The traveling salesman problem with distances one and two
Mathematics of Operations Research
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
On the approximability of the traveling salesman problem (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
When Hamming Meets Euclid: The Approximability of Geometric TSP and Steiner Tree
SIAM Journal on Computing
On Some Tighter Inapproximability Results (Extended Abstract)
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Approximation Hardness of TSP with Bounded Metrics
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs
Journal of the ACM (JACM)
8/7-approximation algorithm for (1,2)-TSP
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Bipartite multigraphs with expander-like properties
Discrete Applied Mathematics
On approximating the maximum simple sharing problem
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Approximating the maximum sharing problem
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Improved inapproximability results for the shortest superstring and related problems
CATS '13 Proceedings of the Nineteenth Computing: The Australasian Theory Symposium - Volume 141
Guest column: the elusive inapproximability of the TSP
ACM SIGACT News
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The general asymmetric TSP with triangle inequality is known to be approximable only within logarithmic factors. In this paper we study the asymmetric and symmetric TSP problems with bounded metrics, i.e., metrics where the distances are integers between one and some constant upper bound. In this case, the problem is known to be approximable within a constant factor. We prove that it is NP-hard to approximate the asymmetric TSP with distances one and two within 321/320-@e and that it is NP-hard to approximate the symmetric TSP with distances one and two within 741/740-@e for every constant @e0. Recently, Papadimitriou and Vempala announced improved approximation hardness results for both symmetric and asymmetric TSP with graph metric. We show that a similar construction can be used to obtain only slightly weaker approximation hardness results for TSP with triangle inequality and distances that are integers between one and eight. This shows that the Papadimitriou-Vempala construction is ''local'' in nature and, intuitively, indicates that it cannot be used to obtain hardness factors that grow with the size of the instance.