A Single Shortest Path Algorithm for Graphs with Separators

Kurt Mehlhorn, Bernd H. Schmidt

Abstract: We show how to solve a single source shortest path problem on a planar network in time O(n3/2log n). The algorithm works for arbitrary edge weights (positive and negative) and is based on the planar separator theorem. More generally, the algorithm works in time O(na+blog n + n3a+ nd) on graphs G=(V, E) which have a separator of size na, have at most nb edges and where the separator can be found in time nd.