An improved approximation algorithm for the maximum TSP

Authors:
Tongquan Zhang;Ying Yin;Jianping Li
Affiliations:
School of Mathematics and Computer Science, Yunnan Nationalities University, Kunming, 650031, PR China;Department of Mathematics, Faculty of Science, Kunming University of Science and Technology, Kunming, 650093, PR China;Department of Mathematics, School of Mathematics and Statistics, Yunnan University, Kunming, 650091, PR China
Venue:
Theoretical Computer Science
Year:
2010

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Abstract

In this paper, we consider the maximum traveling salesman problem with @c-parameterized triangle inequality for @c@?[12,1), which means that the edge weights in the given complete graph G=(V,E,w) satisfy w(uv)@?@c@?(w(ux)+w(xv)) for all distinct nodes u,x,v@?V. For the maximum traveling salesman problem with @c-parameterized triangle inequality, R. Hassin and S. Rubinstein gave a constant factor approximation algorithm with polynomial running time, they achieved a performance ratio @c only for @c@?[12,57) in [8], which is the best known result. We design a k@c+1-2@ck@c-approximation algorithm for the maximum traveling salesman problem with @c-parameterized triangle inequality by using a similar idea but very different method to that in [11], where k=min{|C"i||i=1,2,...,m},C"1,C"2,...,C"m is an optimal solution of the minimum cycle cover in G, which is better than the @c-approximation algorithm for almost all @c@?[12,1).