In this paper we give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks. Given an error parameter ε such that 0 < ε, our algorit...
We obtain the following results related to dynamic versions of the shortest-paths problem: (i) Reductions that show that the incremental and decremental singlesource shortest-paths...
We propose an approximation method to answer point-to-point shortest path queries in undirected edge-weighted graphs, based on random sampling and Voronoi duals. We compute a simp...
Shinichi Honiden, Michael E. Houle, Christian Somm...
We observe that the classical maximum flow problem in any directed planar graph G can be reformulated as a parametric shortest path problem in the oriented dual graph G . This ref...
We study novel combinatorial properties of graphs that allow us to devise a completely new approach to dynamic all pairs shortest paths problems. Our approach yields a fully dynam...