On semidefinite programming relaxations of the traveling salesman problem
Optimization and Control
2009-02-12 v1 Combinatorics
Abstract
We consider a new semidefinite programming (SDP) relaxation of the symmetric traveling salesman problem (TSP) that may be obtained via an SDP relaxation of the more general quadratic assignment problem (QAP). We show that the new relaxation dominates the one in [D. Cvetkovic, M. Cangalovic, and V. Kovacevic-Vujcic, Semidefinite programming methods for the symmetric traveling salesman problem, in Proc. 7th Int. IPCO Conference, Springer, London, 1999, pp. 126--136]. Unlike the bound of Cvetkovic et al., the new SDP bound is not dominated by the Held-Karp linear programming bound, or vice versa.
Cite
@article{arxiv.0902.1843,
title = {On semidefinite programming relaxations of the traveling salesman problem},
author = {Etienne de Klerk and Dmitrii V. Pasechnik and Renata Sotirov},
journal= {arXiv preprint arXiv:0902.1843},
year = {2009}
}
Comments
18 pages, 1 figure (corrects the figure in the published version), LaTeX, MetaPost for the figure