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- W1776341569 abstract "We show that the expected time for a smart to catch a drunk on an $n$-vertex graph is at most $n + {rm o}(n)$. More precisely, let $G$ be a simple, connected, undirected graph with distinguished points $u$ and $v$ among its $n$ vertices. A cop begins at $u$ and a robber at $v$; they move alternately from vertex to adjacent vertex. The robber moves randomly, according to a simple random walk on $G$; the cop sees all and moves as she wishes, with the object of capturing the robber---that is, occupying the same vertex---in least expected time. We show that the cop succeeds in expected time no more than $n + {rm o}(n)$. Since there are graphs in which capture time is at least $n - o(n)$, this is roughly best possible. We note also that no function of the diameter can be a bound on capture time." @default.
- W1776341569 created "2016-06-24" @default.
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- W1776341569 date "2013-05-20" @default.
- W1776341569 modified "2023-09-27" @default.
- W1776341569 title "Capturing the Drunk Robber on a Graph" @default.
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