Optimizing the Constrained Estimate of Random Walks

We introduce the problem of optimizing the constrained estimate of random walks on the probability networks (which are formally defined as the weighted directed graphs in which the total outgoing weight of any node is at most 1). In this problem, it is required to find the size-constrained set of nodes, which maximized the hitting probability (before the time limit) of the randomly initialized random walk. The problem is proved NP-Hard, and we propose an algorithm with polynomial time complexity and constant approximation ratio.