evaluation and enumeration problems for regular path
play

Evaluation and Enumeration Problems for Regular Path Queries Wim - PowerPoint PPT Presentation

Apr 11, 2023 •154 likes •1.03k views

Evaluation and Enumeration Problems for Regular Path Queries Wim Martens and Tina Trautner University of Bayreuth Practice QUERYING PATHS IN GRAPH DATABASES WIM MARTENS AND TINA TRAUTNER Graph Database d Prague a o r road road

  1. Evaluation and Enumeration Problems for Regular Path Queries Wim Martens and Tina Trautner University of Bayreuth

  2. Practice QUERYING PATHS IN GRAPH DATABASES WIM MARTENS AND TINA TRAUTNER

  3. Graph Database d Prague a o r road road Bayreuth road r o a d Passau Vienna road l i a r road road Salzburg Munich Node- and Edge-labeled directed graph WIM MARTENS AND TINA TRAUTNER

  4. Warm Up Question d Prague a o r road road Bayreuth road r o a d Passau Vienna road l i a r road road Salzburg Munich How many paths from Bayreuth to Vienna match the regular path query (road)* ? WIM MARTENS AND TINA TRAUTNER

  5. Warm Up Question d Prague a o r road road Bayreuth road r o a d Passau Vienna road l i a r road road Salzburg Munich How many paths from Bayreuth to Vienna match the regular path query (road)* ? (How many paths from Bayreuth to Vienna only use road-edges?) WIM MARTENS AND TINA TRAUTNER

  6. Warm Up Question d Prague a o r road road Bayreuth road r o a d Passau Vienna road l i a r road road Salzburg Munich How many paths from Bayreuth to Vienna match the regular path query (road)* ? (How many paths from Bayreuth to Vienna only use road-edges?) [Theoreticians]: ∞ [SPARQL 2018]: 1 [SPARQL 2012]: 3 [Cypher]: 5 WIM MARTENS AND TINA TRAUTNER

  7. Warm Up Question d Prague a o r road road Bayreuth road r o a d Passau Vienna road l i a r road road Salzburg Munich How many paths from Bayreuth to Vienna match the regular path query (road)* ? (How many paths from Bayreuth to Vienna only use road-edges?) all paths [Theoreticians]: ∞ [SPARQL 2018]: 1 is there at least one path? paths without node repetition [SPARQL 2012]: 3 [Cypher]: 5 paths without edge repetition WIM MARTENS AND TINA TRAUTNER

  8. Warm Up Question d Prague a o r road road Bayreuth road r o a d Passau Vienna road l i a r road road Salzburg Munich How many paths from Bayreuth to Vienna match the regular path query (road)* ? (How many paths from Bayreuth to Vienna only use road-edges?) all paths [Theoreticians]: ∞ [SPARQL 2018]: 1 is there at least one path? paths without node repetition [SPARQL 2012]: 3 [Cypher]: 5 paths without edge repetition WIM MARTENS AND TINA TRAUTNER

  9. Warm Up Question d Prague a o r road road Bayreuth road r o a d Passau Vienna road l i a r road road Salzburg Munich How many paths from Bayreuth to Vienna match the regular path query (road)* ? (How many paths from Bayreuth to Vienna only use road-edges?) all paths [Theoreticians]: ∞ [SPARQL 2018]: 1 is there at least one path? paths without node repetition [SPARQL 2012]: 3 [Cypher]: 5 paths without edge repetition WIM MARTENS AND TINA TRAUTNER

  10. Warm Up Question d Prague a o r road road Bayreuth road r o a d Passau Vienna road l i a r road road Salzburg Munich How many paths from Bayreuth to Vienna match the regular path query (road)* ? (How many paths from Bayreuth to Vienna only use road-edges?) all paths [Theoreticians]: ∞ [SPARQL 2018]: 1 is there at least one path? paths without node repetition [SPARQL 2012]: 3 [Cypher]: 5 paths without edge repetition WIM MARTENS AND TINA TRAUTNER

  11. Warm Up Question d Prague a o r road road Bayreuth road r o a d Passau Vienna road l i a r road road Salzburg Munich How many paths from Bayreuth to Vienna match the regular path query (road)* ? (How many paths from Bayreuth to Vienna only use road-edges?) all paths [Theoreticians]: ∞ [SPARQL 2018]: 1 is there at least one path? paths without node repetition [SPARQL 2012]: 3 [Cypher]: 5 paths without edge repetition WIM MARTENS AND TINA TRAUTNER

  12. Warm Up Question d Prague a o r road road Bayreuth road r o a d Passau Vienna road l i a r road road Salzburg Munich How many paths from Bayreuth to Vienna match the regular path query (road)* ? (How many paths from Bayreuth to Vienna only use road-edges?) all paths [Theoreticians]: ∞ [SPARQL 2018]: 1 is there at least one path? paths without node repetition [SPARQL 2012]: 3 [Cypher]: 5 paths without edge repetition WIM MARTENS AND TINA TRAUTNER

  13. Warm Up Question d Prague a o r road road Bayreuth road r o a d Passau Vienna road l i a r road road Salzburg Munich How many paths from Bayreuth to Vienna match the regular path query (road)* ? (How many paths from Bayreuth to Vienna only use road-edges?) all paths [Theoreticians]: ∞ [SPARQL 2018]: 1 is there at least one path? paths without node repetition [SPARQL 2012]: 3 [Cypher]: 5 paths without edge repetition WIM MARTENS AND TINA TRAUTNER

  14. The Point There are different ways of matching paths in graphs and any of them can make sense WIM MARTENS AND TINA TRAUTNER

  15. The Point There are different ways of matching paths in graphs and any of them can make sense But which variant do you want to use in a system? WIM MARTENS AND TINA TRAUTNER

  16. Theory ON QUERYING PATHS IN GRAPH DATABASES WIM MARTENS AND TINA TRAUTNER

  17. Computational Problems Input graph (the data) Regular expression ! called regular path query (RPQ) WIM MARTENS AND TINA TRAUTNER

  18. Computational Problems Input graph (the data) Regular expression ! called regular path query (RPQ) Problem Path existence Is there a path from to that matches ! ? WIM MARTENS AND TINA TRAUTNER

  19. Computational Problems Input graph (the data) Regular expression ! called regular path query (RPQ) Problem Path counting How many paths from to match ! ? WIM MARTENS AND TINA TRAUTNER

  20. Computational Problems Input graph (the data) Regular expression ! called regular path query (RPQ) Problem Path enumeration Enumerate the paths from to that match ! WIM MARTENS AND TINA TRAUTNER

  21. Considering Different Paths Arbitrary paths Boolean paths Paths without node repetitions Paths without edge repetitions WIM MARTENS AND TINA TRAUTNER

  22. Considering Different Paths Arbitrary paths Boolean paths Paths without node repetitions Paths without edge repetitions WIM MARTENS AND TINA TRAUTNER

  23. Considering Different Paths Arbitrary paths Paths without node repetitions WIM MARTENS AND TINA TRAUTNER

  24. Considering Different Paths Arbitrary paths Simple paths WIM MARTENS AND TINA TRAUTNER

  25. Complexity of RPQ Evaluation Existence Counting Enumeration Arbitrary paths Simple paths in P in FP polynomial delay NP-hard #P-hard too much delay WIM MARTENS AND TINA TRAUTNER

  26. Complexity of RPQ Evaluation Existence Coun,ng Enumeration Arbitrary paths Simple paths “user happy”: in P in FP polynomial delay “user unhappy”: NP-hard #P-hard too much delay WIM MARTENS AND TINA TRAUTNER

  27. Complexity of RPQ Evaluation Existence Counting Enumeration Arbitrary paths Simple paths “user happy”: in P in FP polynomial delay “user unhappy”: NP-hard #P-hard too much delay WIM MARTENS AND TINA TRAUTNER

  28. Complexity of RPQ Evaluation Existence Counting Enumeration Arbitrary paths Simple paths similar to counting words in language of regular expression #P-complete [Kannan et al., SODA 1995] WIM MARTENS AND TINA TRAUTNER

  29. Complexity of RPQ Evaluation Existence Counting Enumeration Arbitrary paths Simple paths Is there a simple path matching ! ∗ #! ∗ ? NP-complete [Mendelzon, Wood, SICOMP 1995] essentially because „simple path via a node“ is NP-hard [Fortune et al., TCS 1980] Is there a simple path matching !! ∗ ? NP-complete [Lapaugh, Papadimitriou, Networks 1984] WIM MARTENS AND TINA TRAUTNER

  30. Complexity of RPQ Evaluation Existence Counting Enumeration Arbitrary paths Simple paths Is there a simple path matching ! ∗ #! ∗ ? NP-complete [Mendelzon, Wood, SICOMP 1995] essentially because „simple path via a node“ is NP-hard [Fortune et al., TCS 1980] Is there a simple path matching !! ∗ ? NP-complete [Lapaugh, Papadimitriou, Networks 1984] [Bagan, Bonifati, Groz PODS 2013] Dichotomy for which expressions the data complexity of this problem is in P or NP-complete WIM MARTENS AND TINA TRAUTNER

  31. Theory VS Systems Theory: Systems: WIM MARTENS AND TINA TRAUTNER

  32. Theory VS Systems Theory: „Simple paths are computationally difficult, even for very small RPQs“ Systems: WIM MARTENS AND TINA TRAUTNER

  33. Theory VS Systems Theory: „Simple paths are computationally difficult, even for very small RPQs“ Systems: „But we use simple paths and we‘re fine“ WIM MARTENS AND TINA TRAUTNER

  34. What is going on with these ths ? sim simple ple pa paths WIM MARTENS AND TINA TRAUTNER

  35. RPQs in SPARQL Query Logs [Bonifati, M., Timm, PVLDB 2017] Extracted 247,404 RPQs from SPARQL query logs (2009 - 2017) (from DBPedia, biological databases, British museum, Wikidata, …) WIM MARTENS AND TINA TRAUTNER

  36. RPQs in SPARQL Query Logs [Bonifati, M., Timm, PVLDB 2017] Extracted 247,404 RPQs from SPARQL query logs (2009 - 2017) (from DBPedia, biological databases, British museum, Wikidata, …) Only very few different kinds of RPQs ( ± 17) WIM MARTENS AND TINA TRAUTNER

Recommend

Efficient Regular Path Query Evaluation in PGX Author : Supervisor : Xuming Meng dr. G.H.L. F

Efficient Regular Path Query Evaluation in PGX Author : Supervisor : Xuming Meng dr. G.H.L. F

Efficient Regular Path Query Evaluation in PGX Author : Supervisor : Xuming Meng dr. G.H.L. F LETCHER 15-08-2016 Introduction & Problem Statement Regular Path Query ( RPQ ) in PGX . - an in-memory parallel graph analytics framework,

650 views • 15 slides
Optimization of in collaboration with: Parke Godfrey and Jarek Gryz Regular Path Queries in

Optimization of in collaboration with: Parke Godfrey and Jarek Gryz Regular Path Queries in

Optimization of in collaboration with: Parke Godfrey and Jarek Gryz Regular Path Queries in Large Graphs Nikolay Yakovets Optimization of RPQs Scalable & e ffi cient evaluation of regular path queries Evaluation Implementation RPQs

876 views • 35 slides
An Analysis of the Feasibility of Graph Compression Techniques for Indexing Regular Path Queries

An Analysis of the Feasibility of Graph Compression Techniques for Indexing Regular Path Queries

An Analysis of the Feasibility of Graph Compression Techniques for Indexing Regular Path Queries Frank Tetzel, Hannes Voigt, Marcus Paradies, Wolfgang Lehner May 19, 2017 1 Regular Path Queries (RPQs) Matching paths conforming to regular

755 views • 15 slides
Path Query Patterns CIP2017-02-06 a.k.a. (Conjunctive) Regular Path Queries Regular

Path Query Patterns CIP2017-02-06 a.k.a. (Conjunctive) Regular Path Queries Regular

Path Query Patterns CIP2017-02-06 a.k.a. (Conjunctive) Regular Path Queries Regular expressions over Graphs Tobias Lindaaker tobias@neotechnology.com opencypher.org | opencypher@googlegroups.com opencypher.org |

316 views • 15 slides
Sample Graph Problems Path problems. Graph Operations And Connectedness problems.

Sample Graph Problems Path problems. Graph Operations And Connectedness problems.

Sample Graph Problems Path problems. Graph Operations And Connectedness problems. Representation Spanning tree problems. Path Finding Another Path Between 1 and 8 Path between 1 and 8. 2 2 4 3 4 3 8 8 8 8 1 1 6 10

95 views • 9 slides
Dynamic Complexity: From Regular Languages to Regular Path Queries Thomas Schwentick AutoMathA

Dynamic Complexity: From Regular Languages to Regular Path Queries Thomas Schwentick AutoMathA

(20 Years of) Dynamic Complexity: From Regular Languages to Regular Path Queries Thomas Schwentick AutoMathA 2015 Leipzig, May 2015 Lehrstuhl Logik in der Informatik The general setting (1/2) s s s Input t t t Aux. data Reach(s,t)?

686 views • 37 slides
Exploiting Branch Constraints without Exhaustive Path Enumeration Ting Chen, Tulika Mitra,

Exploiting Branch Constraints without Exhaustive Path Enumeration Ting Chen, Tulika Mitra,

Exploiting Branch Constraints without Exhaustive Path Enumeration Ting Chen, Tulika Mitra, Abhik Roychoudhury, Vivy Suhendra National University of Singapore Static WCET Analysis Flow analysis Loop bounds and infeasible paths

560 views • 16 slides
Evaluation of an MPN Method for the Rapid Enumeration of Pseudomonas aeruginosa from Swimming

Evaluation of an MPN Method for the Rapid Enumeration of Pseudomonas aeruginosa from Swimming

Evaluation of an MPN Method for the Rapid Enumeration of Pseudomonas aeruginosa from Swimming Pool and Spa Waters David Sartory SWM Consulting Pseudomonas aeruginosa Gram-negative rod-shaped bacterium and opportunistic pathogen Found

205 views • 16 slides
Decidability 12-0 Decidable Problems Interesting problems regarding regular

Decidability 12-0 Decidable Problems Interesting problems regarding regular

Griffith University 3130CIT Theory of Computation (Based on slides by Harald Sndergaard of The University of Melbourne) Decidability 12-0 Decidable Problems Interesting problems regarding regular languages are

351 views • 20 slides
Example Shortest Path Problems 8 6 2 1 1 3 3 1 16 7 5 Directed weighted graph. 6

Example Shortest Path Problems 8 6 2 1 1 3 3 1 16 7 5 Directed weighted graph. 6

Example Shortest Path Problems 8 6 2 1 1 3 3 1 16 7 5 Directed weighted graph. 6 4 10 4 Path length is sum of weights of edges on path. 2 4 7 7 5 3 The vertex at which the path begins is the source vertex. 14

237 views • 4 slides
Regular Expressions 1 / 12 https://xkcd.com/208/ 2 / 12 Regular Expressions In computer

Regular Expressions 1 / 12 https://xkcd.com/208/ 2 / 12 Regular Expressions In computer

Regular Expressions 1 / 12 https://xkcd.com/208/ 2 / 12 Regular Expressions In computer science, a language is a set of strings. Like any set, a language can be specified by enumeration (listing all the elements) or with a rule (or set of

340 views • 13 slides
Performance Evaluation: State space enumeration Markov Models, revisited State

Performance Evaluation: State space enumeration Markov Models, revisited State

Working with Markov models Performance Evaluation: State space enumeration Markov Models, revisited State transition identification Parameterization CSCI 8710 Calibration and solution E. Kraemer Example 1: Random

252 views • 8 slides
Processing Regular Path Queries Using Views or What Do We Need for Integrating Semistructured

Processing Regular Path Queries Using Views or What Do We Need for Integrating Semistructured

Processing Regular Path Queries Using Views or What Do We Need for Integrating Semistructured Data? Diego Calvanese University of Rome La Sapienza joint work with G. De Giacomo, M. Lenzerini, M.Y. Vardi Logic-based Methods for Information

660 views • 39 slides
Two problems remain Two problems remain Both RNG and GG remove some edges a short path

Two problems remain Two problems remain Both RNG and GG remove some edges a short path

Two problems remain Two problems remain Both RNG and GG remove some edges a short path may not exist! The shortest path on RNG or GG might be much longer than the shortest path on the original longer than the shortest path on the

761 views • 51 slides
MA/CSSE 474 Theory of Computation How many regular/non-regular languages are there? Closure

MA/CSSE 474 Theory of Computation How many regular/non-regular languages are there? Closure

1/7/2016 MA/CSSE 474 Theory of Computation How many regular/non-regular languages are there? Closure properties of Regular Languages (if there is time) Pumping Theorem Your Questions? Previous class days' HW 7 problems material

299 views • 16 slides
There is a path before each person that seems right, but in the end it leads to death. Proverbs

There is a path before each person that seems right, but in the end it leads to death. Proverbs

There is a path before each person that seems right, but in the end it leads to death. Proverbs 14:12 (NLT) The Principle of the Path Matthew 7:24 - 29 Most personal problems cannot be FIXED Most personal problems can be AVOIDED path way

679 views • 29 slides
Hamiltonian Path I For some problems it is difficult to find an algorithm in P We first discuss

Hamiltonian Path I For some problems it is difficult to find an algorithm in P We first discuss

Hamiltonian Path I For some problems it is difficult to find an algorithm in P We first discuss an example of finding a Hamiltonian Path Definition: for a given directed graph find a path going through all nodes once Fig 7.17 October 30,

321 views • 10 slides
Optimization Problems and Local Search Russell and Norvig 4.1 Optimization Problems n

Optimization Problems and Local Search Russell and Norvig 4.1 Optimization Problems n

Optimization Problems and Local Search Russell and Norvig 4.1 Optimization Problems n Previously: systematic exploration of search space. q Path to goal is the solution n For some problems path is irrelevant. q Example: 8-queens 8 Queens Stated

630 views • 18 slides
CDLG PATHS The notion of REGULAR SOLUTION for a path dependent PDE (1) needs to deal with

CDLG PATHS The notion of REGULAR SOLUTION for a path dependent PDE (1) needs to deal with

Introduction Path dependent second order PDEs Martingale problem for second order elliptic differential operators with path dependent coefficients Time consistent dynamic risk measures P ATH - PEPENDENT PARABOLIC PDE S AND P ATH - DEPENDENT F

832 views • 43 slides
Problems of Enumeration and Realizability on Matroids, Simplicial Complexes, and Graphs Yvonne

Problems of Enumeration and Realizability on Matroids, Simplicial Complexes, and Graphs Yvonne

Problems of Enumeration and Realizability on Matroids, Simplicial Complexes, and Graphs Yvonne Kemper August 6, 2014 Yvonne Kemper PoEaRoMSCaG In Honor of a Diagram g s r a h p Yvonne Kemper PoEaRoMSCaG Wait, what were those things

1.27k views • 89 slides
NP-Completeness 18-0 Some Problems in NP Consider again the Hamiltonian path

NP-Completeness 18-0 Some Problems in NP Consider again the Hamiltonian path

Griffith University 3130CIT Theory of Computation (Based on slides by Harald Sndergaard of The University of Melbourne) NP-Completeness 18-0 Some Problems in NP Consider again the Hamiltonian path problem

764 views • 21 slides
An Improved Algorithm to Accelerate Regular Expression Evaluation Michela Becchi and Patrick

An Improved Algorithm to Accelerate Regular Expression Evaluation Michela Becchi and Patrick

An Improved Algorithm to Accelerate Regular Expression Evaluation Michela Becchi and Patrick Crowley ANCS 2007 Context Regular expression matching is a critical operation in networking Intrusion detection Context based billing

391 views • 24 slides
Random Regular Graph & Generalized De Bruijn Graph with k -shortest Path Routing Peyman

Random Regular Graph & Generalized De Bruijn Graph with k -shortest Path Routing Peyman

Random Regular Graph & Generalized De Bruijn Graph with k -shortest Path Routing Peyman Faizian , Md Atiqul Mollah, Xin Yuan Scott Pakin, Michael Lang Florida State University Los Alamos National Laboratory Where it All Started Random

523 views • 23 slides
High Confidence Rule Mining h f d l Row Enumeration for Microarray Analysis Confidence

High Confidence Rule Mining h f d l Row Enumeration for Microarray Analysis Confidence

2007-11-26 Outline Introduction High Confidence Rule Mining h f d l Row Enumeration for Microarray Analysis Confidence based Prune Strategy MAXCONF Algorithm Kang Deng Evaluation U i University of Alberta it f Alb t

83 views • 7 slides

More recommend