论文信息 - Worst Case Performance of an Approximation Algorithm for Asymmetric TSP

Worst Case Performance of an Approximation Algorithm for Asymmetric TSP

In 1982 Frieze, Galbiati and Maffioli (Networks 12:23-39) published their famous algorithm for approximating the TSP tour in an asymmetric graph with triangle inequality. They show that the algorithm approximates the TSP tour within a factor of log2 n. We construct a family of graphs for which the algorithm (with some implementation details specified by us) gives an approximation which is log2 n / (2 + 2e) times the optimum solution. This shows that the analysis by Frieze et al. is tight up to a constant factor and can hopefully give deeper understanding of the problem and new ideas in developing an improved approximation algorithm.

Anna Palbom

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

[2] John E. Hopcroft,et al. Complexity of Computer Computations , 1974, IFIP Congress.

[3] Günter Schaar. Remarks on Hamiltonian Properties of Powers of Digraphs , 1994, Discret. Appl. Math..

[4] Santosh S. Vempala,et al. On The Approximability Of The Traveling Salesman Problem , 2006, Comb..

[5] Markus Bläser,et al. A new approximation algorithm for the asymmetric TSP with triangle inequality , 2003, TALG.

[6] Teofilo F. Gonzalez,et al. P-Complete Approximation Problems , 1976, J. ACM.

[7] Moshe Lewenstein,et al. Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[8] S Townsend. Spermicides for family planning and disease protection: an update. , 1991, Network.

[9] Raymond E. Miller,et al. Complexity of Computer Computations , 1972 .