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A PolynomialTime Approximation Scheme for Weighted Planar Graph TSP

Summary: A Polynomial­Time Approximation Scheme for
Weighted Planar Graph TSP
Sanjeev Arora \Lambda
Princeton U.
Michelangelo Grigni y
Emory U.
David Karger z Philip Klein x
Brown U.
Andrzej Woloszyn
Emory U.
Given a planar graph on n nodes with costs (weights) on
its edges, define 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
finds a salesman tour of total cost at most (1 + '') times
optimal in time n O(1='' 2 ) .
We also present a quasi­polynomial time algorithm for
the Steiner version of this problem.
1 Introduction


Source: Arora, Sanjeev - Department of Computer Science, Princeton University
Klein, Philip N. - Department of Computer Science, Brown University


Collections: Computer Technologies and Information Sciences