On Semidefinite Programming Relaxations of Association Schemes with Application to Combinatorial Optimization Problems

CentER Discussion Paper Series No. 2009-54

20 Pages Posted: 5 Jul 2009

See all articles by Etienne de Klerk

Etienne de Klerk

Tilburg University

Dmitrii V. Pasechnik

Tilburg University - Center for Economic Research (CentER)

Date Written: July 2, 2009

Abstract

We construct convex, semidefinite programming (SDP) relaxations of the convex hull of association schemes with given parameters. As an application, we obtain new and known SDP relaxations of several combinatorial optimizations problems, including the traveling salesman and cycle covering problems (by considering the Lee association scheme) and the maximum p-section problem (by considering the scheme of the complete p-partite graph).

Thus, the approach in this paper may be seen as a unified framework to generate SDP relaxations of various combinatorial optimization problems.

Keywords: traveling salesman problem, maximum bisection, semidefinite programming, association schemes

JEL Classification: C61

Suggested Citation

de Klerk, Etienne and Pasechnik, Dmitrii V., On Semidefinite Programming Relaxations of Association Schemes with Application to Combinatorial Optimization Problems (July 2, 2009). CentER Discussion Paper Series No. 2009-54. Available at SSRN: https://ssrn.com/abstract=1429264 or http://dx.doi.org/10.2139/ssrn.1429264

Etienne De Klerk (Contact Author)

Tilburg University ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Dmitrii V. Pasechnik

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

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