Fast approximation algorithms for fractional packing and covering problems
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Efficient approximation algorithms for semidefinite programs arising from MAX CUT and COLORING
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Primal-Dual Schema Based Approximation Algorithms (Abstract)
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
0(\sqrt {\log n)} Approximation to SPARSEST CUT in Õ(n2) Time
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Combinatorica
A combinatorial, primal-dual approach to semidefinite programs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Beating Simplex for Fractional Packing and Covering Linear Programs
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Approximating Semidefinite Packing Programs
SIAM Journal on Optimization
An efficiently computable support measure for frequent subgraph pattern mining
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
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The Lovász Θ-function [Lov79] on a graph G = (V, E) can be defined as the maximum of the sum of the entries of a positive semidefinite matrix X, whose trace Tr(X) equals 1, and Xij = 0 whenever {i, j} ∈ E. This function appears as a subroutine for many algorithms for graph problems such as maximum independent set and maximum clique. We apply Arora and Kale's primal-dual method for SDP to design an approximate algorithm for the Θ-function with an additive error of δ 0, which runs in time O(α2n2/δ2 logn ċ Me), where α = Θ(G) and Me = O(n3) is the time for a matrix exponentiation operation. Moreover, our techniques generalize to the weighted Lovász Θ-function, and both the maximum independent set weight and the maximum clique weight for vertex weighted perfect graphs can be approximated within a factor of (1+ơ) in time O(ơ-2n5 log n).