Shortest paths and centrality in uncertain networks

Computing the shortest path between a pair of nodes is a fundamental graph primitive, which has critical applications in vehicle routing, finding functional pathways in biological networks, survivable network design, among many others. In this work, we study shortest-path queries over uncertain networks, i.e., graphs where every edge is associated with a probability of existence. We show that, for a given path, it is # P -hard to compute the probability of it being the shortest path, and we also derive other interesting properties highlighting the complexity of computing the Most Probable Shortest Paths (MPSPs). We thus devise sampling-based efficient algorithms, with end-to-end accuracy guarantees, to compute the MPSP. As a concrete application, we show how to compute a novel concept of betweenness centrality in an uncertain graph using MPSPs. Our thorough experimental results and rich real-world case studies on sensor networks and brain networks validate the effectiveness, efficiency, scalability, and usefulness of our solution.

An efficient mining algorithm for maximal frequent patterns in uncertain graph database

Mining maximal frequent patterns is significant in many fields, but the mining efficiency is often low. The bottleneck lies in too many candidate subgraphs and extensive subgraph isomorphism tests. In this paper we propose an efficient mining algorithm. There are two key ideas behind the proposed methods. The first is to divide each edge of every certain graph (converted from equivalent uncertain graph) and build search tree, avoiding too many candidate subgraphs. The second is to search the tree built in the first step in order, avoiding extensive subgraph isomorphism tests. The evaluation of our approach demonstrates the significant cost savings with respect to the state-of-the-art approach not only on the real-world datasets as well as on synthetic uncertain graph databases.