On Solution Discovery via Reconfiguration

TL;DR

This paper introduces a unified framework for solution discovery through reconfiguration, enabling efficient modifications to find feasible solutions in combinatorial problems, and analyzes its complexity across various problems.

Contribution

It formalizes a new reconfiguration-based approach for solution discovery, integrating local search and reoptimization, and studies its complexity on key combinatorial problems.

Findings

Framework effectively constructs feasible solutions via small modifications.

Complexity analysis reveals tractable and intractable instances for various problems.

Unified approach bridges local search, reoptimization, and reconfiguration techniques.

Abstract

The dynamics of real-world applications and systems require efficient methods for improving infeasible solutions or restoring corrupted ones by making modifications to the current state of a system in a restricted way. We propose a new framework of solution discovery via reconfiguration for constructing a feasible solution for a given problem by executing a sequence of small modifications starting from a given state. Our framework integrates and formalizes different aspects of classical local search, reoptimization, and combinatorial reconfiguration. We exemplify our framework on a multitude of fundamental combinatorial problems, namely Vertex Cover, Independent Set, Dominating Set, and Coloring. We study the classical as well as the parameterized complexity of the solution discovery variants of those problems and explore the boundary between tractable and intractable instances.