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

Authors:
Philip N. Klein
Affiliations:
Brown University, Providence, Rhode Island
Venue:
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Year:
2006

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Abstract

Let ε0 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+ε 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.