On k-Path Covers and their applications

For a directed graph G with vertex set V, we call a subset a k-(All-)Path Cover if C contains a node from any simple path in G consisting of k nodes. This paper considers the problem of constructing small k-Path Covers in the context of road networks with millions of nodes and edges. In many application scenarios, the set C and its induced overlay graph constitute a very compact synopsis of G, which is the basis for the currently fastest data structure for personalized shortest path queries, visually pleasing overlays of subsampled paths, and efficient reporting, retrieval and aggregation of associated data in spatial network databases. Apart from a theoretic investigation of the problem, we provide efficient algorithms that produce very small k-Path Covers for large real-world road networks (with a posteriori guarantees via instance-based lower bounds). We also apply our algorithms to other (social, collaboration, web, etc.) networks and can improve in several instances upon previous approaches.