Analyzing the Held-Karp TSP bound: a monotonicity property with application
Information Processing Letters
The traveling salesman problem with distances one and two
Mathematics of Operations Research
A polynomial-time approximation scheme for weighted planar graph TSP
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Approximability of dense and sparse instances of minimum 2-connectivity, TSP and path problems
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
An approximation scheme for planar graph TSP
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
SIAM Journal on Discrete Mathematics
8/7-approximation algorithm for (1,2)-TSP
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
An improved upper bound for the TSP in cubic 3-edge-connected graphs
Operations Research Letters
A proof of the Boyd-Carr conjecture
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On the integrality gap of the subtour LP for the 1,2-TSP
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
TSP tours in cubic graphs: beyond 4/3
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says that the integrality gap, i.e., the worst case ratio between the optimal values of the TSP and its linear programming relaxation, is 4/3. Using polyhedral techniques in an interesting way, we obtain a polynomial-time 4/3-approximation algorithm for this problem on cubic graphs, improving upon Christofides' 3/2-approximation, and upon the 3/2 - 5/389 ≈ 1.487-approximation ratio by Gamarnik, Lewenstein and Svirdenko for the case the graphs are also 3-edge connected. We also prove that, as an upper bound, the 4/3 conjecture is true for this problem on cubic graphs. For subcubic graphs we obtain a polynomial-time 7/5-approximation algorithm and a 7/5 bound on the integrality gap.