Publication

A Constant-Factor Approximation Algorithm for the Asymmetric Traveling Salesman Problem

Ola Nils Anders Svensson, Jakub Tarnawski
2018
Conference Papers

Abstract

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 result confirms the conjectured constant integrality gap of that relaxation.

Official source

https://infoscience.epfl.ch/entities/publication/f37c69d0-f772-49ca-bb02-b0aa3a0185a7

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Ola Nils Anders Svensson, Jakub Tarnawski
2018
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/f37c69d0-f772-49ca-bb02-b0aa3a0185a7

About this result

Related concepts (13)

Approximation algorithm

In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the field of theoretical computer science as a consequence of the widely believed P ≠ NP conjecture. Under this conjecture, a wide class of optimization problems cannot be solved exactly in polynomial time.

Travelling salesman problem

The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP.

Linear programming relaxation

In mathematics, the relaxation of a (mixed) integer linear program is the problem that arises by removing the integrality constraint of each variable. For example, in a 0–1 integer program, all constraints are of the form The relaxation of the original integer program instead uses a collection of linear constraints The resulting relaxation is a linear program, hence the name.

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