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}
}
  • Tobias Mömke, O. Svensson
  • Published 15 April 2011
  • Computer Science, Mathematics
  • 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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… 
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122 Citations
Highly Influential Citations
28
Background Citations
46
Methods Citations
25
Results Citations
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122 Citations

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Removing and Adding Edges for the Traveling Salesman Problem
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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
  • M. Mucha
  • Computer Science, Mathematics
    ArXiv
  • 2011
TLDR
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
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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
TLDR
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
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  • Tobias Mömke
  • Mathematics, Computer Science
    Inf. Process. Lett.
  • 2015
-approximation for Graphic Tsp * Introduction and Related Work
TLDR
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
TLDR
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
TLDR
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
TLDR
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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References

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Improved Analysis for Graphic TSP Approximation via Matchings
  • M. Mucha
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    ArXiv
  • 2011
TLDR
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.
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