Integer and combinatorial optimization
Integer and combinatorial optimization
Semidefinite Programming Relaxation for NonconvexQuadratic Programs
Journal of Global Optimization
Computational Experience with Stable Set Relaxations
SIAM Journal on Optimization
Simple and Fast: Improving a Branch-And-Bound Algorithm for Maximum Clique
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Exploring the Relationship Between Max-Cut and Stable Set Relaxations
Mathematical Programming: Series A and B
Semidefinite programming relaxations for graph coloring and maximal clique problems
Mathematical Programming: Series A and B
Coefficient strengthening: a tool for reformulating mixed-integer programs
Mathematical Programming: Series A and B
A Branch and Cut solver for the maximum stable set problem
Journal of Combinatorial Optimization
A branch-and-cut algorithm for the maximum cardinality stable set problem
Operations Research Letters
On the Slater condition for the SDP relaxations of nonconvex sets
Operations Research Letters
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A new exact approach to the stable set problem is presented, which attempts to avoids the pitfalls of existing approaches based on linear and semidefinite programming. The method begins by constructing an ellipsoid that contains the stable set polytope and has the property that the upper bound obtained by optimising over it is equal to the Lovász theta number. This ellipsoid is then used to derive cutting planes, which can be used within a linear programming-based branch-and-cut algorithm. Preliminary computational results indicate that the cutting planes are strong and easy to generate.