Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs
Journal of the ACM (JACM)
On the Integrality Ratio for the Asymmetric Traveling Salesman Problem
Mathematics of Operations Research
Traveling salesman path problems
Mathematical Programming: Series A and B
A new approximation algorithm for the asymmetric TSP with triangle inequality
ACM Transactions on Algorithms (TALG)
The Directed Minimum Latency Problem
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
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
Poly-logarithmic Approximation Algorithms for Directed Vehicle Routing Problems
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
An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Asymmetric traveling salesman path and directed latency problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximation algorithms for the directed k-tour and k-stroll problems
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Improving christofides' algorithm for the s-t path TSP
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Eight-Fifth approximation for the path TSP
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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The Asymmetric Traveling Salesperson Path (ATSPP) problem is one where, given an asymmetric metric space (V,d) with specified vertices s and t, the goal is to find an s-t path of minimum length that visits all the vertices in V. This problem is closely related to the Asymmetric TSP (ATSP) problem, which seeks to find a tour (instead of an s-t path) visiting all the nodes: for ATSP, a ρ-approximation guarantee implies an O(ρ)-approximation for ATSPP. However, no such connection is known for the integrality gaps of the linear programming relxations for these problems: the current-best approximation algorithm for ATSPP is O(logn/loglogn), whereas the best bound on the integrality gap of the natural LP relaxation (the subtour elmination LP) for ATSPP is O(logn). In this paper, we close this gap, and improve the current best bound on the integrality gap from O(logn) to O(logn/loglogn). The resulting algorithm uses the structure of narrow s-t cuts in the LP solution to construct a (random) tree witnessing this integrality gap. We also give a simpler family of instances showing the integrality gap of this LP is at least 2.