A Polynomial-Time Approximation Scheme for Weighted Planar Graph TSP

Given a planar graph on n nodes with costs weights on its edges, de ne the distance between nodes i and j as the length of the shortest path between i and j. Consider this as an instance of metric TSP. For any " 0, our algorithm nds a salesman tour of total cost at most 1 + " times optimal in time nO1="2 . We also present a quasi-polynomial time algorithm for the Steiner version of this problem.

• Type: Conference
• Year: 1998
• Where: SODA
• Authors: Sanjeev Arora, Michelangelo Grigni, David R. Karger, Philip N. Klein, Andrzej Woloszyn
• Keywords: Algorithms, Costs Weights, Planar Graph, Shortest Path, SODA 1998