A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming
Mathematics of Operations Research
Local versus global properties of metric spaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
New lower bounds for approximation algorithms in the lovasz-schrijver hierarchy
New lower bounds for approximation algorithms in the lovasz-schrijver hierarchy
Tight integrality gaps for Lovasz-Schrijver LP relaxations of vertex cover and max cut
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A Linear Round Lower Bound for Lovasz-Schrijver SDP Relaxations of Vertex Cover
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Linear programming relaxations of maxcut
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms Using Hierarchies of Semidefinite Programming Relaxations
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Integrality gaps of 2 - o(1) for Vertex Cover SDPs in the Lovész-Schrijver Hierarchy
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Local Global Tradeoffs in Metric Embeddings
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Beating the Random Ordering is Hard: Inapproximability of Maximum Acyclic Subgraph
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Linear Level Lasserre Lower Bounds for Certain k-CSPs
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Sherali-adams relaxations of the matching polytope
Proceedings of the forty-first annual ACM symposium on Theory of computing
Optimal Sherali-Adams Gaps from Pairwise Independence
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Hardness amplification in proof complexity
Proceedings of the forty-second ACM symposium on Theory of computing
Graph expansion and the unique games conjecture
Proceedings of the forty-second ACM symposium on Theory of computing
On linear and semidefinite programming relaxations for hypergraph matching
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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
Improving integrality gaps via Chvátal-Gomory rounding
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Local Global Tradeoffs in Metric Embeddings
SIAM Journal on Computing
How well can primal-dual and local-ratio algorithms perform?
ACM Transactions on Algorithms (TALG)
Integrality gaps of linear and semi-definite programming relaxations for Knapsack
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Integrality Gaps of $2-o(1)$ for Vertex Cover SDPs in the Lovász-Schrijver Hierarchy
SIAM Journal on Computing
Sherali-Adams relaxations and indistinguishability in counting logics
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Polynomial integrality gaps for strong SDP relaxations of Densest k-subgraph
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Subsampling mathematical relaxations and average-case complexity
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
On the rank of cutting-plane proof systems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Exponential Lower Bounds and Integrality Gaps for Tree-Like Lovász-Schrijver Procedures
SIAM Journal on Computing
Sparsest cut on bounded treewidth graphs: algorithms and hardness results
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Some trade-off results for polynomial calculus: extended abstract
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On integrality ratios for asymmetric TSP in the sherali-adams hierarchy
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Proceedings of the 5th conference on Innovations in theoretical computer science
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We prove strong lower bounds on integrality gaps of Sherali-Adams relaxations for MAX CUT, Vertex Cover, Sparsest Cut and other problems. Our constructions show gaps for Sherali-Adams relaxations that survive nδ rounds of lift and project. For MAX CUT and Vertex Cover, these show that even nδ rounds of Sherali-Adams do not yield a better than 2-ε approximation. The main combinatorial challenge in constructing these gap examples is the construction of a fractional solution that is far from an integer solution, but yet admits consistent distributions of local solutions for all small subsets of variables. Satisfying this consistency requirement is one of the major hurdles to constructing Sherali-Adams gap examples. We present a modular recipe for achieving this, building on previous work on metrics with a local-global structure. We develop a conceptually simple geometric approach to constructing Sherali-Adams gap examples via constructions of consistent local SDP solutions. This geometric approach is surprisingly versatile. We construct Sherali-Adams gap examples for Unique Games based on our construction for MAX CUT together with a parallel repetition like procedure. This in turn allows us to obtain Sherali-Adams gap examples for any problem that has a Unique Games based hardness result (with some additional conditions on the reduction from Unique Games). Using this, we construct 2-ε gap examples for Maximum Acyclic Subgraph that rules out any family of linear constraints with support at most nδ.