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.

翻译：现实世界应用与系统的动态特性要求我们能高效地改进不可行解，或通过以受限方式对系统当前状态进行修改来恢复损坏的解。我们提出一种新的解发现框架，该框架基于重配置思想，通过从给定初始状态出发执行一系列微小修改来为给定问题构建可行解。该框架整合并形式化了经典局部搜索、重优化与组合重配置的不同方面。我们以多个基础组合问题为例阐述该框架，包括顶点覆盖、独立集、支配集和图着色问题。我们研究了这些问题的解发现变体的经典复杂度与参数化复杂度，并探索了可解实例与难解实例之间的边界。