In the solution discovery variant of a vertex (edge) subset problem $\Pi$ on graphs, we are given an initial configuration of tokens on the vertices (edges) of an input graph $G$ together with a budget $b$. The question is whether we can transform this configuration into a feasible solution of $\Pi$ on $G$ with at most $b$ modification steps. We consider the token sliding variant of the solution discovery framework, where each modification step consists of sliding a token to an adjacent vertex (edge). The framework of solution discovery was recently introduced by Fellows et al. [Fellows et al., ECAI 2023] and for many solution discovery problems the classical as well as the parameterized complexity has been established. In this work, we study the kernelization complexity of the solution discovery variants of Vertex Cover, Independent Set, Dominating Set, Shortest Path, Matching, and Vertex Cut with respect to the parameters number of tokens $k$, discovery budget $b$, as well as structural parameters such as pathwidth.

翻译：在图上的顶点（边）子集问题 $\Pi$ 的解发现变体中，我们给定输入图 $G$ 的顶点（边）上初始的令牌配置以及一个预算 $b$。问题在于我们是否能够通过最多 $b$ 次修改步骤，将此配置转换为 $G$ 上 $\Pi$ 的一个可行解。我们考虑解发现框架的令牌滑动变体，其中每个修改步骤包括将一个令牌滑动到相邻的顶点（边）。解发现框架最近由 Fellows 等人 [Fellows et al., ECAI 2023] 引入，并且对于许多解发现问题，其经典复杂性以及参数化复杂性已经确立。在本工作中，我们研究了顶点覆盖、独立集、支配集、最短路径、匹配以及顶点割的解发现变体关于参数令牌数量 $k$、发现预算 $b$ 以及路径宽度等结构参数的核化复杂性。