A new approximation algorithm for the asymmetric TSP with triangle inequality
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Constrained TSP and Low-Power Computing
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Proceedings of the 18th Conference on Foundations of Software Technology and Theoretical Computer Science
On the Integrality Ratio for Asymmetric TSP
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs
Journal of the ACM (JACM)
Lower bounds for maximum parsimony with gene order data
RCG'05 Proceedings of the 2005 international conference on Comparative Genomics
Improved algorithms for orienteering and related problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The on-line asymmetric traveling salesman problem
Journal of Discrete Algorithms
Improved Approximation Ratios for Traveling Salesperson Tours and Paths in Directed Graphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
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Given an arc-weighted directed graph G = (V,A,ℓ) and a pair of vertices s,t, we seek to find an s-twalk of minimum length that visits all the vertices in V. If ℓ satisfies the asymmetric triangle inequality, the problem is equivalent to that of finding an s-tpath of minimum length that visits all the vertices. We refer to this problem as ATSPP. When s = t this is the well known asymmetric traveling salesman tour problem (ATSP). Although an O(logn) approximation ratio has long been known for ATSP, the best known ratio for ATSPP is $O(\sqrt{n})$. In this paper we present a polynomial time algorithm for ATSPP that has approximation ratio of O(logn). The algorithm generalizes to the problem of finding a minimum length path or cycle that is required to visit a subset of vertices in a given order.