On Solution Discovery via Reconfiguration

Michael R. Fellows; Mario Grobler; Nicole Megow; Amer E. Mouawad; Vijayaragunathan Ramamoorthi; Frances A. Rosamond; Daniel Schmand; Sebastian Siebertz

arXiv · 2304.14295

On Solution Discovery via Reconfiguration

Michael R. Fellows·Mario Grobler·Nicole Megow·Amer E. Mouawad·Vijayaragunathan Ramamoorthi·Frances A. Rosamond·Daniel Schmand·Sebastian Siebertz

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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.

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Michael R. Fellows, Mario Grobler, Nicole Megow, Amer E. Mouawad, Vijayaragunathan Ramamoorthi, Frances A. Rosamond, Daniel Schmand, Sebastian Siebertz. 2023-04-27. On Solution Discovery via Reconfiguration. https://arxiv.org/abs/2304.14295

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