7 research outputs found
Cops vs. Gambler
We consider a variation of cop vs.\ robber on graph in which the robber is
not restricted by the graph edges; instead, he picks a time-independent
probability distribution on and moves according to this fixed
distribution. The cop moves from vertex to adjacent vertex with the goal of
minimizing expected capture time. Players move simultaneously. We show that
when the gambler's distribution is known, the expected capture time (with best
play) on any connected -vertex graph is exactly . We also give bounds on
the (generally greater) expected capture time when the gambler's distribution
is unknown to the cop.Comment: 6 pages, 0 figure
Cops vs. Gambler
Abstract We consider a variation of cop vs. robber on graph in which the robber is not restricted by the graph edges; instead, he picks a time-independent probability distribution on V (G) and moves according to this fixed distribution. The cop moves from vertex to adjacent vertex with the goal of minimizing expected capture time. Players move simultaneously. We show that when the gambler's distribution is known, the expected capture time (with best play) on any connected n-vertex graph is exactly n. We also give bounds on the (generally greater) expected capture time when the gambler's distribution is unknown to the cop