In view of the fact that an ε-optimal tour can be found in the Euclidean case in time that it is polynomial with a fixed degree, independent of ε, it seems natural to ask whether the same holds true for the planar case. We give an algorithm requiring O(c1c2/ n) time to find an ε-optimal traveling salesman tour in the metric defined by a planar graph with nonnegative edge-lengths.
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Foundations of Computer Science, 2005. FOCS 2005. 46th Annual IEEE Symposium on
Date of Conference: 23-25 Oct. 2005