Reliable subgraphs can be used, for example, to find and rank nontrivial links between given vertices, to concisely visualize
large graphs, or to reduce the size of input for computationally demanding graph algorithms. We propose two new heuristics
for solving the most reliable subgraph extraction problem on large, undirected probabilistic graphs. Such a problem is specified
by a probabilistic ... [Show full abstract] graph G subject to random edge failures, a set of terminal vertices, and an integer K. The objective is to remove K edges from G such that the probability of connecting the terminals in the remaining subgraph is maximized. We provide some technical details
and a rough analysis of the proposed algorithms. The practical performance of the methods is evaluated on real probabilistic
graphs from the biological domain. The results indicate that the methods scale much better to large input graphs, both computationally
and in terms of the quality of the result.