Computing Optimal Hypertree Decompositions with SAT

Hypertree width is a prominent hypergraph invariant with many algorithmic applications in constraint satisfaction and databases. We propose a novel characterization for hypertree width in terms of linear elimination orderings. We utilize this characterization to generate a new SAT encoding that we evaluate on an extensive set of benchmark instances. We compare it to state-of-the-art exact methods for computing optimal hypertree width. Our results show that the encoding based on the new characterization is not only significantly more compact than known encodings but also outperforms the other methods.

[1]  Wim Martens,et al.  Navigating the Maze of Wikidata Query Logs , 2019, WWW.

[2]  Stefan Szeider,et al.  Computing Optimal Hypertree Decompositions , 2020, ALENEX.

[3]  Stefan Szeider,et al.  An SMT Approach to Fractional Hypertree Width , 2018, CP.

[4]  Olivier Bailleux,et al.  Efficient CNF Encoding of Boolean Cardinality Constraints , 2003, CP.

[5]  Helmut Veith,et al.  Encoding Treewidth into SAT , 2009, SAT.

[6]  Stefan Szeider,et al.  SAT-Encodings for Special Treewidth and Pathwidth , 2017, SAT.

[7]  Hans L. Bodlaender,et al.  A Branch and Bound Algorithm for Exact, Upper, and Lower Bounds on Treewidth , 2006, AAIM.

[8]  Georg Gottlob,et al.  HyperBench: A Benchmark and Tool for Hypergraphs and Empirical Findings , 2018, AMW.

[9]  Boris Motik,et al.  Benchmarking the Chase , 2017, PODS.

[10]  Sebastian Berndt,et al.  Jdrasil: A Modular Library for Computing Tree Decompositions , 2017, SEA.

[11]  Alon Y. Halevy,et al.  MiniCon: A scalable algorithm for answering queries using views , 2000, The VLDB Journal.

[12]  Joao Marques-Silva,et al.  PySAT: A Python Toolkit for Prototyping with SAT Oracles , 2018, SAT.

[13]  Vasco M. Manquinho,et al.  Incremental Cardinality Constraints for MaxSAT , 2014, CP.

[14]  Georg Gottlob,et al.  Hypertree decompositions and tractable queries , 1998, J. Comput. Syst. Sci..

[15]  Georg Gottlob,et al.  Hypertree Decompositions: Structure, Algorithms, and Applications , 2005, WG.

[16]  Johannes Klaus Fichte,et al.  The PACE 2019 Parameterized Algorithms and Computational Experiments Challenge: The Fourth Iteration (Invited Paper) , 2019, IPEC.

[17]  Dániel Marx,et al.  Constraint solving via fractional edge covers , 2006, SODA '06.

[18]  Hans L. Bodlaender,et al.  Discovering Treewidth , 2005, SOFSEM.

[19]  Wim Martens,et al.  An Analytical Study of Large SPARQL Query Logs , 2017, Proc. VLDB Endow..

[20]  Vibhav Gogate,et al.  A Complete Anytime Algorithm for Treewidth , 2004, UAI.

[21]  Georg Gottlob,et al.  A backtracking-based algorithm for hypertree decomposition , 2007, JEAL.

[22]  Georg Gottlob,et al.  Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width , 2001, PODS '01.