# Approximating Graphic TSP by Matchings

@article{Mmke2011ApproximatingGT, title={Approximating Graphic TSP by Matchings}, author={Tobias M{\"o}mke and Ola Svensson}, journal={2011 IEEE 52nd Annual Symposium on Foundations of Computer Science}, year={2011}, pages={560-569} }

We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of certain edges leading to a decreased cost. For the TSP on graphic metrics (graph-TSP), the approach yields a 1.461-approximation algorithm with respect to the Held-Karp lower bound. For graph-TSP restricted to a class of graphs that contains degree three bounded…

## 122 Citations

Removing and Adding Edges for the Traveling Salesman Problem

- Computer Science, MathematicsJ. ACM
- 2016

A framework for approximating the metric TSP based on a novel use of matchings, which allows for generalizations in a natural way and leads to analogous results for the s, t-path traveling salesman problem on graphic metrics where the start and end vertices are prespecified.

Improved Analysis for Graphic TSP Approximation via Matchings

- Computer Science, MathematicsArXiv
- 2011

This paper provides an improved analysis for the approach presented in [8], yielding a bound of 35 24 on the approximation factor, as well as a Bound of 19 12 + e for any e > 0 for a more general Travelling Salesman Path Problem in graphic metrics.

Shorter tours by nicer ears: 7/5-approximation for the graph-TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs

- Computer Science, MathematicsArXiv
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The key new ingredient of all algorithms is a special kind of ear-decomposition optimized using forest representations of hypergraphs that provides the lower bounds that are used to deduce the approximation ratios.

Shorter tours by nicer ears: 7/5-Approximation for the graph-TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs

- Computer Science, MathematicsComb.
- 2014

The key new ingredient of all algorithms is a special kind of ear-decomposition optimized using forest representations of hypergraphs that provides the lower bounds that are used to deduce the approximation ratios.

A -approximation algorithm for Graphic TSP in cubic bipartite graphs

- Mathematics, Computer ScienceDiscret. Appl. Math.
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An improved approximation algorithm for the traveling salesman problem with relaxed triangle inequality

- Mathematics, Computer ScienceInf. Process. Lett.
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-approximation for Graphic Tsp * Introduction and Related Work

- Computer Science
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This paper provides an improved analysis of the approach presented in [8], yielding a bound of 13 9 on the approximation factor, as well as a Bound of 19 12 + ε for any ε > 0 for a more general Travelling Salesman Path Problem in graphic metrics.

LP-Based Approximation Algorithms for Traveling Salesman Path Problems

- Computer ScienceArXiv
- 2011

It is shown that the recent result of Oveis Gharan, Saberi and Singh on the traveling salesman circuit problem under the unit-weight graphical metric can be modified for the path case to complement Hoogeveen's algorithm in the critical case, providing an improved performance guarantee of (5/3 - epsilon).

A note on bounded weighted graphic metric TSP

- Computer Science, Mathematics
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This paper investigates TSP for so-called βbounded metrics and determines that, for any β ≥ 1, the randomized approach of Oveis Gharan, Saberi and Singh achieves a better-than-3/2 guarantee for β-bounded metric spaces.

13/9-approximation for Graphic TSP

- Computer ScienceSTACS
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This paper provides an improved analysis of the approach used by Momke and Svensson, yielding a bound of 13/9 on the approximation factor, as well as a Bound of 19/12+epsilon for any epsilon>0 for a more general Travelling Salesman Path Problem in graphic metrics.

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