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...
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 provide the first linear-space data structure with provable sublinear query time for exact point-topoint shortest path queries in planar graphs. We prove that for any planar gr...
We introduce a generic approach for counting subgraphs in a graph. The main idea is to relate counting subgraphs to counting graph homomorphisms. This approach provides new algori...