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Exponential Steepest Ascent from Valued Constraint Graphs of Pathwidth Four

Authors Artem Kaznatcheev , Melle van Marle

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Author Details

Artem Kaznatcheev
  • Department of Mathematics, and Department of Information and Computing Sciences, Utrecht University, The Netherlands
Melle van Marle
  • Department of Mathematics, and Department of Information and Computing Sciences, Utrecht University, The Netherlands

Acknowledgements

AK would like to thank Dave Cohen and Peter Jeavons for helpful discussions. AK and MvM would also like to thank Daniel Dadush for helpful feedback and questions.

Cite AsGet BibTex

Artem Kaznatcheev and Melle van Marle. Exponential Steepest Ascent from Valued Constraint Graphs of Pathwidth Four. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CP.2024.17

Abstract

We examine the complexity of maximising fitness via local search on valued constraint satisfaction problems (VCSPs). We consider two kinds of local ascents: (1) steepest ascents, where each step changes the domain that produces a maximal increase in fitness; and (2) ≺-ordered ascents, where - of the domains with available fitness increasing changes - each step changes the ≺-minimal domain. We provide a general padding argument to simulate any ordered ascent by a steepest ascent. We construct a VCSP that is a path of binary constraints between alternating 2-state and 3-state domains with exponentially long ordered ascents. We apply our padding argument to this VCSP to obtain a Boolean VCSP that has a constraint (hyper)graph of arity 5 and pathwidth 4 with exponential steepest ascents. This is an improvement on the previous best known construction for long steepest ascents, which had arity 8 and pathwidth 7.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
Keywords
  • valued constraint satisfaction problem
  • steepest ascent
  • local search
  • bounded treewidth
  • intractability

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