An approximation algorithm for the asymmetric travelling salesman problem with distances one and two
Information Processing Letters
The traveling salesman problem with distances one and two
Mathematics of Operations Research
Performance Guarantees for Approximation Algorithms Depending on Parametrized Triangle Inequalities
SIAM Journal on Discrete Mathematics
Combinatorial optimization
Towards a 4/3 approximation for the asymmetric traveling salesman problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Performance Guarantees for the TSP with a Parameterized Triangle Inequality
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
A new approximation algorithm for the asymmetric TSP with triangle inequality
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
An improved approximation algorithm for the asymmetric TSP with strengthened triangle inequality
Journal of Discrete Algorithms
A new approximation algorithm for the asymmetric TSP with triangle inequality
ACM Transactions on Algorithms (TALG)
An improved approximation algorithm for the asymmetric TSP with strengthened triangle inequality
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Approximating survivable networks with β-metric costs
Journal of Discrete Algorithms
Approximation algorithms for restricted cycle covers based on cycle decompositions
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Approximation algorithms for multi-criteria traveling salesman problems
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
| Hi-index | 0.00 |
We give a constant factor ( 驴/1-驴 + 驴) approximation for the asymmetric traveling salesman problem in graphs with costs on the edges satisfying 驴-parametrized triangle inequality (驴-Asymmetric graphs) for 驴 驴 [1/2, 1). We also give an improvement of the algorithm with approximation factor approaching 驴/1-驴.We also explore the cmax/cmin ratio of edge costs in a general asymmetric graph. We show that for 驴 驴 [1/2, 1/驴3 ), cmax/cmin 驴 2驴3/1-3驴2, while for 驴 驴 [ 1/驴3, 1), this ratio can be arbitrarily large. We make use of this result to give a better analysis to our main algorithm. We also observe that when cmax/cmin 驴2/1-驴-驴2 with 驴 驴 (1/2, 驴5-1/2), the minimum cost and the maximum cost edges in the graph are unique and are reverse to each other.