The traveling salesman problem on cubic and subcubic graphs
@article{Boyd2011TheTS, title={The traveling salesman problem on cubic and subcubic graphs}, author={Sylvia C. Boyd and Ren{\'e} Sitters and Suzanne van der Ster and Leen Stougie}, journal={Mathematical Programming}, year={2011}, volume={144}, pages={227-245} }
We study the traveling 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 value of a TSP instance and that of its linear programming relaxation (the subtour elimination relaxation), is 4/3. We present the first algorithm for cubic graphs with approximation ratio…
38 Citations
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- Computer Science
- 2014
An approximation algorithm is presented that gives a 2-edge-connected spanning subgraph with the number of edges at most n+k−1 − k−2 k−1 with a novel use of circulations, which improves both the approximation ratio and the simplicity of the proof compared to i a result by Huh in 2004.
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- MathematicsMath. Program.
- 2015
It is shown computationally that the integrality gap is at most 10/9 for all instances with at most 12 cities and under a weaker assumption, which is an analog of a recent conjecture by Schalekamp et al., it is shown that this conjecture is true when the optimal subtour LP solution has a certain structure.
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- Mathematics, Computer ScienceIPCO
- 2016
Improved approximation guarantees for the traveling salesman problem on cubic bipartite graphs and cubic graphs are shown and the techniques of Mömke and Svensson can be combined with the technique of Correa, Larré and Soto to obtain a tour of length at most.
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- Mathematics, Computer Science
- 2017
This work presents a procedure to decompose an optimal solution for the subtour linear program into spanning, connected subgraphs that cover each 2-edge cut an even number of times, and designs a simple-approximation algorithm for 2EC on subcubic, node-weighted graphs.
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- Mathematics, Computer ScienceInf. Process. Lett.
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On Applying Methods for Graph-TSP to Metric TSP
- Computer Science
- 2016
A new heuristic for metric TSP is developed based on extending ideas successfully used by Mömke and Svensson for the special case of graph-TSP to the more general case of metric T SP, and the exact value of the ratio between the cost of the optimal TSP tour and the optimal subtour linear programming relaxation is found, which was previously unknown.
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- Mathematics, Computer ScienceArXiv
- 2015
Improved approximation guarantees for the traveling salesman problem on cubic graphs, and cubic bipartite graphs, are shown and a simple "local improvement" algorithm is given that finds a tour of length at most 5/4 n - 2.
An Improved Analysis of the Mömke-Svensson Algorithm for Graph-TSP on Subquartic Graphs
- Computer Science, MathematicsESA
- 2014
It is shown that the approximation guarantee holds for all graphs that have an optimal solution to a standard linear programming relaxation of graph-TSP with subquartic support and that Momke and Svensson's algorithm has an approximation guarantee of at most $25/18$ on sub Quartic graphs.
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- 2021
The results show that if the everywhere 2 3 vector is an optimal solution for the subtour elimination linear programming relaxation for TSP, then a tour with weight at most 27 19 times that of an optimal tour can be found efficiently.
Approximating the Regular Graphic TSP in Near Linear Time
- Computer Science, MathematicsFSTTCS
- 2015
The key ingredient of the algorithm is a technique that uses edge-coloring algorithms to sample a cycle cover with $O(n/\log k)$ cycles with high probability, in near linear time.
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