# 8/7-approximation algorithm for (1,2)-TSP

@article{Berman200687approximationAF, title={8/7-approximation algorithm for (1,2)-TSP}, author={Piotr Berman and Marek Karpinski}, journal={Electron. Colloquium Comput. Complex.}, year={2006} }

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 that problem. As a direct application we get a 7/6-approximation algorithm for the Maximum Path Cover Problem, similarly improving upon the best known approximation factor for that problem. The result depends on a new method of consecutive path cover improvements and on a new analysis of certainâ€¦Â

## 111 Citations

New Approximation Algorithms for (1, 2)-TSP

- Computer ScienceICALP
- 2018

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.

On the Approximation Ratio of the 3-Opt Algorithm for the (1, 2)-TSP

- Computer ScienceOper. Res. Lett.
- 2021

An Approximate Algorithm for Triangle TSP with a Four-Vertex-Three-Line Inequality

- Computer ScienceInt. J. Appl. Metaheuristic Comput.
- 2015

This work gives an approximate algorithm with a four-vertex-three-line inequality for the triangle TSP that can find the better approximations than the double-nearest neighbor algorithm for most TSP instances.

An approximation algorithm for the minimum two peripatetic salesmen problem with different weight functions

- Computer Science, Mathematics
- 2012

This result improves the available algorithm for this problem with approximation ratio 11/7 and presents a polynomial algorithm with time complexity O(n5) and approximation ratio 4/3 for the minimum 2-peripatetic salesman problem in a complete n-vertex graph.

Approximation algorithms for the 2-peripatetic salesman problem with edge weights 1 and 2

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 2009

Approximation algorithms for solving the 2-peripatetic salesman problem on a complete graph with edge weights 1 and 2

- Mathematics, Computer Science
- 2009

The main result of the paper is the presentation of polynomial algorithms with the currently best guaranteed performance factors 26/21 and 6/5, based on finding the partial tours with a large number of edges in the graphs of a special type.

Constant Factor Approximation for ATSP with Two Edge Weights - (Extended Abstract)

- Computer ScienceIPCO
- 2016

This paper gives a constant factor approximation algorithm for the Asymmetric Traveling Salesman Problem on shortest path metrics of directed graphs with two different edge weights based on a flow decomposition theorem for solutions of the Held-Karp relaxation.

The Traveling Salesman Problem

- Computer Science
- 2012

The TSP is perhaps the best-studied NP-hard combinatorial optimization problem, and there are many techniques which have been applied, and so-called local search algorithms find better solutions for large instances although they do not have a finite performance ratio.

Approximation efficient algorithms with performance guarantees for some hard routing problems

- Computer Science

This work makes several observations on efficient approximation algorithms with proven guarantees for some discrete routing problems that are NP-hard in general case, including the Travelling Salesman Problem and MAX SNP-hard.

An Approximation Algorithm for the Minimum Co-Path Set Problem

- Computer Science, MathematicsAlgorithmica
- 2010

An approximation algorithm for the problem of finding a minimum set of edges in a given graph G whose removal from G leaves a graph in which each connected component is a path, which achieves a ratio of 10-7 and runs in O(n1.5) time.

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