The ACO Seminar (2013–2014)

We consider a variation of cop vs. robber on graph. The robber is not restricted by the graph edges and instead 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 distribution is known, the expected capture time (with best play) on any connected n-vertex graph is exactly n. Time permitting, we will also discuss what is known about the case of an unknown distribution.