An Improved Approximation Algorithm for the Traveling Salesman Problem with Relaxed Triangle Inequality
Data Structures and Algorithms
2014-12-23 v1
Abstract
Given a complete edge-weighted graph G, we present a polynomial time algorithm to compute a degree-four-bounded spanning Eulerian subgraph of 2G that has at most 1.5 times the weight of an optimal TSP solution of G. Based on this algorithm and a novel use of orientations in graphs, we obtain a (3 beta/4 + 3 beta^2/4)-approximation algorithm for TSP with beta-relaxed triangle inequality (beta-TSP), where beta >= 1. A graph G is an instance of beta-TSP, if it is a complete graph with non-negative edge weights that are restricted as follows. For each triple of vertices u,v,w in V(G), c({u,v}) <= beta (c({u,w}) + c({w,v})).
Cite
@article{arxiv.1412.6755,
title = {An Improved Approximation Algorithm for the Traveling Salesman Problem with Relaxed Triangle Inequality},
author = {Tobias Mömke},
journal= {arXiv preprint arXiv:1412.6755},
year = {2014}
}
Comments
8 pages, 1 figure