# 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

## 110 Citations

New Approximation Algorithms for (1, 2)-TSP

- Computer Science, MathematicsICALP
- 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 Science, MathematicsOper. Res. Lett.
- 2021

This paper gives a lower bound of 3 2 for the approximation ratio of the 2-Opt algorithm for the ( 1, 2 )-TSP and introduces the 3-Opt++-algorithm, an improved version of the3-opt algorithm forThe (1-2)-TSP with an exact approximation ratio.

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

- Computer Science, MathematicsInt. 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

- Mathematics
- 2012

We present a polynomial algorithm with time complexity O(n5) and approximation ratio 4/3 (plus some additive constant) for the minimum 2-peripatetic salesman problem in a complete n-vertex graph withâ€¦

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

- Computer Science, MathematicsDiscret. Appl. Math.
- 2009

The NP-hard problem of finding two edge-disjoint Hamiltonian cycles of minimal total weight in a complete (undirected) graph with edge weights 1 and 2 is considered and polynomial time approximation algorithms are proposed.

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

- Mathematics
- 2009

The problem of finding two disjoint Hamiltonian cycles of minimum sum weight is considered in a complete undirected graph with arbitrarily chosen weights of the edges 1 and 2. The main result of theâ€¦

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

- Computer Science, MathematicsIPCO
- 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

We make several observations on efficient approximation algorithms with proven guarantees for some discrete routing problems that are NP-hard in general case. One of the most popular problems of thisâ€¦

An Approximation Algorithm for the Minimum Co-Path Set Problem

- Mathematics, Computer ScienceAlgorithmica
- 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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