otmzaton roblem to get the values of ndvdual sub-uery ncoherency bounds. But ths method of frst selectng sub-ueres and then allocatng the ncoherency bounds has a roblem whch s descrbed next Satsfablty of Condton 3 In the soluton descrbed n the revous secton, we select the set of sub-ueres (and corresondng DAs) and then allocate the uery ncoherency bound among them usng convex otmzaton technues. But the roblem of ncoherency bound allocaton among chosen DAs may not have any feasble soluton. There may be stuatons where, although the data dssemnaton networ s able to satsfy the uery coherency reurements but once the set of sub-ueres (and corresondng DAs) s selected the ncoherency bound allocaton s not ossble. Examle : Consder a clent uery 50S S + 150S 3 wth the ncoherency bound of 80 and data dssemnaton networ consstng of two aggregators D1 and D as gven n Examle 1. There are (at-least) two ossble uery lans to answer the above uery: Plan1: D1 (50S S 3 ); D (S ) Plan: D1 (S 3 ); D (50S S ) In Secton 4.. we are selectng sub-ueres havng mnmum R, thus based on data dynamcs t s ossble that we select lan as the otmal lan. But from the data ncoherency bounds that aggregators D1 and D can ensure, we see that t s not ossble for lan to satsfy the clent secfed ncoherency bound as mnmum ncoherency bound that can be satsfed by the selected aggregators (X=50*1 +00* *0. =100) s greater than the uery ncoherency bound (=80). Thus although there exsts a lan (lan1) whch can satsfy the clent uery ncoherency bound, whle mnmzng the uery executon cost the above method cannot ensure that such a lan wll be selected. What we need s a comromse between the uery satsfablty and erformance. In Secton 4.. we are selectng the sub-ueres wthout consderng the data ncoherency bounds for the selected data aggregators. We correct that by selectng sub-ueres usng αx a ( Ra + ) as substtute objectve functon nstead of CR a R a. The second term ensures that whle selectng the otmal lan we refer the data aggregators havng tghter data ncoherency bounds (lower values of X a ) thus hgher chances of satsfyng the uery. The tunng arameter () can used to balance the objectves of mnmzng uery executon cost through subueres selecton and meetng the uery coherency reurements. We use X a / CRa n the second term as, accordng to Euaton (14), otmal ncoherency bound allocaton s lely to be done roortonal to CR a. In Secton 5., we measure effects of the tunng arameter on the uery satsfablty. 4.3 Maxmum Gan Heurstc In ths secton we resent an algorthm whch, nstead of mnmzng the estmated uery executon cost, maxmzes the estmated gans of executng clent uery usng sub-ueres. In ths algorthm, for each sub-uery, we calculate the relatve gan of executng t by fndng the sumdff dfference between cases when each data tem s obtaned searately and when all the data tems are aggregated as a sngle sub-uery. Thus, the relatve gan for a sub-uery w +w can be wrtten as: G uery Sesson: Scalable Systems for Dynamc Content = ( w R ( w R + w R + w R + ρw ) 1 w R R ) (16) Ths algorthm can be mlemented by usng crtera maxmze (G uery / a ) to get the set of sub-ueres and corresondng DAs. Then we use the convex otmzaton method outlned n Secton 4. to allocate ncoherency bounds among sub-ueres. To tacle the uery satsfablty ssue the uery gan Euaton (16) s modfed to: 37

8 WWW 007 / Trac: Performance and Scalablty G + w ' α( ) uery = Guery CRuery w X X (17) where X s mnmum ncoherency bound that can be satsfed for the data tem P; C s uery ncoherency bound and R uery s the uery sumdff (= ( w R + wr + ρw wrr ) ). Reasons for selectng the artcular substtute objectve functon are same as ones outlned n Secton In the next Secton, through erformance results, we show that ths algorthm erforms better than the mn-cost heurstc. 5. PERFORMANCE EVALUATION For erformance evaluaton we smulated the data dssemnaton networs of 5 stoc data tems over 5 aggregator nodes such that each aggregator can dssemnate combnatons of u to 10 data tems wth data ncoherency bounds chosen unformly between $0.005 and 0.0. Then we created 500 ortfolo ueres such that each uery has u to 10 randomly (unformly) selected data tems wth weghts varyng between and 10. These ueres were executed wth ncoherency bounds between 0.3 and 1.0 (.e., % of the uery value). In the frst set of exerments, we et the data ncoherency bounds at the data aggregators very low so that uery satsfablty can be ensured. 5.1 Comarson of algorthms For comarson wth our algorthms, resented n the revous secton, we consder varous other uery lan otons. Each uery can be executed by dssemnatng ndvdual data tems or by gettng sub-uery values from DAs. Set of sub-ueres can be selected usng sumdff based aroaches or any other random selecton. Sub-uery (or data) ncoherency bound can ether be re-decded or otmally allocated. Varous combnatons of these dmensons are covered n the followng algorthms: 1. No sub-uery, eual data ncoherency bound (naïve): In ths algorthm, the clent uery s executed wth each data tem beng dssemnated ndeendent of other data tems n the uery. Incoherency bound s dvded eually among the data tems. Ths algorthm acts as a baselne algorthm.. No sub-uery, otmal ncoherency bound (otc): In ths algorthm also data tems are dssemnated searately but ncoherency bound s dvded among data tems so that total number of refreshes can be mnmzed. Ths algorthm s smlar to the one resented n [11]. Here, the ncoherency bound s allocated dynamcally usng Euaton (14). 3. Random sub-uery selecton (random): In ths case, subueres are generated by randomly selectng one data aggregators and allocatng t the maxmal sub-uery consstng of uery data tems whch the aggregator can dssemnate. Then the rocess s reeated for the remanng data tems untl the whole uery s covered. Ths algorthm s desgned to see how the sub-uery selecton based on uery sumdff (Secton 4) wors n comarson to random selecton of sub-ueres. 4. Sub-uery selecton whle mnmzng sumdff (mn-cost): Ths algorthm s descrbed n Secton Sub-uery selecton whle maxmzng gan (max-gan): Ths algorthm s descrbed n Secton 4.3. Sesson: Scalable Systems for Dynamc Content Fgure 5 shows average number of refreshes reured for uery ncoherency bounds of $0.3, $0.5 and $0.8. The naïve algorthm reures more than three tmes the number of messages comared to mn-cost and max-gan algorthms. For ncoherency bound of $0.8 each uery reures 104 messages f t s executed just by otmzng ncoherency bound (otc) comared to 55 when we select the uery lan usng the max-gan algorthm. Further, although the otmzaton roblem s smlar to the coverng a set of data tems (uery) usng ts sub-sets (sub-ueres) for whch the greedy mn-cost algorthm s consdered to be most effcent [7], we see that max-gan algorthm reures 0-5% less messages comared to the mn-cost aroach. Reasons for max-gan algorthm erformng better than other algorthms are exlored n the next set of exerments. Although here we resented results for stoc traces (man-made data) smlar results were obtaned for sensor traces (natural data) as well. Fgure 5: Performance evaluaton of algorthms 5. Effect of Algorthmc Parameters These set of exerments were erformed to get an nsght nto varous characterstcs of our sub-uery selecton method whch lead t to erform better comared to other otons. We consder effects of three arameters on sub-uery selecton and, n turn on uery erformance: data dynamcs, correlaton between data dynamcs and uery satsfablty arameter Effect of data dynamcs In ths set of exerments, we wanted to see whether there s any defnte relatonsh between data dynamcs and sub-uery sze n whch that data tem aears. In ths exerment wth 10 data tems, 45 DAs were smulated such that each DA can dssemnate a dfferent set of data tems. Then 100 ueres were created each wth 3 data tems. In the otmal uery lan, each uery wll be executed wth two sub-ueres: one consstng of data tems and another wth sngle data tem (lan wth three one tem subueres wll be trvally neffcent). As the uery has only 3 data tems, only 3 such uery lans are ossble. We smulated all these otons to get the best uery lan. Fgure 6 shows varaton of average sub-uery sze n whch a artcular data tem aears versus sumdff value of the data tem. We can see that f a data tem s more dynamc, n the otmal lan, t s more lely to be art of larger sub-uery. Ths s an mortant observaton as t ndcates that for effcent uery evaluaton more dynamc data tems should be art of a larger sub-uery. Ths henomenon can be exlaned by the fact that by executng a uery as a combnaton of sub-ueres wll always be more effcent comared to gettng the data tems ndeendently. By combnng 38

9 WWW 007 / Trac: Performance and Scalablty Fgure 6: Effect of data sumdff on sub-uery sze more dynamc data tems we are lely to gan more. For comarson we also show the curve for the sub-uery selecton based on max-gan algorthm. It can be seen that sub-uery selecton usng max-gan s aroxmately same as that selected by the otmal soluton. By usng max-gan algorthm we acheve our objectve of dssemnatng more dynamc data tems as art of larger sub-ueres. For the max-gan algorthm, smlar results were obtaned for larger uery szes as well. In comarson, n the mn-cost algorthm most dynamc data tem s more lely to be dssemnated as sngle tem uery. Ths haens because the sumdff value of a more dynamc data tem wll be hgh thus n each ste of the mn-cost algorthm (Fgure 4), there s less chance of selectng a sub-uery wth more dynamc data tem. Thus, t s very lely that the hghly dynamc data tem wll be dssemnated as a sngle tem sub-uery resultng n bad erformance of the clent uery. Stll the mn-cost algorthm erforms better comared to random algorthm as t tres to execute the uery wth lesser number of sub-ueres. 5.. Effect of correlaton between data dynamcs To measure the effects of correlaton between data dynamcs (cosne smlarty) on the uery erformance, we comared the uery erformance wth the case when all the data tems are assumed to be ndeendent (.e., =0). For erformng these exerments we constructed 10 synthetc data traces so that values of for varous data tem ars were dstrbuted unformly between -1 and +1. Then 45 DAs were smulated so that each DA can dssemnate data tems. 100 ueres were generated, each wth 4 data tems. In ths case, each uery wll get executed wth sub-ueres of data tems each. Combnaton of sub-ueres wll be decded based on correlaton between data tems (sumdff values of all the data tems were the same). Table 1 comares the Table1: Effect of correlaton on number of refreshes Incoherency Bound Avg. number of msgs when s consdered Avg. number of msgs when s assumed to be results when cosne smlarty s taen nto account and when cosne smlarty s assumed to be 0 for all data tem ars. It can be seen that by consderng cosne smlarty number of refreshes reduce by aroxmately 1%. Ths result ndcates that for subuery selecton data dynamcs may be more mortant factor than the cosne smlarty between the data tems. Sesson: Scalable Systems for Dynamc Content 5..3 Effect of uery satsfablty arameter To smulate the stuaton where selected aggregators may not be able to satsfy the uery ncoherency bounds, we modfed the smulaton set u used n Secton 5.1 to set the mnmum data ncoherency bounds whch DAs can satsfy to be between.015 and Value of was vared between 0-0. The case =0 corresonds to the algorthm wthout dealng wth the uery satsfablty. Fgure 7 shows uery executon cost and number of unanswerable ueres as the value of s vared. As shown n the fgure as the value of s ncreased, ercentage of the unsatsfed ueres decreased for varous values of uery ncoherency bounds. Due to changed data ncoherency bounds of DAs, we found that 0% of ueres can not be satsfed even by the data aggregators wth tghtest data ncoherency bounds. Thus, whle resentng the results, we remove those ueres. At the uery ncoherency bound of $0.8, 40% are ueres can not be satsfed by the otmally Fgure 7: Effect of on uery satsfablty selected data aggregators but as we ncrease the value of to 10, only 3% ueres are unanswered. Such a value can be chosen to balance the erformance and satsfablty of ueres. For examle, a dynamc CDN may am at uery satsfablty of 95% for a gven dstrbuton of uery ncoherency bounds. If at any tme uery satsfablty s below the target, value of can be ncreased whereas n case of over achevng the target, the value of can be decreased to mrove the uery erformance Summary of erformance results Followng features of the uery lannng algorthm mrove erformance: Dvdng the uery nto sub-ueres and executng them at secfcally chosen data aggregators. Decdng the uery lan usng data sumdff based mechansm secfcally by maxmzng sub-uery gans. Includng more dynamc data as art of a larger sub-uery. We also showed that the max-gan algorthm s very close to the otmal algorthm n selectng sub-ueres based on data dynamcs. 6. RELATED WORK Varous mechansms for effcently mantanng ncoherency bounded aggregaton ueres over contnuously changng data tems are roosed n the lterature [11, 1, 16]. Our wor dstngushes tself by beng sub-uery based evaluaton to mnmze number of refreshes. In [11], authors roose usng data flters at the sources; nstead we assgn ncoherency bounds to sub-ueres whch reduce the number of refreshes for uery evaluaton, as exlaned n Secton 39

10 WWW 007 / Trac: Performance and Scalablty 5. Further, we roose that more dynamc data tems should be executed as art of larger sub-uery. In [], authors resent technue of reorganzng a data dssemnaton networ when clent reurements change. Instead, we try to answer the clent uery usng the exstng networ. Reorganzng aggregators s a longer term actvty whereas uery lannng can be done for short as well as long runnng ueres on more dynamc bass. Pull based data dssemnaton technues, where clents or data aggregators ull data tems such that uery reurements are met, are descrbed n [9,16]. For mnmzng the number of ulls, both model the ndvdual data tems and redct data values. In comarson, we consder the stuaton where dfferent sub-ueres, nvolvng multle data tems, can be evaluated at dfferent nodes. Further, ncoherency bound s aled over the sub-uery rather than to ndvdual data tems, leadng to effcent evaluaton of the uery. Satal and temoral correlatons between sensor data are used to reduce data refresh nstances n [17, 18]. We also consder correlaton n terms of cosne smlarty between data tems, but we use t for dvdng clent uery nto sub-ueres. Our wor can be extended by usng temoral and satal roertes of data tems for redctng ther correlaton measures. A method of assgnng clents data ueres to aggregators n a content dstrbuton networ s gven n [1]. We do for clent ueres consstng of multle data tems what [1] does for clent reurng ndvdual data tems. 7. CONCLUSIONS Ths aer resents a cost based aroach to mnmze the number of refreshes reured to execute an ncoherency bounded contnuous uery. For otmal executon we dvde the uery nto sub-ueres and evaluate each sub-uery at a chosen aggregator. Performance results show that by our method the uery can be executed usng less than one thrd the messages reured for exstng schemes. Further we showed that by executng ueres such that more dynamc data tems are art of a larger sub-uery we can mrove erformance. Our method of uery executon can be mlemented usng schemes smlar to that used n CDNs. Our uery cost model can also be used for other uroses such as load balancng varous aggregators, otmal uery executon lan at an aggregator node, etc. Usng the cost model for other alcatons and develong the cost model for more comlex ueres s our future wor. Acnowledgement: We would le to than Venatesan Charavarthy and Vnaya Pandt for helful dscusson on varous algorthms. 8. REFERENCES [1] A. Davs, J. Parh and W. Wehl. Edge Comutng: Extendng Enterrse Alcatons to the Edge of the Internet. WWW 004 [] D. VanderMeer, A. Datta, K. Dutta, H. Thomas and K. Ramamrtham. Proxy-Based Acceleraton of Dynamcally Generated Content on the World Wde Web. ACM Transactons on Database Systems (TODS) Vol. 9, June 004. [3] J. Dlley, B. Maggs, J. Parh, H. Proo, R. Staraman and B. Wehl. Globally Dstrbuted Content Delvery, IEEE Internet Comutng Set 00. Sesson: Scalable Systems for Dynamc Content [4] S. Rangarajan, S. Muerjee and P. Rodrguez. User Secfc Reuest Redrecton n a Content Delvery Networ, 8 th Intl. Worsho on Web Content Cachng and Dstrbuton (IWCW), 003. [5] S. Shah, K. Ramamrtham, and P. Shenoy. Mantanng Coherency of Dynamc Data n Cooeratng Reostores. VLDB 00. [6] Dynama: Cachng Technology for Dynmac Content Revealed. [7] D. S. Hochbaum. Aroxmaton algorthms for the set coverng and vertex cover roblems. SIAM Journal on Comutng, vol. 11 (3), 198. [8] Zongmng Fe. A Novel Aroach to Managng Consstency n Content Dstrbuton. WCW 001 [9] R. Guta, A. Pur, and K. Ramamrtham. Executng Incoherency Bounded Contnuous Queres at Web Data Aggregators. WWW 005. [10] Otmzed Executon of Contnuous Queres, APS 006, [11] C. Olston, J. Jang, and J. Wdom. Adatve Flter for Contnuous Queres over Dstrbuted Data Streams. SIGMOD 003. [1] S. Shah, K. Ramamrtham, and C. Ravshanar. Clent Assgnment n Content Dssemnaton Networs for Dynamc Data. VLDB 005. [13] NEFSC Scentfc Comuter System htt://sole.wh.who.edu/~jmannng//cruse/serve1.cg [14] Query cost model valdaton for sensor data. [15] D. S. Hochbaum. Aroxmaton algorthms for the set coverng and vertex cover roblems. SIAM Journal on Comutng, vol. 11 (3), 198. [16] S. Zhu and C. Ravshanar. Stochastc Consstency and Scalable Pull-Based Cachng for Erratc Data Sources. VLDB 004. [17] D. Chu, A. Deshande, J. Hellersten, W. Hong. Aroxmate Data Collecton n Sensor Networs usng Probablstc Models. ICDE 006. [18] A. Deshande, C. Guestrn, S. R. Madden, J. M. Hellersten, and W. Hong. Model-Drven Data Acuston n Sensor Networs. VLDB, 004. [19] Pearson Product moment correlaton coeffcent. htt:// / [0] Lam, W. and Ho, C.Y. Usng a Generalzed Instance Set for Automatc Text Categorzaton. SIGIR, [1] G. Cormode and M. Garofalas. Setchng Streams through the Net: Dstrbuted Aroxmate Query Tracng. VLDB 005. [] S. Agrawal, K. Ramamrtham and S. Shah. Constructon of a Temoral Coherency Preservng Dynamc Data Dssemnaton Networ. RTSS