On semidefinite programming relaxations of the traveling salesman problem

de Klerk, Etienne; Pasechnik, Dmitrii V.; Sotirov, Renata

On semidefinite programming relaxations of the traveling salesman problem

Authors

de Klerk, Etienne

Pasechnik, Dmitrii V.

Sotirov, Renata

Description

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.
18 pages, 1 figure (corrects the figure in the published version), LaTeX, MetaPost for the figure