The Most Reliable Subgraph Problem

We introduce the problem of finding the most reliable subgraph: given a probabilistic graph Gsubject to random edge failures, a set of terminal vertices, and an integer Kfind a subgraph Hi¾? Ghaving Kfewer edges than G, such that the probability of connecting the terminals in His maximized. The solution has applications in link analysis and visualization. We begin by formally defining the problem in a general form, after which we focus on a two-terminal, undirected case. Although the problem is most likely computationally intractable, we give a polynomial-time algorithm for a special case where Gis seriesparallel. For the general case, we propose a computationally efficient greedy heuristic. Our experiments on simulated graphs illustrate the usefulness of the concept of most reliable subgraph, and suggest that the heuristic for the general case is quite competitive.