A fully dynamic approximation scheme for all-pairs shortest paths in planar graphs

Abstract

In this paper we give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks. Given an error parameter e such that 0<e≤1, our algorithm maintains approximate allpairs shortest-paths in an undirected planar graph G with nonnegative edge lengths. The approximate paths are guaranteed to be accurate to within a (1+e)-factor. The time bounds for both query and update for our algorithm wis O(e−1n2/3 log2n log D), where n is the number of nodes in G and D is the sum of its edge lengths.