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… 
Removing and Adding Edges for the Traveling Salesman Problem
TLDR
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
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.
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
-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.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 40 REFERENCES
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.
TSP on Cubic and Subcubic Graphs
TLDR
It is proved that, as an upper bound, the 4/3 conjecture is true for this problem on cubic graphs, and a polynomial-time 7/5-approximation algorithm and a 7/ 5 bound on the integrality gap are obtained.
A Randomized Rounding Approach to the Traveling Salesman Problem
TLDR
This work gives a (3/2-\eps_0)-approximation algorithm that finds a spanning tree whose cost is upper bounded by the optimum, then it finds the minimum cost Eulerian augmentation (or T-join) of that tree.
The traveling salesman problem on a graph and some related integer polyhedra
TLDR
Some facet inducing inequalities of the convex hull of the solutions to the Graphical Traveling Salesman Problem are given and the so-called comb inequalities of Grötschel and Padberg are generalized.
The Traveling-Salesman Problem and Minimum Spanning Trees
TLDR
It is shown that maxπwπ = C* precisely when a certain well-known linear program has an optimal solution in integers.
Analyzing the Held-Karp TSP Bound: A Monotonicity Property with Application
Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem
TLDR
An O(n3) heuristic algorithm is described for solving d-city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition and a worst-case analysis of this heuristic shows that the ratio of the answer obtained to the optimum TSP solution is strictly less than 3/2.
On the Relationship between the Biconnectivity Augmentation and Traveling Salesman Problems
Guillotine Subdivisions Approximate Polygonal Subdivisions: A Simple Polynomial-Time Approximation Scheme for Geometric TSP, k-MST, and Related Problems
TLDR
A consequence of the main theorem is a simple polynomial-time approximation scheme for geometric instances of several network optimization problems, including the Steiner minimum spanning tree, the traveling salesperson problem (TSP), and the k-MST problem.
Maximum matching and a polyhedron with 0,1-vertices
TLDR
The emphasis in this paper is on relating the matching problem to the theory of continuous linear programming, and the algorithm described does not involve any "blind-alley programming" -which, essentially, amounts to testing a great many combinations.
...
1
2
3
4
...