Eppstein [5] characterized the minor-closed graph families for which the treewidth is bounded by a function of the diameter, which includes e.g. planar graphs. This characterizatio...
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 give an algorithm requiring O(c1/2 n) time to find an -optimal traveling salesman tour in the shortest-path metric defined by an undirected planar graph with nonnegative edgele...
Given a graph G = (V, E) and a positive integer k, the PARTITION INTO CLIQUES (PIC) decision problem consists of deciding whether there exists a partition of V into k disjoint sub...
Abstract. We present new approximation schemes for various classical problems of finding the minimum-weight spanning subgraph in edge-weighted undirected planar graphs that are re...