The traveling salesman problem with few inner points

Authors:
Vladimir G. DeıNeko;Michael Hoffmann;Yoshio Okamoto;Gerhard J. Woeginger
Affiliations:
Warwick Business School, The University of Warwick, Conventry CV4 7AL, UK;Institute of Theoretical Computer Science, ETH Zurich, CH-8092 Zurich, Switzerland;Institute of Theoretical Computer Science, ETH Zurich, CH-8092 Zurich, Switzerland;Department of Mathematics and Computer Science, Technical University of Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Venue:
Operations Research Letters
Year:
2006

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Abstract

We propose two algorithms for the planar Euclidean traveling salesman problem. The first runs in O(k!kn) time and O(k) space, and the second runs in O(2^kk^2n) time and O(2^kkn) space, where n denotes the number of input points and k denotes the number of points interior to the convex hull.