Cut problems and their application to divide-and-conquer
Approximation algorithms for NP-hard problems
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)
Divide-and-conquer approximation algorithms via spreading metrics
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
Finite metric spaces: combinatorics, geometry and algorithms
Proceedings of the eighteenth annual symposium on Computational geometry
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
New Approximation Techniques for Some Linear Ordering Problems
SIAM Journal on Computing
Euclidean distortion and the sparsest cut
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On the Hardness of Approximating Multicut and Sparsest-Cut
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Improved lower bounds for embeddings into L1
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
l22 spreading metrics for vertex ordering problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Unique games on expanding constraint graphs are easy: extended abstract
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On partitioning graphs via single commodity flows
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Overcoming the l1 non-embeddability barrier: algorithms for product metrics
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Partitioning graphs into balanced components
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
Vertex cover resists SDPs tightened by local hypermetric inequalities
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Bilipschitz snowflakes and metrics of negative type
Proceedings of the forty-second ACM symposium on Theory of computing
Approximating sparsest cut in graphs of bounded treewidth
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Approximate Lasserre integrality gap for unique games
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Near-optimal distortion bounds for embedding doubling spaces into L1
Proceedings of the forty-third annual ACM symposium on Theory of computing
Inapproximability Results for Maximum Edge Biclique, Minimum Linear Arrangement, and Sparsest Cut
SIAM Journal on Computing
Sparsest cut on quotients of the hypercube
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Sparsest cut on quotients of the hypercube
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
A PRG for lipschitz functions of polynomials with applications to sparsest cut
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Majority is stablest: discrete and SoS
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Arora, Rao and Vazirani [2] showed that the standard semi-definite programming (SDP) relaxation of the Sparsest Cut problem with the triangle inequality constraints has an integrality gap of O(√log n). They conjectured that the gap is bounded from above by a constant. In this paper, we disprove this conjecture (referred to as the ARV-Conjecture) by constructing an Ω(log log n) integrality gap instance. Khot and Vishnoi [16] had earlier disproved the non-uniform version of the ARV-Conjecture.A simple "stretching" of the integrality gap instance for the Sparsest Cut problem serves as an Ω(log log n) integrality gap instance for the SDP relaxation of the Minimum Linear Arrangement problem. This SDP relaxation was considered in [6, 11], where it was shown that its integrality gap is bounded from above by O(√log n log log n).