发表机构
Queen’s University（女王大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究如何确定图是否为k - 警察获胜图，将其转化为非确定性规划问题，利用先进规划器计算，警察移动设为非确定性，强盗移动为确定性，还用图论变体扩展基础模型。
AI 中文摘要
警察与强盗问题是图论中一个经过充分研究的问题。其场景是在一个无向图上有一个强盗和一个或多个警察，他们轮流在图中移动，警察试图抓住强盗。关注的属性是，给定初始放置的任何配置，k个警察是否足以确保在有限轮次后至少有一个警察与强盗占据同一顶点；若成功，该图被称为“k - 警察获胜”图。在这项工作中，我们将确定一个图是否为k - 警察获胜图的问题转化为一个非确定性规划问题，并使用最先进的规划器来计算此属性。警察的移动被视为非确定性移动（以涵盖所有可能策略），而强盗的移动本质上是确定性的。我们还使用图论文献中的几种变体扩展了基础模型。
英文摘要
Cops and Robbers is a well-studied problem in graph theory. The setting consists of a robber and one or more cops placed on an undirected graph. Taking turns moving throughout the graph, the cops try to capture the robber. The property of interest is whether $k$ cops suffice to ensure at least one cop occupies the same vertex as the robber, after a finite number of turns, given any configuration of their initial placement; if successful, the graph is referred to as ``$k$-copwin''. In this work, we cast the problem of determining whether a graph is $k$-copwin as a non-deterministic planning problem and use state-of-the-art planners to compute this property. The cop movement is cast as non-deterministic movement (to capture all possible strategies), while the robber movement is deterministic in nature. We also extend the base model using several variations from the graph theory literature.
