Semidefinite programming in combinatorial optimization
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Integrality gaps for sparsest cut and minimum linear arrangement problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
The influence of variables on Boolean functions
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Integrality Gaps for Strong SDP Relaxations of UNIQUE GAMES
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
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We present a simple construction and analysis of an Ω(log log N) integrality gap for the well-known Sparsest Cut semi-definite program (SDP). This holds for the uniform demands version (i.e. edge expansion). The same quantitative gap was proved earlier by Devanur, Khot, Saket, and Vishnoi [STOC 2006], following an integrality gap for non-uniform demands due to Khot and Vishnoi [FOCS 2005]. These previous constructions involve a complicated SDP solution and analysis, while our gap instance, vector solution, and analysis are somewhat simpler and more intuitive. Furthermore, our approach is rather general, and provides a variety of different gap examples derived from quotients of the hypercube. It also illustrates why the lower bound is stuck at Ω(log log N), and why new ideas are needed in order to derive stronger examples.