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Complexity of Local Search for CSPs Parameterized by Constraint Difference

Authors Aditya Anand , Vincent Cohen-Addad , Tommaso D'Orsi , Anupam Gupta , Euiwoong Lee , Debmalya Panigrahi , Sijin Peng

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ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Constraint Satisfaction Problems
  • Parameterized Local Search
  • Optimization

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Abstract

In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible subset S of a universe U, the new input consists of a current solution P (not necessarily feasible) as well as an ordinary input for the problem. Given the existence of a feasible solution S^*, the goal is to find a feasible solution as good as S^* in parameterized time f(k)⋅n^O(1), where k denotes the distance |PΔ S^*|. This model generalizes numerous classical parameterized optimization problems whose parameter k is the minimum number of elements removed from U to make it feasible, which corresponds to the case P = U. 
We apply this model to widely studied Constraint Satisfaction Problems (CSPs), where U is the set of constraints, and a subset U' of constraints is feasible if there is an assignment to the variables satisfying all constraints in U'. We give a complete characterization of the parameterized complexity of all boolean-alphabet symmetric CSPs, where the predicate’s acceptance depends on the number of true literals.

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Aditya Anand, Vincent Cohen-Addad, Tommaso D'Orsi, Anupam Gupta, Euiwoong Lee, Debmalya Panigrahi, and Sijin Peng. Complexity of Local Search for CSPs Parameterized by Constraint Difference. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.IPEC.2025.26

Author Details

Aditya Anand
  • University of Michigan, Ann Arbor, MI, USA
Vincent Cohen-Addad
  • Google Research, NYC, USA
Tommaso D'Orsi
  • Bocconi University, Milan, Italy
Anupam Gupta
  • New York University, NY, USA
Euiwoong Lee
  • University of Michigan, Ann Arbor, MI, USA
Debmalya Panigrahi
  • Duke University, Durham, NC, USA
Sijin Peng
  • Massachusetts Institute of Technology, Cambridge, MA, USA

Funding

  • Gupta, Anupam: Supported in part by NSF awards CCF-2224718 and CCF-2422926.
  • Lee, Euiwoong: Supported in part by NSF award CCF-2236669 and by Google, Inc.
  • Panigrahi, Debmalya: Supported in part by NSF awards CCF-1955703 and CCF-2329230.

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