On solution discovery via reconfiguration

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 or configuration. 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.