Given a positive integer n and a positive semidefinite matrix A = (Aij ) ∈ Rm×m the positive semidefinite Grothendieck problem with rank-nconstraint is (SDPn) maximize mX i=1 ...
Min Ones Constraint Satisfaction Problems, i.e., the task of finding a satisfying assignment with at most k true variables (Min Ones SAT(Γ)), can express a number of interesting ...
In this paper we present semidefinite programming (SDP) gap instances for the following variants of the Label-Cover problem, closely related to the Unique Games Conjecture: (i) 2-...
Venkatesan Guruswami, Subhash Khot, Ryan O'Donnell...
We say that a polynomial f(x1, . . . , xn) is indecomposable if it cannot be written as a product of two polynomials that are defined over disjoint sets of variables. The polynom...
Some of the currently best-known approximation algorithms for network design are based on random sampling. One of the key steps of such algorithms is connecting a set of source nod...
Abstract. We study the “subgraph connectivity” problem for undirected graphs with sublinear vertex update time. In this problem, we can make vertices active or inactive in a gr...
Assuming the Unique Games Conjecture (UGC), we show optimal inapproximability results for two classic scheduling problems. We obtain a hardness of 2 − ε for the problem of mini...
The minimization problem for Horn formulas is to find a Horn formula equivalent to a given Horn formula, using a minimum number of clauses. A 2log1−ǫ (n) -inapproximability re...