Ellipsoidal relaxations of the stable set problem : theory and algorithms

Giandomenico, Monia and Letchford, Adam and Rossi, Fabrizio and Smriglio, Stefano (2015) Ellipsoidal relaxations of the stable set problem : theory and algorithms. SIAM Journal on Optimization, 25 (3). pp. 1944-1963. ISSN 1052-6234

[thumbnail of ellipsoids-source]
PDF (ellipsoids-source)
ellipsoids_source.pdf - Accepted Version
Available under License Creative Commons Attribution.

Download (376kB)


A new exact approach to the stable set problem is presented, which attempts to avoid 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 Lovasz theta number. This ellipsoid can then be used to construct useful convex relaxations of the stable set problem, which can be embedded within a branch-and-bound framework. Extensive computational results are given, which indicate the potential of the approach.

Item Type:
Journal Article
Journal or Publication Title:
SIAM Journal on Optimization
Additional Information:
Copyright © 2015, Society for Industrial and Applied Mathematics
Uncontrolled Keywords:
?? combinatorial optimisationsemidefinite programmingbranch-and-cuttheoretical computer sciencesoftwarediscipline-based research ??
ID Code:
Deposited By:
Deposited On:
27 Jul 2015 12:12
Last Modified:
18 Dec 2023 01:29