A historical note on the 3/2-approximation algorithm for the metric traveling salesman problem

@article{vanBevern2020AHN,
  title={A historical note on the 3/2-approximation algorithm for the metric traveling salesman problem},
  author={Ren{\'e} van Bevern and Viktoriia A. Slugina},
  journal={ArXiv},
  year={2020},
  volume={abs/2004.02437}
}
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  • Journal of the Operations Research Society of China
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References

SHOWING 1-10 OF 85 REFERENCES
8/7-approximation algorithm for (1,2)-TSP
We design a polynomial time 8/7-approximation algorithm for the Traveling Salesman Problem in which all distances are either one or two. This improves over the best known approximation factor for
Approximation algorithms for some routing problems
Several polynomial time approximation algorithms for some NP-complete routing problems are presented, and the worst-case ratios of the cost of the obtained route to that of an optimal are determined.
The Salesman’s Improved Paths through Forests
TLDR
A new, strongly polynomial-time algorithm and improved analysis for the metric s-t path Traveling Salesman Problem (TSP) and it is shown that these new methods lead to improving the integrality ratio and approximation guarantee below 1.53, as was shown in the preliminary, shortened version of this article.
New Approximation Algorithms for (1, 2)-TSP
TLDR
This work gives faster and simpler approximation algorithms for the (1,2)-TSP problem, a well-studied variant of the traveling salesperson problem where all distances between cities are either 1 or 2, and their analysis is simpler than the previously best 8/7-approximation.
An Analysis of Several Heuristics for the Traveling Salesman Problem
Several polynomial time algorithms finding “good,” but not necessarily optimal, tours for the traveling salesman problem are considered. We measure the closeness of a tour by the ratio of the
The Travelling Salesman Problem
  • S. Näher
  • Computer Science
    Algorithms Unplugged
  • 2011
TLDR
The author explains how a so-called “approximation algorithm” can find a tour that is maybe not the shortest one but one whose length usually is quite close to the optimum.
Approaching 3/2 for the s-t-path TSP
TLDR
There is a polynomial-time algorithm with approximation guarantee 3/2+ε for the s-t-path TSP, for any fixed ε > 0, that “guesses” lonely cuts and edges and strengthens the LP.
Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane
  • R. Karp
  • Mathematics, Computer Science
    Math. Oper. Res.
  • 1977
TLDR
This work considers partitioning algorithms for the approximate solution of large instances of the traveling-salesman problem in the plane, in which partitioning is used in conjunction with existing heuristic algorithms.
The Travelling Salesman and the PQ-Tree
TLDR
This work shows how to compute in O(2dn3) time the shortest travelling salesman tour contained in II(T), which may be interpreted as a common generalization of the well-known Held and Karp dynamic programming algorithm for the TSP and for finding the shortest pyramidal TSP tour.
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.
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