Properties. Properties. Properties. Images. Key Methods. Properties. Internal nodes (other than the root) have between km and M index entries

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1 * - + Genealizing DB Seach Tee Genealized Seach Tee fo Databae Sytem by Joeph M. Helletein, Jeffey F. Naghton, and Ai Pfeiffe Andy Danne Saa Spenkle Balanced tee High fanot Key pedicate, may oelap! " # $ % & '! $ % " ( ) (! ( Motiation Genealizing DB Seach Tee Extenible data and qey model Eae contction of index tcte fo new data and qey type adding new data type Genealized tee tcte fo databae ytem maintaining data and aking qeie Genealized each key + any abitay pedicate that hold fo each datm below the key flexible, abitay neted bcategoie Databae each tee:. hieachy of patition of a data et, in which each patition ha a categoization that hold fo all data in the patition Otline Rnning Example: Image Motiation Genealized Seach Tee (GiST) Algoithm Application GiST Limitation, Extenion Conclion / < : < ; < = A B C D A E F G H I G J K L M N O P Q R S T R U V W V X Y Z W Y [ P T P [ [ M N Y Z W Y [ P R S [ Z P \ ] ^ ^ _ ` a b c ] ] d e f g h i h j k l m i n i h o p q n m p p f t h w p n x i f w y p z g { } ~ { ~ ƒ { ~ 1

2 Ÿ Ÿ Popetie Popetie Intenal node (othe than the oot) hae between km and M index entie ˆ k: minimm fill facto, < ½ ˆ enty: (key/pedicate, pointe) Š Œ Š Ž Š Intenal pedicate ealate to te fo all data intance in btee May not hae hieachical atifiability of pedicate like R-tee ž œ Popetie Image Intenal node (othe than the oot) hae between km and M index entie Root ha at leat two childen nle it i a leaf node All leaf node appea on ame leel Balance tee Bond height of tee ª Ÿ «š š ± Ÿ Ÿ ± ² ± ± ³ < < Popetie Leaf node pedicate ealate to te gien ale of data intance œ ž Ÿ Method ed by GiST to maintain inaiant Implemented by index deelope Application-pecific policie š š œ š š ž 2

3 ö Conitent( Enty E, Pedicate q ) Union( Enty E[] ) Compe( Enty E ) Decompe( Enty E ) Penalty( Enty E1, Enty E2 ) PickSplit( Enty E[] ) Union( Enty E[] ) pedicate fom a et of entie ae meged into one pedicate ø ø ù ø ú û ø ü ý þ ÿ Recall: Enty i (pedicate p, pointe pt) Conitent( Enty E, Pedicate q ) µ etn fale if p AND q ae gaanteed natifiable µ detemine which tee() to each µ fale poitie bt no fale negatie Compe( Enty E ) compeed epeentation of pedicate p Image Seach B+-tee Compe Ï Ð Ó Ô Õ Ö Ø Ù Ú Û Ü Ý Þ Ý ß à á Ý Ú á â Ð â Û * * +, -. / , /, / ¹ < º» ¼ º» ¼ ½ ¹ < ¾» ¼ À Á Â Ã Ä Â Å Æ Ç Æ É ¹ Æ Ç Æ É ¹ ã ä å æ ç æ è é å è ê ä ë ì ä è í î ï è í æ Á Ê Â ¹ Ë Å Ì Å Î Ä Ä ¹ É É Á Ê î ð ë î ñ é ò ì ñ ð é ó é ñ ñ ä ô ò õ ë é é å! " # $ % " & " ' ( % ) 3

4 B+-tee Compe #2 M C H H M G H H B C D E F G H H J C N : ; < 8 = 8 >? 7 8 = 8 >? ; < 8 = = : A B C D E F G H H E F G I J B K L G H 8 9 : ; 8 = 8 A O P Q R S T U V W X Y Z Z R U [ R\ [ U S P ] P ^ P W P _ P W P T ` Y a 8 9 : ; 8 = 8 8 = 8 >? ; 8 = = : ; Penalty( Enty E1, Enty E2 ) penalty fo ineting E2 into E1 btee local not global penalty ed fo deciding whee to inet entie o whee to plit a pedicate R-tee example t minimizing inceaed aea, minimizing oelap, minimizing peimete B+-tee Compe #3 o e j j p d e f g h i j j l e q ^ P b Q Y _ P W P T ` Y a ^ P W P T ` Y _ P W W Q Y a c d e f g h i j j g h i k l d m n i j ^ P b Q Y _ P W W Q Y a ^ P b Q Y _ P W W Q Y a c PickSplit( Enty E[] ) plit et of entie E into two et of entie, each with ~km entie may o may not e badne metic (e.g., mlti-way penalty) to detemine how to plit entie Otline Decompe( Enty E ) π = compeed(p) = ncompe(π), pt potentially loy do not eqie p iff Motiation Genealized Seach Tee (GiST) Algoithm Application GiST Limitation, Extenion Conclion 4

5 ¾ ½ Algoithm Algoithm: Inet Seache, inet, and delete ae baed on the implemented key method geneic algoithm fo pdating and acceing index tcte application-pecific infomation i extacted into key method Algoithm ae handled by GiST, not defined by e Inet( GiST R, Enty E ) tat at oot find leaf whee E hold be ineted may eqie chooing among eeal diffeent btee at each leel along path inet E may eqie plitting leaf node and popagating/adjting key p the tee Algoithm: Seach Algoithm: Chooe Sbtee Seach( GiST R, Pedicate q ) tat at oot go down path o path whee key pedicate ae conitent q each leaf w final conitency check etn aay of object o aay of object pointe Only e Conitent key method Genealization x exact match, ange qeie Calclate penalty of ineting enty in btee domain-pecific penalty minimize penalty locally not globally Image Seach R-tee Inet š œ ž Ÿ š š ž y z { < } ~ } ~ y z { < ~ ƒ y z y y ƒ z y ˆ Š Œ Ž ˆ ˆ Š Œ Œ Œ Š Œ ˆ Œ Š Œ Œ ˆ Inet R 9 into R-tee pick a egion containing R 9 and follow the child pointe ¾ Ç ¾ Ä ¾ Å ª «¾ Á ± ² ³ µ ¹ º»¼ ½ ¾ ¾ À ¾ Â ¾ Ã ¾ Å Æ 5

6 Ê Ê Ì Ì Ì Ê Algoithm: Split Application Union on new element É ceate a new key Modify old key É edce oelap, tighte contol Adjt key p toched path GiST confine application pecific code to ix key method Implementing a new tee only eqie coding of key method. GiST handle inet, delete and each Pape dice B+, R and RD Tee implementation Algoithm: Delete Application: B+-tee Delete( GiST G, Pedicate q ) Ê find element baed on q contain qey to etn one element delete maintain balance, inaiant p tee Contain( [x, y), ) If x Ë < y, etn te; othewie, etn fale Eqal( x, ) If x =, etn te; othewie, etn fale Otline Application: B+-tee Motiation Genealized Seach Tee (GiST) Algoithm Application GiST Limitation, Extenion Conclion Conitent( E, q ) If p=contain([x p,y p ),) AND q=contain([x q,y q ),), etn te if (x p <y q ) AND (y p >x q ), fale othewie If p=contain([x p,y p ),) AND q=eqal(x q,), etn te if x p Ë x q <y p, fale othewie Union({E 1,, E n }) E i =([x i,y i ), pt i ) etn [Min(x 1,, x n ), Max(y 1,, y n )) 6

7 Î Î Application: B+-tee Otline Compe(E=([x, y), pt)) Ï Retn x, nle E i the leftmot key on an intenal node (etn a 0-byte object) Decompe(E=(π, pt)) Ï Contct an inteal [x, y) Ï If E i leftmot key in intenal node, x = Ð ; othewie, x = π If E i ightmot key in intenal node, y = Ð ; othewie, y = nextkey(); Motiation Genealized Seach Tee (GiST) Algoithm Application GiST Limitation, Extenion Conclion Application: B+-tee GiST Limitation/Extenion Penalty( E = ([x 1,y 1 ), pt 1 ), F = ([x 2,y 2 ), pt 2 ) ) If E i leftmot pointe on it node, etn Max(y 2 y 1, 0) If E i ightmot pointe on it node, etn Max(x 1 x 2, 0) Othewie, etn Max(y 2 y 1, 0) + Max(x 1 x 2, 0) Aggegate qeie Neaet-neighbo, i.e., like qeie both addeed in Genealizing Seach in Genealized Seach Tee, ICDE 1999 Concency, ecoey implementation naïe: tict 2PL addeed in Concency and Recoey in Genealized Seach Tee, SIGMOD 1997 Application: B+-tee GiST Conclion PickSplit( P ) P = { E 1,, E n } E i < E j fo i < j Retn P 1 = { E 1,, E floo(n/2) } and P 2 = { E ceiling(n/2),, E n } Gaantee a minimm fill facto of M/2 Identify the fndamental of each tee One ADT decibe many each tee, e.g. B+-tee, R-tee, etc. Allow extenible data and qey type 7

8 Ô Ô Ô Ô Ó Ó Dicion Qetion? Time fo qiz! Qiz Define a GiST. What ae it pimay benefit? Wold yo e a GiST to implement a new DB each tee? Specifically, conide eae of implementing yo tee. What ae the tadeoff? What i Saa faoite colo? By how mch did thi peentation impoe yo ndetanding of GiST? Scale: [1. moe confed than ee, 5. damnnea an expet] 8

Framework for functional tree simulation applied to 'golden delicious' apple trees

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