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A SAT Approach to Branchwidth

Authors:

Sebastian Ordyniak,

Stefan SzeiderAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 20, Issue 3

Article No.: 15, Pages 1 - 24

https://doi.org/10.1145/3326159

Published: 31 May 2019 Publication History

Abstract

Branch decomposition is a prominent method for structurally decomposing a graph, a hypergraph, or a propositional formula in conjunctive normal form. The width of a branch decomposition provides a measure of how well the object is decomposed. For many applications, it is crucial to computing a branch decomposition whose width is as small as possible. We propose an approach based on Boolean Satisfiability (SAT) to finding branch decompositions of small width. The core of our approach is an efficient SAT encoding that determines with a single SAT-call whether a given hypergraph admits a branch decomposition of a certain width. For our encoding, we propose a natural partition-based characterization of branch decompositions. The encoding size imposes a limit on the size of the given hypergraph. To break through this barrier and to scale the SAT approach to larger instances, we develop a new heuristic approach where the SAT encoding is used to locally improve a given candidate decomposition until a fixed-point is reached. This new SAT-based local improvement method scales now to instances with several thousands of vertices and edges.

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Cited By

Reichl FSlivovsky FSzeider SWilliams BChen YNeville J(2023)Circuit minimization with QBF-based exact synthesisProceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v37i4.25524(4087-4094)Online publication date: 7-Feb-2023
https://dl.acm.org/doi/10.1609/aaai.v37i4.25524
Schidler ASzeider S(2023)SAT-boosted Tabu Search for Coloring Massive GraphsACM Journal of Experimental Algorithmics10.1145/360311228(1-19)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.1145/3603112
Bannach MBerndt S(2022)Recent Advances in Positive-Instance Driven Graph SearchingAlgorithms10.3390/a1502004215:2(42)Online publication date: 27-Jan-2022
https://doi.org/10.3390/a15020042
Show More Cited By

Index Terms

A SAT Approach to Branchwidth
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Hypergraphs
2. Theory of computation
  1. Logic
    1. Constraint and logic programming

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Information

Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 20, Issue 3

July 2019

202 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/3338853

Editor:
Orna Kupferman
School of Computer Science and Engineering, Hebrew University, Israel

Issue’s Table of Contents

Copyright © 2019 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 31 May 2019

Accepted: 01 April 2019

Revised: 01 November 2018

Received: 01 February 2018

Published in TOCL Volume 20, Issue 3

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Cited By

Reichl FSlivovsky FSzeider SWilliams BChen YNeville J(2023)Circuit minimization with QBF-based exact synthesisProceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v37i4.25524(4087-4094)Online publication date: 7-Feb-2023
https://dl.acm.org/doi/10.1609/aaai.v37i4.25524
Schidler ASzeider S(2023)SAT-boosted Tabu Search for Coloring Massive GraphsACM Journal of Experimental Algorithmics10.1145/360311228(1-19)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.1145/3603112
Bannach MBerndt S(2022)Recent Advances in Positive-Instance Driven Graph SearchingAlgorithms10.3390/a1502004215:2(42)Online publication date: 27-Jan-2022
https://doi.org/10.3390/a15020042
Fleming NGöös MImpagliazzo RPitassi TRobere RTan LWigderson A(2021)On the power and limitations of branch and cutProceedings of the 36th Computational Complexity Conference10.4230/LIPIcs.CCC.2021.6Online publication date: 20-Jul-2021
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2021.6
Peruvemba Ramaswamy VSzeider S(2020)MaxSAT-Based Postprocessing for TreedepthPrinciples and Practice of Constraint Programming10.1007/978-3-030-58475-7_28(478-495)Online publication date: 2-Sep-2020
https://doi.org/10.1007/978-3-030-58475-7_28

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