Complexity of Reconfiguration Problems for Constraint Satisfaction

TL;DR

This paper investigates the computational complexity of reconfiguring solutions in constraint satisfaction problems, identifying conditions under which the problem is tractable or intractable.

Contribution

It provides a comprehensive complexity analysis of the reconfiguration problem for CSP, establishing new boundaries between solvable and hard cases.

Findings

Certain CSP classes allow polynomial-time reconfiguration algorithms.

Reconfiguration is PSPACE-complete for some CSP variants.

The paper delineates tractable and intractable cases based on problem parameters.

Abstract

Constraint satisfaction problem (CSP) is a well-studied combinatorial search problem, in which we are asked to find an assignment of values to given variables so as to satisfy all of given constraints. We study a reconfiguration variant of CSP, in which we are given an instance of CSP together with its two satisfying assignments, and asked to determine whether one assignment can be transformed into the other by changing a single variable assignment at a time, while always remaining satisfying assignment. This problem generalizes several well-studied reconfiguration problems such as Boolean satisfiability reconfiguration, vertex coloring reconfiguration, homomorphism reconfiguration. In this paper, we study the problem from the viewpoints of polynomial-time solvability and parameterized complexity, and give several interesting boundaries of tractable and intractable cases.