A subset spanner for Planar graphs, : with application to subset TSP

Let > 0 be a constant. For any edge-weighted planar graph G and a subset S of nodes of G, there is a subgraph H of G of weight a constant times that of the minimum Steiner tree for S such that distances in H between nodes in S are at most 1+ times the corresponding distances in G. As a consequence, there is an O(n log n)-time approximation scheme for finding a TSP among a given subset of nodes of a planar graph. This is the first PTAS for the problem. Categories and Subject Descriptors F.2.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity--Nonnumerical Algorithms and Problems General Terms Algorithms Keywords approximation scheme,planar graph,traveling salesman problem,spanner

• Type: Conference
• Year: 2006
• Where: STOC
• Authors: Philip N. Klein
• Keywords: Algorithms, Minimum Steiner Tree, Problems General Terms, Scheme, STOC 2006