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

  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},
A constant-factor approximation algorithm for the asymmetric traveling salesman problem
We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem. Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our
A Constant-factor Approximation Algorithm for the Asymmetric Traveling Salesman Problem
A constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP) is given, showing that any algorithm for Subtour Partition Cover can be turned into an algorithm for ATSP while only losing a small constant factor in the performance guarantee.
Travelling Santa Problem: Optimization of a Million-Households Tour Within One Hour
  • T. Strutz
  • Computer Science
    Frontiers in Robotics and AI
  • 2021
A new approach for two-dimensional symmetric problems with more than a million coordinates is proposed that is able to create good initial tours within few minutes and is superior to state-of-the-art methods when applied to TSP instances with non-uniformly distributed coordinates.
The Multi-vehicle Ride-Sharing Problem
The experimental results show that the ride-sharing scheme produced by the proposed two-phase algorithm not only has small total travel distance compared to state-of-the-art baselines, but also enjoys a small makespan and total latency, which crucially relate to each single rider's traveling time, which suggests that the algorithm also enhances rider experience while being energy-efficient.
Approximation Algorithms for Multi-vehicle Stacker Crane Problems
A (slightly) improved approximation algorithm for metric TSP
For some > 10−36 the authors give a randomized 3/2− approximation algorithm for metric TSP, which is equivalent to a randomized 2/3− approximation for standard TSP.
Approximating TSP walks in subcubic graphs
We prove that every simple 2-connected subcubic graph on n vertices with n2 vertices of degree 2 has a TSP walk of length at most 5n+n2 4 − 1, confirming a conjecture of Dvořák, Král’, and Mohar.
From Symmetry to Asymmetry: Generalizing TSP Approximations by Parametrization
The tree doubling and Christofides algorithm are generalized and a parameterized 3-approximation is derived, where the parameter is the number of asymmetric edges in a given minimum spanning arborescence, which yields algorithms to efficiently compute constant factor approximations also for moderately asymmetric TSP instances.


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
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
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
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
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
  • Computer Science
    Math. Oper. Res.
  • 1977
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
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
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.