A Survey of P2P multidimensional indexing structures Ewout M. Bongers, Johan Pouwelse TU Delft – Course IN4306 – !"terature #ur$e% Abstract — Traditional databases have long 0ase, on geo6lo(at"ons 37gure 84. Th"s "s "nfeas"0le since reaped the benefits of multidimensional w"thout an "n,e.. But e$en ha$"ng an "n,e. o$er the indexes. Numerous proposals in the literature "n,"$",ual ,"-ens"ons "s not enough. 9"th su(h "n,e.es describe multidimensional index designs for P2P the re, an, green 1uer% regions "n the 7gure woul, systems. Ho!ever" none of these designs have nee, to 0e 1uer"e, an, then "nterse(te,, a $er% (ostl% had real !orld implementations. Several an, "ne:("ent operat"on. Th"s )roble- grows when proposals for P2P multidimensional indexes are ,"-ens"ons are a,,e,. Contrar% to th"s, a true -ult","-ens"onal "n,e. not onl% sear(hes all ,"-ens"ons revie!ed and analy#ed. $net and %&'(tree are "n one 1uer%, 0ut e$en gets -ore sele(t"$e as the most promising from a technical standpoint. ,"-ens"ons are a,,e,. All of the proposed designs assume honest nodes and are thus open to abuse. This is a In s"ngl% s%ste- s"tuat"ons, ,ata0ase an, games critical )a! that must be solved before any of engineers ha$e ,e$"se, a )lethora of "n,e."ng stru(tures for -ult","-ens"onal ,ata. These are use, for the proposed systems can be used. e$er%th"ng from enter)r"se ,ata warehouses to (oll"s"on ,ete(t"on "n 3D. Howe$er these stru(tures are not I. INT&'DUCTI'N su"te, to use "n a P2P en$"ron-ent, "f not ,ownr"ght #"n(e the"r "n(e)t"on P2P networ+s ha$e "n(lu,e, "-)oss"0le. #u))ort"ng these -ult","-ens"onal range so-e for- of "n,e."ng to lo(ate "te-s of "nterest. #u(h 1uer"es has )ro$en to 0e (hallenging for P2P networ+s. as DHTs that ena0le +e%wor, sear(h 1uer"es. 2uer"es Therefor th"s sur$e% atte-)ts to answer the 1uest"on; for ranges of +e%s ha$e )ro$en to 0e sl"ghtl% -ore What is the state of the art for multidimensional range (halleng"ng for P2P. But the hol% gra"l of "n,e."ng 3"n queries in P2P networks? general4 "s su))ort"ng a -ult","-ens"onal range 1uer% The organ"5at"on of th"s l"terature sur$e% "s as follows. an, th"s "s -ore (hallenging st"ll to real"5e "n P2P. #e(t"on II shows )rom"nent "n,e."ng stru(tures as To "llustrate the usefulness of -ult","-ens"onal range foun, "n P2P l"terature. #+") l"sts an, s+") graphs are 1uer"es, "-agine want"ng to sear(h a P2P networ+ 0r"e<% ,"s(usse,, as the% are (entral to -an% of the "n,e. stru(tures. #e(t"on III anal%5es the strengths an, weaknesses of the ,"=erent "n,e."ng stru(tures. #e(t"on I> looks at se(ur"t% "ssues surroun,"ng the "n,e."ng stru(tures. II. MU!TIDIMEN#I'N?! INDE@INA #T&UCTU&E# The -etho,s ,e$"se, for -ult","-ens"onal "n,e."ng 3su--ar"5e, "n table 84 roughl% fall "nto two 0as"( )igure 2" A skip list DIE (ategor"es, 7rst "s re,u("ng the ,"-ens"onal"t%, the se(on, "s )art"t"on"ng the -ult","-ens"onal s)ace. &e,u("ng ,"-ens"onal"t% "s usuall% ,one w"th a s)ace 7ll"ng (ur$e, a (ur$e that se1uent"all% nu-0ers all the ,"s(rete )oints of -ult","-ens"onal s)ace. Th"s s"ngle ,"-ens"onal s)ace "s then store, us"ng (on$ent"onal -etho,s l"+e D/Ts or s+") graphs. #)ace )art"t"on"ng "s re(urs"$el% su0,"$","ng s)ace to %"el, regions that (ontain a relat"$el% s-all nu-0er of +e%s. As w"ll 0e shown there are all -anner of $ar"et"es that -". an, (o-0"ne )art"t"on"ng w"th re,u(t"on. #ome "n,e."ng stru(tures are 0ase, on the well +nown )igure *" A skip graph DIE DHT, 0ut others are 0ase, on the lesser +nown s+") "nsert"on an, ,elet"on are -u(h s"-)ler. graph, wh"(h "s "n turn 0ase, on the s+") l"st. Bor the 0ene7t of the lesser "nfor-e, reader, the s+") l"st an, #ear(h"ng 0egins w"th the h"ghest le$el an, ,es(en,s graph w"ll 0e )resente, 7rst. ,own "f the ne.t +e% "n the l"n+e, l"st "s larger than the sear(h +e%. Eventuall% on le$el 0, the sear(h +e% (an 0e A. Skip Lists foun, 3or the start of a range4. The nu-0er of ste)s In 1990 Pugh D8E "ntro,u(e, #+") !"sts. The ,ata nee,e, to 7n, a +e% "s on a$erage '3log n4, w"th the stru(ture starts as a nor-al l"n+e, l"st 3le$el 04. 9"th a log 0ase a fun(t"on of p. Insert"on "s as s"-)le as 7.e, )ro0ab"l"t% p ea(h ele-ent "n the l"st also "nsert"ng an ele-ent "n the le$el 0 l"st, an, ran,om"5"ng )art"(")ates "n a h"gher le$el l"n+e, l"st 3le$el 8, *, "f "t shoul, 0e "n(lu,e, "n the ne.t le$el, an, l"n+ "t "n 3, ...4. B% (hoos"ng a su"ta0le p, the e.)e(tat"on "s that "f nee,e,. Delet"on re1u"res that the ele-ent 0e the h"ghest le$el "s )opulate, w"th a few no,es, an, unl"n+e, from all l"sts "t "s "n(lu,e, "n. The s+") l"st (an thus Fs+")G through the lowest le$el l"st. The also has $er% fa$ora0le (on(urren(% (haracter"st"(s. stru(ture has 3w"th"ng a (ertain -argin of error4 B. Skip Graphs (haracter"st"(s that are $er% s"-"lar to BH trees 3where the )arameter p ,eter-"nes the fan out4. Howe$er As)nes an, #hah D*E, ada)te, the (on(e)t of s+") l"sts to )eer to )eer s%ste-s "n the for- of a s+") gra)h. Node Scaling Performance Dimension Scaling Performance Load Balance Robust Security Drawback Messaging Storage Messaging Storage Skip List O(log i) O(i) - - - - - Not P2P Skip Graph O(log n) O(log n) - - - - - Single Dimensional SCRAP O(log n) O(log n) ? O(1) Passive - - Very poor locality CISS O(log n) O(log n) O(1) O(1) Active ± - Poor locality Squid O(log n) O(log n) O(1) O(1) Passive+Active ± - Poor locality MAAN O(log n) O(log n) O(1) O(k) Passive ± - Depend on selectivity Mercury O(log n) O(log n) O(1) O(k) Passive ± - Depend on selectivity MURK O(log n) ? ? O(kc) Passive - - Storage Cost & Balance Znet O(log n) O(log n) O(1) O(k) Passive+Active ± - Poor locality SkipIndex O(log n) O(log n) O(1) O(k) Active + - Poor locality VBI+R-Tree O(log n) O(log n) ? O(1) Active + - Congestion & Complex Ta le !" #omparison of multidimensional P2P indexing structures &i" data items' n" network nodes' k: dimensions( Man% -ult","-ens"onal 1uer% solut"ons are 0ase, on th"s (on(e)t of s+") gra)hs. The le$el 0 "s the sa-e as the regular s+") l"st, "t "s an or,ere, l"st of ele-ents 3no,es "n the (ase of a P2P o$erla%4. Bor le$el 8 "nstead of ran,om"5"ng a Jo"n6or6 not $alue, ea(h ele-ent ran,om"5es what le$el 8 l"st to Jo"n. #"n(e -ost P2P s%ste-s use ran,om"5e, no,e ",Ks, As)nes an, #hah suggest to use the no,e ID for these ran,om $alues. If le$el 8 "s (ons"sts of n l"sts, the 7rst log(n( 0"ts of the ran,om $alue shoul, 0e use, to ,eter-"ne what le$el 8 l"st to Join. Bor the ne.t le$el the 7rst 2log(n( ran,om 0"ts ,e(",e what l"st to Jo"n. Th"s (ont"nues unt"l the e-)t% l"st "s reache,. Not"(e that ea(h l"st "s ",ent"7e, 0% a 0"t str"ng. All ele-ents #C&AP assu-es that the ,"-ens"ons are 56(ur$e "n a l"st share that l"sts ",ent"7(at"on 0"t str"ng as l"near"5able. Th"s -eans "nterlea$"ng the 0"nar% )re7. of the"r own ran,om IDs. re)resentat"on of $alues from each ,"-ens"on. Thus the The s+") gra)h stru(ture )ro$",es a P2P o$erla% L., %M tu)le L0100, 0101M woul, 0e -ap)e, to $alue stru(ture that wor+s as an or,ere, l"st.