6 research outputs found
Effectively Counting s-t Simple Paths in Directed Graphs
Full text linkAn important tool in analyzing complex social and information networks is s-t
simple path counting, which is known to be #P-complete. In this paper, we study
efficient s-t simple path counting in directed graphs. For a given pair of
vertices s and t in a directed graph, first we propose a pruning technique that
can efficiently and considerably reduce the search space. Then, we discuss how
this technique can be adjusted with exact and approximate algorithms, to
improve their efficiency. In the end, by performing extensive experiments over
several networks from different domains, we show high empirical efficiency of
our proposed technique. Our algorithm is not a competitor of existing methods,
rather, it is a friend that can be used as a fast pre-processing step, before
applying any existing algorithm
Shortest paths and centrality in uncertain networks
Get PDFComputing 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
