Expressing combinatorial optimization problems by linear programs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The cut polytope and the Boolean quadric polytope
Discrete Mathematics
A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
On the distributional complexity of disjointness
Theoretical Computer Science
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
Communication complexity
Quantum computation and quantum information
Quantum computation and quantum information
Quantum communication and complexity
Theoretical Computer Science - Natural computing
Proving Integrality Gaps without Knowing the Linear Program
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Nondeterministic Quantum Query and Communication Complexities
SIAM Journal on Computing
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Lower bounds for local search by quantum arguments
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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
Linear programming relaxations of maxcut
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum Computer Science: An Introduction
Quantum Computer Science: An Introduction
Integrality gaps for Sherali-Adams relaxations
Proceedings of the forty-first annual ACM symposium on Theory of computing
On the complexity of communication complexity
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
The Communication Complexity of Set-Disjointness with Small Sets and 0-1 Intersection
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Geometry of Cuts and Metrics
Theta Bodies for Polynomial Ideals
SIAM Journal on Optimization
Integrality Gaps of $2-o(1)$ for Vertex Cover SDPs in the Lovász-Schrijver Hierarchy
SIAM Journal on Computing
Symmetry matters for the sizes of extended formulations
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
On the Shannon capacity of a graph
IEEE Transactions on Information Theory
Extended formulations, nonnegative factorizations, and randomized communication protocols
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Lifts of Convex Sets and Cone Factorizations
Mathematics of Operations Research
An information complexity approach to extended formulations
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On the extension complexity of combinatorial polytopes
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
An upper bound for nonnegative rank
Journal of Combinatorial Theory Series A
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We solve a 20-year old problem posed by Yannakakis and prove that there exists no polynomial-size linear program (LP) whose associated polytope projects to the traveling salesman polytope, even if the LP is not required to be symmetric. Moreover, we prove that this holds also for the cut polytope and the stable set polytope. These results were discovered through a new connection that we make between one-way quantum communication protocols and semidefinite programming reformulations of LPs.