The cover time of deterministic random walks
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
SIAM Journal on Discrete Mathematics
| Hi-index | 0.00 |
We analyze and solve a game in which a player chooses which of several Markov chains to advance, with the object of minimizing the expected time (or cost) for one of the chains to reach a target state. The solution entails computing (in polynomial time) a function $\gamma$---a variety of "Gittins index"---on the states of the individual chains, the minimization of which produces an optimal strategy.It turns out that $\gamma$ is a useful cousin of the expected hitting time of a Markov chain but is defined, for example, even for random walks on infinite graphs. We derive the basic properties of $\gamma$ and consider its values in some natural situations.