TEMPLATE FOR ENTRY in Encyclopedia of Database Systems: GRID FILE. Yannis Manolopoulos

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1 TEMPLATE FOR ENTRY in Enylopedi of Dtse Systems: GRID FILE Apostolos N. Ppdopoulos Ynnis Mnolopoulos Ynnis Theodoridis Vssilis Tsotrs Deprtment of Informtis Aristotle University of Thessloniki Thessloniki, Greee Deprtment of Informtis Aristotle Universityof Thessloniki Thessloniki, Greee Deprtment of Informtis University of Pireus Pireus, Greee Deprtment of Computer Siene nd Engineering University of Cliforni t Riverside Riverside, CA, USA tsotrs@s.ur.edu SYNONYMS DEFINITION [5 or fewer words defining the entry title] The Grid File is multidimensionl indexing sheme ple to effiiently index dtse reords in symmetril mnner, i.e. y voiding the distintion etween primry nd seondry keys. The struture is dynmi nd dpts grefully to its ontents under insertions nd deletions. A single reord retrievl osts two disk esses t most (upper ound), wheres rnge queries nd prtil mth queries re lso exeuted effiiently. The Grid File n e thought of s generliztion of dynmi hshing (e.g., extendile hshing) in multiple dimensions. HISTORICAL BACKGROUND [5 or fewer words desriing when/why the onept or tehnique developed] Until the 8 s there hve een proposed mny file strutures for the proessing of single ttriute queries, i.e. queries on the primry key or ny seondry key for whih orresponding index hs een uilt. Multi-ttriute queries re the ones where the user seeks ojets tht stisfy onstrints (suh s equlity or rnge) on severl ttriutes. Suh queries n e exeuted y essing ll the orresponding indies (if they exist) nd omine the prtil results, or resort to sequentil snning. To speed up the proessing of multiple ttriute queries etter solution is to rete n index tht leds the serh diretly to the ojets of interest. Suh n index n e designed if we envision dt reord with k ttriutes s point in k-dimensionl spe. A multi-ttriute rnge query would then e hyperretngle in this k-dimensionl spe nd the nswer to it would e ll points inside this retngle. Aess methods tht n hndle multi-dimensionl points re lled Point Aess Methods (PAMs). Bentley in 975 proposed suh si PAM, whih is lled k-dimensionl tree or k-d tree []. The Grid File is yet nother struture designed to hndle similr ses, proposed y Nievergelt, Hintererger nd Sevik in 98 [9]. Sine then, severl vritions hve een proposed in the literture in n effort to optimize its spe nd time performne ehvior. SCIENTIFIC FUNDAMENTALS [illustrtion nd elortion of the entry title definition, nd outline the key points] The Grid File n e viewed s n ess method omprising of two seprte prts: () the diretory, nd () the liner sles. To oneive this, ssume tht we wnt to index n Employee file using two ttriutes, sy slry nd dept (extension to more dimensions is strightforwrd). The Grid File imposes grid on the two-dimensionl ttriute spe. Eh ell in this grid orresponds to one dt pge. The dt points tht fll inside given ell re stored in the ell s orresponding pge. Eh ell must thus store

2 pointer to its orresponding pge. This informtion is stored in the Grid File s diretory. However, ells tht re empty do not use pge. Rther, two or more ells n shre pge (i.e., point to the sme pge). The grid dpts to the dt density y introduing more divisions in res where there re more points. The informtion of how eh dimension is divided (nd thus how dt vlues re ssigned to ells) is kept through liner sles. There is one liner sle per dimension (indexed ttriute). Eh liner sle is one-dimensionl rry tht divides the vlues on prtiulr dimension in suh wy tht reords (points) re uniformly distriuted ross ells. An exmple of Grid File on the Dept nd Slry ttriutes ppers in Figure. The dotted lines indite ells tht shre dt pge Liner sle on Dept Grid Diretory 5 6 < K -K -5K 5-6K 6-9K 9-K > K Liner sle on Slry pointers to sme dt pge 5 6 Figure. A Grid File. Serhing for reord with given ttriute vlues involves two opertions: () the Grid File s diretory is serhed to lote the ell tht the reord is hosted () the ell s pointer is followed to ess the orresponding dt pge (sy A) nd () the reord is serhed only in dt pge A. If the reord is found in A then the serh termintes suessfully, otherwise the serh for the speifi reord is unsuessful (i.e., the reord does not exist). The Grid File n lso ddress multi-dimensionl rnge queries y seleting from eh dimension s liner sle the pproprite ells. For exmple, suh query my sk for ll employee reords with the slry ttriute rnging etween K nd K nd the dept ttriute rnging etween nd 6. Agin, the first step exmines the diretory nd determines the ells tht re interseted y the query rnge in oth ttriutes, then the orresponding pointers to dt pges re olleted nd finlly the dt pges re exmined for relevnt reords. Apprently, the essed ells my lso ontin some reords outside the query rnge. These reords re evidently eliminted from further onsidertion nd they re not returned s prt of the query nswer. Inserting new reord in this method is strightforwrd. First, the two liner sles re serhed so s to mp the reord s slry nd dept ttriute vlues in eh dimension. This mpping provides ell in the diretory. This ell is then essed nd using its pointer, the pproprite pge, sy A, for the new reord is found. If this pge hs enough spe to ommodte the new reord the insertion proess is omplete. Otherwise, new pge B is lloted. If pge A ws pointed y more thn one ells, the pointers of these ells re rerrnged so s some will point to pge A nd some to pge B (nd the reords of pge A re redistriuted ordingly etween A nd B). If pge A ws pointed y single ell nd overflows, reorgniztion of the Grid File is needed. This reorgniztion will expnd the diretory nd the sles y introduing new olumn (or row) of ells. In the sequel, we illustrte the insertion proess y n exmple given in Figure. White dots orrespond to existing reords, wheres lk dots re used to indite new reords eing inserted to the Grid File. We ssume tht eh dt pge n host t most three reords. Prtilly, this numer is lrger in rel

3 pplitions nd depends on the size of the dt pge nd the numer of ttriutes. We ssume tht initilly the Grid File is empty (does not ontin ny reords). The first three reords n e esily ommodted in the single dt pge A pointed y the single ell of the diretory (orresponding to the whole dt spe), s it is illustrted in Figure (). The next inserted reord is d. However, the new reord n not e hosted y dt pge A euse its pity is exeeded. Therefore, nother dt pge B is lloted nd reords re distriuted to the two dt pges s it is shown in Figure (). The next two insertions for reords e nd f do not use ny reorgniztion sine the new reords n e esily ommodted in the orresponding dt pges pointed y the ells. This se is illustrted in Figure (). Finlly, the insertion of reord g uses n overflow in dt pge A. The orresponding ell is split gin using the other ttriute nd one more dt pge is lloted nd reords re distriuted ordingly. The finl shpe of the Grid File is given in Figure (d).,, A d,, d A B e f d,, e A, d, f B g e f d, g A, d, f B, e C () insertion of, nd () insertion of d () insertion of e nd f (d) insertion of g Figure. Insertions in the Grid File. Deletions re lso supported, ut they re hndled differently. Initilly, the deleted reord is loted using the diretory nd the orresponding dt pge is determined. If the reord is found it is deleted from the dt pge. Insted of overflowing dt pges deletions my use the underutiliztion effet whih mens tht severl dt pges my ontin too few reords. Therefore, pproprite merging opertions re required to mintin the storge utiliztion of the Grid File t n eptle level. For detiled desription of the methods used for merging s well s for splitting the reder is direted to referene [8]. The Grid File hs set of nie properties: () it is sed on simple mehnisms for insertion, deletion nd serh, () it gurntees only two disk esses for ext mth queries (one for the diretory nd one for the dt pge), nd, () it trets ll indexed ttriutes symmetrilly whih leds to simple diretory mngement poliies. However, it hs set of serious disdvntges suh s: () it introdues spe overhed for the diretory, whih n e lrge for high-dimensionl spes, () it hs n extr updte overhed, sine reorgniztion ffets mny ells nd not only the ell with the overflowing pge, nd, () it suffers from performne degrdtion if the ttriutes re orrelted, sine the uniform sheme for performing splits is not dequte to gurntee performne effiieny. Towrds improving the ehvior of the Grid File severl reserh efforts hve een performed. We riefly highlight some of them in the following lines. One of the first vritions, the BANG File, hs een proposed y Freeston []. The BANG File is sed on self-lned tree-sed diretory whih etter reflets hnges of the dt distriution. To hieve etter storge utiliztion the Twin Grid File hs een proposed y Hulflesz, Six nd Widmyer in [6]. The new sheme is s effiient s the originl Grid File during rnge query proessing ut shows signifint improvements regrding storge utiliztion. Blnken et l proposed the Generlized Grid File [] whih offers fst ess for single ttriute queries. The Multilevel Grid File [] is nother reserh effort to improve the performne of the originl struture for ext-mth, prtil-mth nd rnge queries. This new sheme uses multiple grid levels nd sueeds in etter diretory mngement nd more effiient query proessing thn the originl struture. In ddition to the vritions proposed in the literture, there re efforts to use the Grid File in prllel environment, towrds more effiient dt mngement. In [] the uthors study the prolem of prtitioning Grid File to multiple disk devies towrds more effiient serh. When dt pge split is

4 performed, the new dt pge is refully lloted to disk. Sine disks n e essed in prllel, severl dt pges n e red simultneously during rnge query proessing, offering signifint performne improvements in omprison to single-disk system. More omplex queries on Grid Files, like sptil joins, hve een lso prllelized [7] towrds redued query response times. A different pproh hs een followed y [8]. The uthors hve proposed method to lod Grid File in prllel. The dt file is initilly prtitioned to the ville proessors using dynmi progrmming nd smpling, nd then eh proessor uilds its own prt of the Grid File. KEY APPLICATIONS [urrent nd potentil users] Sptil Dtses In Sptil Dtses it is ommonly required to join sptil dt sets or perform nerest neighor serhes. Severl lgorithms hve een proposed for suh opertions y dopting the Grid File s the underlying ess method []. Dt Mining The Grid File n e, lso, used for lustering dt sets to identify orreltion hrteristis of the underlying vlue spe. This stems from its ility to group ptterns into loks nd luster them with respet to the loks y topologil neighor serh lgorithm []. Dt Wrehouses The Grid File n e used for effiient dt ue storge in wrehouses []. FUTURE DIRECTIONS* The Grid File hs eventully ome up s populr theoretil ess method. However, lthough is hs een widely honored in theory, in prtie it hs not een used y the dtse industry. Also, the ft tht n entry for the Grid File exist in Wikipedi [5] shows tht the sujet is rther stilized. EXPERIMENTAL RESULTS * A detiled performne evlution of the Grid File n e found in [9], where the uthors offer detiled experimentl setion studying the properties of the struture regrding pity of dt pges, diretory size nd evlution of splitting nd merging poliies. Moreover, interesting experimentl results n e found in [, 6] whih ompre the originl Grid File with the orresponding vrition proposed in eh work. CROSS REFERENCES [Other topis in the Enylopedi whih my e of interest to the reder of this entry. It is enourged to rediret the reders to n overview entry in the sujet re] EXTENDIBLE HASHING K-D TREES MULTIDIMENSIONAL INDEXING RANGE QUERY SPATIAL JOIN

5 RECOMMENDED READING* [Between 5 nd 5 ittions to importnt literture, e.g., in journls, onferene proeedings, nd wesites] [] Beker L., Hinrihs K., Finke U. (99): A New Algorithm for Computing Joins with Grid Files. ICDE 99: [] Bentley, J.L. (975): Multidimensionl Binry Serh Trees Used for Assoitive Serhing. Communitions of the ACM, 8(9): [] Blnken H.M., Ijem A., Meek P., vn den Akker B. (99): The Generlized Grid File: Desription nd Performne Aspets. ICDE Conferene 99: [] Freeston M. (987): The BANG File: A New Kind of Grid File. SIGMOD Conferene 987: [5] Grid File. Lemm t Wikipedi. [6] Hutflesz A., Six H.-W., Widmyer P. (988): Twin Grid Files: Spe Optimizing Aess Shemes. SIGMOD Conferene 988: 8-9. [7] Kim J.-D, Hong B.-H. (999): Prllel Sptil Join Algorithms using Grid Files. DANTE Conferene 999: 6-. [8] Li J., Rotem D., Srivstv J. (99): Algorithms for Loding Prllel Grid Files. SIGMOD Conferene 99: [9] Nievergelt, J., Hintererger, H., Sevik K.K. (98): The Grid File: n Adptle, Symmetri Multikey File Struture, ACM Trnstions on Dtse Systems, 9():8-7. [] Lim, Y., Kim, M. (): A Bitmp Index for Multidimensionl Dt Cues. DEXA Conferene : [] Luo, C., Hou, W.C., Wng, C.F., Wng, H., Yu X. (6): Grid File for Effiient Dt Cue Storge. Computers nd their Applitions, pp.-9. [] Shikut, E., Erhrt, M. (997): The BANG-Clustering System: Grid-Bsed Dt Anlysis, IDA, p.5, 997. [] Whng K.-Y., Krishnmurthy R. (99): The Multilevel Grid File - A Dynmi Hierrhil Multidimensionl File Struture. DASFAA Conferene 99: [] Zhou Y., Shekhr S., Coyle M. (99): Disk Allotion Methods for Prllelizing Grid Files. ICDE Conferene 99: -5.