连通图上未知概率对手的防入侵算法
An anti-incursion algorithm for unknown probabilistic adversaries on connected graphs
摘要：
赌徒使用概率分布$p_{1}, \ldots, p_{n}$在图的顶点$1, \ldots, n$上移动。警察在图中追捕赌徒，只能在相邻的顶点之间移动。在被警察抓住之前，赌徒可以走多少步？Komarov和Winkler证明了当警察不知道赌徒的分布时，在任意连通的$n$ -顶点图上，期望捕获时间的上界近似为$1.97n$.我们通过修改警察的追求算法，提高了这个上限约$1.95n$。
英文摘要：
A gambler moves on the vertices $1, \ldots, n$ of a graph using the probability distribution $p_{1}, \ldots, p_{n}$. A cop pursues the gambler on the graph, only being able to move between adjacent vertices. What is the expected number of moves that the gambler can make until the cop catches them? Komarov and Winkler proved an upper bound of approximately $1.97n$ for the expected capture time on any connected $n$-vertex graph when the cop does not know the gambler's distribution. We improve this upper bound to approximately $1.95n$ by modifying the cop's pursuit algorithm.
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。
