On the Integrality Ratio for the Asymmetric Traveling Salesman Problem

We improve the lower bound on the integrality ratio of the Held-Karp bound for asymmetric TSP with triangle inequality from 4/3 to 2.

[1]  Richard M. Karp,et al.  The traveling-salesman problem and minimum spanning trees: Part II , 1971, Math. Program..

[2]  N. Biggs THE TRAVELING SALESMAN PROBLEM A Guided Tour of Combinatorial Optimization , 1986 .

[3]  David S. Johnson,et al.  Experimental Analysis of Heuristics for the STSP , 2007 .

[4]  David S. Johnson,et al.  Asymptotic experimental analysis for the Held-Karp traveling salesman bound , 1996, SODA '96.

[5]  Michel X. Goemans,et al.  Survivable networks, linear programming relaxations and the parsimonious property , 1993, Math. Program..

[6]  Pablo Moscato,et al.  On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts : Towards Memetic Algorithms , 1989 .

[7]  Sylvia C. Boyd,et al.  Optimizing over the subtour polytope of the travelling salesman problem , 1990, Math. Program..

[8]  Richard M. Karp,et al.  The Traveling-Salesman Problem and Minimum Spanning Trees , 1970, Oper. Res..

[9]  Sylvia C. Boyd,et al.  Finding the Exact Integrality Gap for Small Traveling Salesman Problems , 2002, Math. Oper. Res..

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

[11]  Joseph S. B. Mitchell,et al.  Guillotine Subdivisions Approximate Polygonal Subdivisions: A Simple Polynomial-Time Approximation Scheme for Geometric TSP, k-MST, and Related Problems , 1999, SIAM J. Comput..

[12]  David P. Williamson,et al.  Analyzing the Held-Karp TSP Bound: A Monotonicity Property with Application , 1990, Inf. Process. Lett..

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

[14]  Sanjeev Arora,et al.  Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems , 1998, JACM.

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

[16]  L. Wolsey Heuristic analysis, linear programming and branch and bound , 1980 .

[17]  Robert D. Carr,et al.  On the Held-Karp relaxation for the asymmetric and symmetric traveling salesman problems , 2004, Math. Program..

[18]  David P. Williamson ANALYSIS OF THE HELD-KARP HEURISTIC FOR THE TRAVELING SALESMAN PROBLEM , 1990 .

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

[20]  ATSPDavid S. JohnsonAT Experimental Analysis of Heuristics for the Stsp , 2001 .

[21]  Sanjeev Arora,et al.  Polynomial time approximation schemes for Euclidean TSP and other geometric problems , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[22]  Abraham P. Punnen,et al.  The traveling salesman problem and its variations , 2007 .

[23]  Clyde L. Monma,et al.  Minimum-weight two-connected spanning networks , 1990, Math. Program..

[24]  L M Adleman,et al.  Molecular computation of solutions to combinatorial problems. , 1994, Science.

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

[26]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.