弦图上MCS部分搜索序的多项式时间算法
A Polynomial-Time Algorithm for MCS Partial Search Order on Chordal Graphs
AI总结：
针对弦图上最大基数搜索的部分搜索序问题，提出多项式时间动态规划算法，解决了相关开放问题，并提出可能具独立价值的层结构概念与相关性质。
摘要：
我们研究了Scheffler[WG 2022]近期提出的部分搜索序问题（PSOP）。给定一个图$G$以及$G$顶点集上的一个偏序，该问题判定是否存在与给定偏序一致的$\mathcal{S}$-序，其中$\mathcal{S}$是BFS、DFS等图搜索范式。该问题自然推广了过去几年受到广泛关注的端点问题，也推广了近期文献中刚研究的所谓$\mathcal{F}$-树识别问题。我们的主要贡献是提出了一种多项式时间动态规划算法，用于求解限定在弦图上的最大基数搜索（MCS）的PSOP，这解决了Scheffler[WG 2022]工作中遗留的最引人关注的开放问题之一。为得到该结果，我们提出了层结构的概念，并研究了诸多相关的结构性质，这些性质可能具有独立研究价值。
英文摘要：
We study the partial search order problem (PSOP) proposed recently by Scheffler [WG 2022]. Given a graph $G$ together with a partial order over the set of vertices of $G$, this problem determines if there is an $\mathcal{S}$-ordering that is consistent with the given partial order, where $\mathcal{S}$ is a graph search paradigm like BFS, DFS, etc. This problem naturally generalizes the end-vertex problem which has received much attention over the past few years. It also generalizes the so-called ${\mathcal{F}}$-tree recognition problem which has just been studied in the literature recently. Our main contribution is a polynomial-time dynamic programming algorithm for the PSOP of the maximum cardinality search (MCS) restricted to chordal graphs. This resolves one of the most intriguing open questions left in the work of Scheffler [WG 2022]. To obtain our result, we propose the notion of layer structure and study numerous related structural properties which might be of independent interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
