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Integrality gaps for Sherali-Adams relaxations
TLDR
A conceptually simple geometric approach to constructing Sherali-Adams gap examples via constructions of consistent local SDP solutions is developed, which is surprisingly versatile. Expand
Near-optimal algorithms for unique games
TLDR
This work presents significantly improved approximation algorithms for unique games that are based on rounding a natural semidefinite programming relaxation for the problem and their performance almost matches the integrality gap of this relaxation. Expand
Quadratic forms on graphs
AbstractWe introduce a new graph parameter, called the Grothendieck constant of a graph G=(V,E), which is defined as the least constant K such that for every A:E→ℝ,Expand
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
TLDR
It is shown that the integrality gap of an SDP relaxation of the MINIMUM MULTICUT problem is Ω(log n). Expand
How to Play Unique Games Using Embeddings
TLDR
This paper introduces new embedding techniques for rounding semidefinite relaxations of problems with large domain size and presents a new approximation algorithm for unique games. Expand
Algorithms for stable and perturbation-resilient problems
TLDR
An exact algorithm is given for 2-perturbation resilient instances of clustering problems with natural center-based objectives and an exact algorithm for (2-2/k)-stable instances of Minimum Multiway Cut with k terminals is given. Expand
Quadratic forms on graphs
TLDR
The lower bound for the complete graph improves a result of Kashin and Szarek on Gram matrices of uniformly bounded functions, and settles a problem of Megretski and of Charikar and Wirth. Expand
Near-optimal algorithms for maximum constraint satisfaction problems
TLDR
Both algorithms are optimal assuming the Unique Games Conjecture and are based on rounding natural semidefinite programming relaxations and are simpler than those previously known. Expand
A new class of non-Shannon-type inequalities for entropies
TLDR
A countable set of non-Shannon-type linear information inequalities for entropies of discrete random variables, i.e., information inequalities which cannot be reduced to the "basic" inequality I(X : Y |Z) 0. Expand
The Power of Asymmetry in Binary Hashing
TLDR
It is shown that even if the similarity is symmetric, the authors can have shorter and more accurate hashes by using two distinct code maps by approximating the similarity between x and x′ as the hamming distance between f (x) and g (x′), for two distinct binary codes f, g. Expand
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