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On semidefinite programming relaxations of maximum k-section

Etienne De Klerk(e.deklerk***at***uvt.nl)
Cristian Dobre(c.dobre***at***uvt.nl)
Dmitrii, V. Pasechnik(dima***at***ntu.edu.sg)
Renata Sotirov(r.sotirov***at***uvt.nl)

Abstract: We derive a new semidefinite programming bound for the maximum k-section problem. For k=2 (i.e. for maximum bisection), the new bound is least as strong as the well-known bound by Frieze and Jerrum [A. Frieze and M. Jerrum. Improved Approximation Algorithms for MAX k-CUT and MAX BISECTION. Algorithmica, 18(1): 67-81, 1997]. For k > 2 the new bound dominates a bound of Karish and Rendl [S.E. Karish, F. Rendl. Semidefinite Programming and Graph Equipartition. In: Topics in Semidefinite and Interior-Point Methods, P.M. Pardalos and H. Wolkowicz, Eds., 1998.] The new bound is derived from a recent semidefinite programming bound by De Klerk and Sotirov for the more general quadratic assignment problem (QAP), but only requires the solution of a much smaller semidefinite program.

Keywords: Maximum bisection, Maximum section, Semidefinite programming, Coherent configurations

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Combinatorial Optimization

Category 3: Integer Programming ((Mixed) Integer Nonlinear Programming )

Citation: Preprint, Tilburg University, The Netherlands, June, 2010

Download: [PDF]

Entry Submitted: 07/27/2010
Entry Accepted: 07/27/2010
Entry Last Modified: 07/27/2010

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