An improved approximation algorithm for the asymmetric TSP with strengthened triangle inequality

We consider the asymmetric traveling salesperson problem with @c-parameterized triangle inequality for @[email protected]?[1/2,1). That means, the edge weights fulfill w(u,v)=<@[email protected]?(w(u,x)+w(x,v)) for all nodes u,v,x. Chandran and Ram [L.S. Chandran, L.S. Ram, Approximations for ATSP with parametrized triangle inequality, in: Proc. 19th Int. Symp. on Theoret. Aspects of Comput. Sci. (STACS), in: Lecture Notes in Comput. Sci., vol. 2285, Springer, Berlin, 2002, pp. 227-237] gave the first constant factor approximation algorithm with polynomial running time for this problem. They achieve performance ratio @c/([email protected]). We devise an approximation algorithm with performance ratio ([email protected])/([email protected]@c^3), which is better for @[email protected]?[0.5437,1), that is, for the particularly interesting large values of @c.

[1]  Markus Bläser.  An Improved Approximation Algorithm for the Asymmetric TSP with Strengthened Triangle Inequality , 2003, ICALP.

[2]  Thomas Andreae,et al.  On the traveling salesman problem restricted to inputs satisfying a relaxed triangle inequality , 2001, Networks.

[3]  Juraj Hromkovic,et al.  Approximation algorithms for the TSP with sharpened triangle inequality , 2000, Inf. Process. Lett..

[4]  Alan M. Frieze,et al.  On the worst-case performance of some algorithms for the asymmetric traveling salesman problem , 1982, Networks.

[5]  Joseph F. Traub,et al.  Algorithms and Complexity: New Directions and Recent Results , 1976 .

[6]  Moshe Lewenstein,et al.  Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs , 2005, JACM.

[7]  Nicos Christofides.  Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem , 1976, Operations Research Forum.

[8]  Hans-Jürgen Bandelt,et al.  Performance Guarantees for Approximation Algorithms Depending on Parametrized Triangle Inequalities , 1995, SIAM J. Discret. Math..

[9]  L. Sunil Chandran,et al.  Approximations for ATSP with Parametrized Triangle Inequality , 2002, STACS.

[10]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[11]  Juraj Hromkovic,et al.  Towards the notion of stability of approximation for hard optimization tasks and the traveling salesman problem , 2002, Theor. Comput. Sci..

[12]  Michael A. Bender,et al.  Performance guarantees for the TSP with a parameterized triangle inequality , 2000, Inf. Process. Lett..