Efficient Techniques for Tree Similarity Queries 1
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1 Efficient Techniques for Tree Similrity Queries 1 Nikolus Augsten Dtbse Reserch Group Deprtment of Computer Sciences University of Slzburg, Austri July 6, 2017 Austrin Computer Science Dy 2017 / IMAGINE 17 1 Prtilly funded by Austrin Science Fund (FWF), FFTED Project P Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 1/24
2 Trees Are Everywhere dt formts (XML, JSON), directory hierrchies ERP: humn resources, enterprise ssets, bills of mteril NLP: syntx trees of nturl lnguges softwre evolution: source code bioinformtics: RNA secondry structure, crbohydrtes, neuronl morphology, phylogenetic trees imge recognition: gesture nd shpe recognition strophysics: ncestry trees of glxies (merger trees) Source: (19M trees, totl of 750M nodes) Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 2/24
3 Similrity Join on Trees tid T 1 T 2 T 3 F tree x y w v z b c b e b h tree F tid b c d T 1 e d T h i 2 x y w T 3 wz Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 3/24
4 Similrity Join on Trees tid T 1 T 2 F tree x y w v z b c b tree b c d e d h i F tid T 1 T 2 T 3 e b h x y w T 3 wz Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 3/24
5 Similrity Join on Trees tid F tree x threshold=2 tree F tid T 1 y w v z 2 b c d e T 1 T 2 b c b d h i T 2 T 3 e b h 1 x y w T 3 wz Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 3/24
6 Outline 1 How similr re two trees? 2 From trees to integer sets 3 Avoiding the nested loop join Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 4/24
7 Outline How similr re two trees? 1 How similr re two trees? 2 From trees to integer sets 3 Avoiding the nested loop join Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 5/24
8 How similr re two trees? Tree Edit Distnce (TED) minimum number of edit opertions to trnsform one tree into nother Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 6/24
9 How similr re two trees? Tree Edit Distnce (TED) minimum number of edit opertions to trnsform one tree into nother TED = 3 Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 6/24
10 How similr re two trees? Stte of the Art in TED Algorithm Time Spce Comments Zhng&Shsh 1989 O(n 4 ) O(n 2 ) O(n 2 log 2 n) runtime for blnced trees Demine et l O(n 3 ) O(n 2 ) worst cse is frequent Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 7/24
11 How similr re two trees? Stte of the Art in TED Algorithm Time Spce Comments Zhng&Shsh 1989 O(n 4 ) O(n 2 ) O(n 2 log 2 n) runtime for blnced trees Demine et l O(n 3 ) O(n 2 ) worst cse is frequent Zhng 0.5 sec Demine 30.9 sec ( 1000 nodes) Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 7/24
12 How similr re two trees? Stte of the Art in TED Algorithm Time Spce Comments Zhng&Shsh 1989 O(n 4 ) O(n 2 ) O(n 2 log 2 n) runtime for blnced trees Demine et l O(n 3 ) O(n 2 ) worst cse is frequent Zhng 0.5 sec Demine 30.9 sec ( 1000 nodes) Zhng Demine ( 1000 nodes) sec 26.0 sec Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 7/24
13 How similr re two trees? Stte of the Art in TED Algorithm Time Spce Comments Zhng&Shsh 1989 O(n 4 ) O(n 2 ) O(n 2 log 2 n) runtime for blnced trees Demine et l O(n 3 ) O(n 2 ) worst cse is frequent Zhng 0.5 sec Demine 30.9 sec ( 1000 nodes) Zhng Demine ( 1000 nodes) sec 26.0 sec Problem: Hrd-coded decomposition strtegies Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 7/24
14 How similr re two trees? Robust Tree Edit Distnce Algorithm (RTED) tree T1 strtegy computtion O(n 2 ) time nd spce optiml strtegy distnce computtion O(n 3 ) time nd O(n 2 ) spce TED tree T2 Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 8/24
15 How similr re two trees? Robust Tree Edit Distnce Algorithm (RTED) tree T1 strtegy computtion O(n 2 ) time nd spce optiml strtegy distnce computtion O(n 3 ) time nd O(n 2 ) spce TED tree T2 Algorithm Time Spce Comments Zhng&Shsh 1989 O(n 4 ) O(n 2 ) O(n 2 log 2 n) runtime for blnced trees Demine et l O(n 3 ) O(n 2 ) worst cse is frequent Pwlik&Augsten (RTED) 2011 O(n 3 ) O(n 2 ) optiml strtegy RTED: fstest known lgorithm for TED. Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 8/24
16 How similr re two trees? Performnce Evlution Runtime mesure runtime (seconds) vry tree shpe tree size 1000 nodes RTED: fstest known lgorithm for TED. Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 9/24
17 Outline From trees to integer sets 1 How similr re two trees? 2 From trees to integer sets 3 Avoiding the nested loop join Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 10/24
18 From trees to integer sets Similrity Join on Trees tid T 1 T 2 T 3 F tree x y w v z b c b e b h tree F tid b c d T 1 e d T h i 2 x y w T 3 wz Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 11/24
19 From trees to integer sets Similrity Join on Trees tid T 1 T 2 F tree x y w v z b c b tree b c d e d h i F tid T 1 T 2 T 3 e b h x y w T 3 wz Nested loop join (NLJ): 1. compute distnce between ll pirs of trees Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 11/24
20 From trees to integer sets Similrity Join on Trees tid F tree x threshold=2 tree F tid T 1 y w v z 2 b c d e T 1 T 2 b c b d h i T 2 T 3 e b h 1 x y w T 3 wz Nested loop join (NLJ): 1. compute distnce between ll pirs of trees 2. return trees within threshold Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 11/24
21 From trees to integer sets Similrity Join on Trees tid F tree x threshold=2 tree F tid T 1 y w v z 2 b c d e T 1 T 2 b c b d h i T 2 T 3 e b h 1 x y w T 3 wz Nested loop join (NLJ): 1. compute distnce between ll pirs of trees 2. return trees within threshold Very expensive: N 2 distnce computtions! Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 11/24
22 From trees to integer sets Stndrd Join Techniques Fil Sorting: Errors destroy sort order customer nme city Fried Slzburg Frodo Auenlnd Mri Wien customer nme Fried Mri Vrodo city Slzburg Wien Auenlnd Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 12/24
23 From trees to integer sets Stndrd Join Techniques Fil Sorting: Errors destroy sort order customer nme city customer nme Fried Slzburg Fried Frodo Auenlnd Mri Mri Wien Vrodo Hshing: Errors chnge hsh vlue city Slzburg Wien Auenlnd 0 Frodo Fried 1 2 Mri Fried 1 Vrodo 2 Mri 3 4 Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 12/24
24 From trees to integer sets pq-grms: From Trees to Sets Split trees into pq-grms (smll subtrees of fixed shpe) b e b c e b b e b b b c e b c b c b c e Hsh pq-grms to integers Intuition: Similr trees mny common pq-grms Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 13/24
25 From trees to integer sets pq-grms Hve Useful Properties Efficiency pq-grm runtime: O(n log n) edit distnce runtime: O(n 3 ) edit dist 2,3-grm dist Filter for edit distnce good pproximtion gurntees lower bound (fnout weighting of opertions) time [sec] number of nodes (n) Tree similrity simplified to set overlp. Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 14/24
26 Outline Avoiding the nested loop join 1 How similr re two trees? 2 From trees to integer sets 3 Avoiding the nested loop join Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 15/24
27 Avoiding the nested loop join Nested Loop Join for Sets A Smll Experiment Dtset: title nd uthor of n = 873k publictions (DBLP) vg. 15 words (min: 2, mx: 289) 409k different words, Zipfin frequency distribution Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 16/24
28 Avoiding the nested loop join Nested Loop Join for Sets A Smll Experiment Dtset: title nd uthor of n = 873k publictions (DBLP) vg. 15 words (min: 2, mx: 289) 409k different words, Zipfin frequency distribution Gol: find ll similr pirs (e.g. 90% overlp) Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 16/24
29 Avoiding the nested loop join Nested Loop Join for Sets A Smll Experiment Dtset: title nd uthor of n = 873k publictions (DBLP) vg. 15 words (min: 2, mx: 289) 409k different words, Zipfin frequency distribution Gol: find ll similr pirs (e.g. 90% overlp) Similrity check is very fst: 6 ns 15 CPU cycles Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 16/24
30 Avoiding the nested loop join Nested Loop Join for Sets A Smll Experiment Dtset: title nd uthor of n = 873k publictions (DBLP) vg. 15 words (min: 2, mx: 289) 409k different words, Zipfin frequency distribution Gol: find ll similr pirs (e.g. 90% overlp) Similrity check is very fst: 6 ns 15 CPU cycles Nested loop join: too mny comprisons! (pprox. 381 billion) Overlp Runtime [s] NLJ does not even scle for very fst checks. Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 16/24
31 Avoiding the nested loop join Trick: Avoid Touching Hopeless Cndidtes Prefix filter 1 : only look t smll prt of the set sort sets nd cut fter prefix no overlp in prefix similrity threshold not rechble r: c e f g r s 4 s: b d e f g 1 Chudhuri, Gnti, Kushik. A primitive opertor for similrity joins in dt clening. ICDE Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 17/24
32 Avoiding the nested loop join Prefix Index Join collection S prefix index lookup collection of probing sets R c c r 6 s 1 s 3 s 4 s 2 s 3 s 5 r 7 Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 18/24
33 Avoiding the nested loop join Prefix Index Join collection S prefix index lookup collection of probing sets R c c r 6 s 1 s 3 s 4 s 2 s 3 s 5 r 7 Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 18/24
34 Avoiding the nested loop join Comprison to Nested Loop Join Overlp Nested Loop Join Prefix Join s 0.26 s s 0.44 s s 1.54 s s 4.93 s Prefix Join 1500 to 8000 times fster thn nested loop join! Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 19/24
35 Summry Conclusion Set similrity join RTED: efficient tree edit distnce pq-grms: from trees to sets prefix: voiding nested loop join Publictions Very Lrge Dtbse Conference (VLDB 2005, 2011, 2016) ACM Trns. on Dtbse Systems (TODS 2010, 2015) Elsevier Informtion Systems (Inf. Syst. 2016) Algorithms nd technology mtter efficient solutions orders of mgnitude fster Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 20/24
36 Conclusion Conclusion nd Outlook technologicl limits lck of understnding Dt Anlysis Informtion Systems mny outlets Dtbse Systems ICDE VLDB SIGMOD Dtbse Theory ICDT PODS technology theoreticl foundtion Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 21/24
37 Conclusion Conclusion nd Outlook technologicl limits lck of understnding Dt Anlysis Informtion Systems mny outlets Dtbse Systems ICDE VLDB SIGMOD Dtbse Theory ICDT PODS technology theoreticl foundtion Efficient technology is key enbler for innovtion in big dt. Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 21/24
38 Conclusion Conclusion nd Outlook technologicl limits lck of understnding Dt Anlysis Informtion Systems mny outlets Dtbse Systems ICDE VLDB SIGMOD Dtbse Theory ICDT PODS technology theoreticl foundtion DACH publictions in top-3 DBS outlets: only 1.5% from Austri Efficient technology is key enbler for innovtion in big dt. Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 21/24
39 Conclusion Conclusion nd Outlook technologicl limits lck of understnding Dt Anlysis Informtion Systems mny outlets Dtbse Systems ICDE VLDB SIGMOD Dtbse Theory ICDT PODS technology theoreticl foundtion DACH publictions in top-3 DBS outlets: only 1.5% from Austri Mster Dt Science in Slzburg: dt nlysis + pplictions + technology Efficient technology is key enbler for innovtion in big dt. Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 21/24
40 Conclusion Conclusion nd Outlook technologicl limits lck of understnding Dt Anlysis Informtion Systems mny outlets Dtbse Systems ICDE VLDB SIGMOD Dtbse Theory ICDT PODS technology theoreticl foundtion DACH publictions in top-3 DBS outlets: only 1.5% from Austri Mster Dt Science in Slzburg: dt nlysis + pplictions + technology Invittion: VLDB 2017 in Munich, EDBT 2018 in Vienn! Efficient technology is key enbler for innovtion in big dt. Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 21/24
41 Thnks! Conclusion Thnks for your ttention! Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 22/24
42 References I Conclusion Nikolus Augsten, Michel Böhlen, nd Johnn Gmper. Approximte mtching of hierrchicl dt using pq-grms. In Proceedings of the Interntionl Conference on Very Lrge Dtbses (VLDB), pges , Trondheim, Norwy, September ACM Press. ISBN Nikolus Augsten, Michel Böhlen, nd Johnn Gmper. The pq-grm distnce between ordered lbeled trees. ACM Trnsctions on Dtbse Systems (TODS), 35(1):1 36, ISSN Willi Mnn, Nikolus Augsten, nd Pngiotis Bouros. An empiricl evlution of set similrity join techniques. PVLDB, 9(9): , ISSN Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 23/24
43 References II Conclusion Mteusz Pwlik nd Nikolus Augsten. RTED: A robust lgorithm for the tree edit distnce. PVLDB, 5(4): , December ISSN Mteusz Pwlik nd Nikolus Augsten. Efficient computtion of the tree edit distnce. ACM Trnsctions on Dtbse Systems (TODS), 40(1):3:1 3:40, Mrch ISSN Mteusz Pwlik nd Nikolus Augsten. Tree edit distnce: Robust nd memory-efficient. Informtion Systems, 56: , ISSN Nikolus Augsten (Univ. of Slzburg) Efficient Tree Similrity Queries July 6, / 24 24/24
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