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

02/28/2021
by   Xianghui Zhong, et al.
0

The (1,2)-TSP is a special case of the TSP where each edge has cost either 1 or 2. In this paper we give a lower bound of 3/2 for the approximation ratio of the 2-Opt algorithm for the (1,2)-TSP. Moreover, we show that the 3-Opt algorithm has an exact approximation ratio of 11/8 for the (1,2)-TSP. Furthermore, we introduce the 3-Opt++-algorithm, an improved version of the 3-Opt algorithm for the (1-2)-TSP with an exact approximation ratio of 4/3.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/09/2018

Beating the integrality ratio for s-t-tours in graphs

Among various variants of the traveling salesman problem, the s-t-path g...
research
06/25/2019

Krivine diffusions attain the Goemans--Williamson approximation ratio

Answering a question of Abbasi-Zadeh, Bansal, Guruganesh, Nikolov, Schwa...
research
07/22/2022

Fair Range k-center

We study the problem of fairness in k-centers clustering on data with di...
research
09/27/2019

On the Approximation Ratio of the k-Opt and Lin-Kernighan Algorithm for Metric TSP

The k-Opt and Lin-Kernighan algorithm are two of the most important loca...
research
10/26/2019

Facility Location Problem in Differential Privacy Model Revisited

In this paper we study the uncapacitated facility location problem in th...
research
09/30/2021

Polynomial Approximation of Symmetric Functions

We study the polynomial approximation of symmetric multivariate function...
research
11/29/2022

Optimizing sparse fermionic Hamiltonians

We consider the problem of approximating the ground state energy of a fe...

Please sign up or login with your details

Forgot password? Click here to reset