Pathwidth-One Vertex Explosion 与 Co-Path 问题
Pathwidth-One Vertex Explosion and Co-Path Problems
- Stein Faculty of Computer and Information Science, Ben-Gurion University of the Negev（本-古里安大学内盖夫斯坦计算机与信息科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对二部图单侧顶点爆炸问题（BOVE）及其推广的受限路径宽度一顶点爆炸问题（restricted POVE），通过建立与 Co-Path Set 和 restricted Co-Path Packing 的双向参数保持归约，改进了相关参数化算法与核。
AI中文摘要：
在二部图单侧顶点爆炸问题（BOVE）中，输入是一个二部图 $G = (T, B, E)$ 和一个非负整数 $k$。目标是判定是否存在一个大小至多为 $k$ 的集合 $S \subseteq B$，使得爆炸 $S$ 中的每个顶点后得到的图的路径宽度至多为 1。受限的路径宽度一顶点爆炸问题（restricted POVE）是 BOVE 的推广。该问题的输入是一个图 $G$、一个非负整数 $k$ 和一个顶点集合 $X \subseteq V(G)$。目标是判定是否存在一个大小至多为 $k$ 的集合 $S \subseteq X$，使得爆炸 $S$ 中的每个顶点后得到的图的路径宽度至多为 1。在本文中，我们展示了 BOVE 与 Co-Path Set 之间以及 restricted POVE 与 restricted Co-Path Packing 之间的参数保持归约（双向）。这些归约产生了针对 BOVE 和 restricted POVE 的改进的参数化算法，以及针对 BOVE 的改进的核。
英文摘要：
In the Bipartite One-sided Vertex Explosion problem (BOVE), the input is a bipartite graph $G = (T, B, E)$ and a nonnegative integer $k$. The goal is to decide whether there is a set $S \subseteq B$ of size at most $k$ such that exploding every vertex in $S$ results in a graph with pathwidth at most one. The restricted Pathwidth One Vertex Explosion problem (restricted POVE) is a generalization of BOVE. The input to this problem is a graph $G$, a nonnegative integer $k$, and a set of vertices $X \subseteq V($ The goal is to decide whether there is a set $S \subseteq X$ of size at most $k$ such that exploding every vertex in $S$ results in a graph with pathwidth at most one. In this paper, we show parameter-preserving reductions in both directions between BOVE and Co-Path Set, and between restricted POVE and restricted Co-Path Packing. These reductions yield improved parameterized algorithms for BOVE and restricted POVE and an improved kernel for BOVE.
