Copositivity cuts for improving SDP bounds on the clique number

Adding cuts based on copositive matrices, we propose to improve Lov´asz’ 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 recently 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 .

• Type: Journal
• Year: 2010
• Where: MP
• Authors: Immanuel M. Bomze, Florian Frommlet, Marco Locatelli
• Keywords: Clique Number, Efficient Copositivity Cuts, MP 2010, Programming Bound Hierarchies