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Title: Reduction of symmetric semidefinite programs using the regular representation
Authors: Klerk, Etienne de.
Pasechnik, Dmitrii V.
Schrijver, Alexander.
Keywords: DRNTU::Science::Mathematics
Issue Date: 2006
Source: Klerk, E. d., Pasechnik, D. V. & Schrijver, A. (2006). Reduction of symmetric semidefinite programs using the regular representation. Mathematical Programming, 109, 613-624.
Series/Report no.: Mathematical programming
Abstract: We consider semidefinite programming problems on which a permutation group is acting.We describe a general technique to reduce the size of such problems, exploiting the symmetry. The technique is based on a low-order matrix ∗-representation of the commutant (centralizer ring) of the matrix algebra generated by the permutation matrices.We apply it to extending amethod of de Klerk et al. that gives a semidefinite programming lower bound to the crossing number of complete bipartite graphs. It implies that cr(K8,n) ≥ 2.9299n2−6n, cr(K9,n) ≥ 3.8676n2 − 8n, and (for any m ≥ 9) lim n→∞ cr(Km,n)/Z(m, n) ≥ 0.8594 m/m − 1, where Z(m,n) is the Zarankiewicz number [1/4(m-1)2][1/4(n-1)2], which is the conjectured value of cr(K m,n ). Here the best factor previously known was 0.8303 instead of 0.8594.
DOI: 10.1007/s10107-006-0039-7
Rights: © 2006 Springer-Verlag. This is the author created version of a work that has been peer reviewed and accepted for publication by Mathematical Programming, Springer-Verlag. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [DOI: ].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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