Analyzing the Held-Karp TSP bound: a monotonicity property with application
Information Processing Letters
A note on the prize collecting traveling salesman problem
Mathematical Programming: Series A and B
Survivable networks, linear programming relaxations and the parsimonious property
Mathematical Programming: Series A and B
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Worst-case comparison of valid inequalities for the TSP
Mathematical Programming: Series A and B
Paths, Trees, and Minimum Latency Tours
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
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
Approximation algorithms for the bottleneck asymmetric traveling salesman problem
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Improved Approximation Algorithms for Prize-Collecting Steiner Tree and TSP
SIAM Journal on Computing
A Randomized Rounding Approach to the Traveling Salesman Problem
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Approximating Graphic TSP by Matchings
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
A 53-approximation algorithm for the clustered traveling salesman tour and path problems
Operations Research Letters
The parsimonious property of cut covering problems and its applications
Operations Research Letters
A rounding by sampling approach to the minimum size k-arc connected subgraph problem
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
TSP tours in cubic graphs: beyond 4/3
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
An improved integrality gap for asymmetric TSP paths
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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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We present a deterministic (1+√5/2)-approximation algorithm for the s-t path TSP for an arbitrary metric. Given a symmetric metric cost on $n$ vertices including two prespecified endpoints, the problem is to find a shortest Hamiltonian path between the two endpoints; Hoogeveen showed that the natural variant of Christofides' algorithm is a 5/3-approximation algorithm for this problem, and this asymptotically tight bound in fact had been the best approximation ratio known until now. We modify this algorithm so that it chooses the initial spanning tree based on an optimal solution to the Held-Karp relaxation rather than a minimum spanning tree; we prove this simple but crucial modification leads to an improved approximation ratio, surpassing the 20-year-old barrier set by the natural Christofides' algorithm variant. Our algorithm also proves an upper bound of 1+√5/2 on the integrality gap of the path-variant Held-Karp relaxation. The techniques devised in this paper can be applied to other optimization problems as well: these applications include improved approximation algorithms and improved LP integrality gap upper bounds for the prize-collecting s-t path problem and the unit-weight graphical metric s-t path TSP.