Mathematical Programming

, Volume 124, Issue 1, pp 13–32

Copositivity cuts for improving SDP bounds on the clique number

  • Immanuel M. Bomze
  • Florian Frommlet
  • Marco Locatelli
Full Length Paper Series B

DOI: 10.1007/s10107-010-0363-9

Cite this article as:
Bomze, I.M., Frommlet, F. & Locatelli, M. Math. Program. (2010) 124: 13. doi:10.1007/s10107-010-0363-9

Abstract

Adding cuts based on copositive matrices, we propose to improve Lovász’ bound θ on the clique number and its tightening θ′ introduced by McEliece, Rodemich, Rumsey, and Schrijver. Candidates for cheap and efficient copositivity cuts of this type are obtained from graphs with known clique number. The cost of previously established semidefinite programming bound hierarchies starting with θ′ rapidly increases with the order (and quality requirements). By contrast, the bounds proposed here are relatively cheap in the sense that computational effort is comparable to that required for θ′.

Keywords

Lovász’ boundSemidefinite programmingMaximum clique problem

Mathematics Subject Classification (2000)

90C2090C2290C2790C35

Copyright information

© Springer and Mathematical Programming Society 2010

Authors and Affiliations

  • Immanuel M. Bomze
    • 1
  • Florian Frommlet
    • 1
  • Marco Locatelli
    • 2
  1. 1.ISDS, University of ViennaViennaAustria
  2. 2.DII, University of ParmaParmaItaly