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Approximate Constraint Satisfaction Requires Large LP Relaxations
"... We prove superpolynomial lower bounds on the size of linear programming relaxations for approximation versions of constraint satisfaction problems. We show that for these problems, polynomialsized linear programs are exactly as powerful as programs arising from a constant number of rounds of the S ..."
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Cited by 16 (2 self)
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We prove superpolynomial lower bounds on the size of linear programming relaxations for approximation versions of constraint satisfaction problems. We show that for these problems, polynomialsized linear programs are exactly as powerful as programs arising from a constant number of rounds of the SheraliAdams hierarchy. In particular, any polynomialsized linear program for Max Cut has an integrality gap of 7/8.
The why and how of nonnegative matrix factorization
 REGULARIZATION, OPTIMIZATION, KERNELS, AND SUPPORT VECTOR MACHINES. CHAPMAN & HALL/CRC
, 2014
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On the Power of Symmetric LP and SDP Relaxations
"... We study the computational power of general symmetric relaxations for combinatorial optimization problems, both in the linear programming (LP) and semidefinite programming (SDP) case. We show new connections to explicit LP and SDP relaxations, like those obtained from standard hierarchies. Concrete ..."
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Cited by 4 (0 self)
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We study the computational power of general symmetric relaxations for combinatorial optimization problems, both in the linear programming (LP) and semidefinite programming (SDP) case. We show new connections to explicit LP and SDP relaxations, like those obtained from standard hierarchies. Concretely, for k < n/4, we show that krounds of sumofsquares / Lasserre relaxations of size k n
Communication complexity of setdisjointness for all probabilities
 In Proceedings of the 18th International Workshop on Randomization and Computation (RANDOM). Schloss Dagstuhl
, 2014
"... We study setdisjointness in a generalized model of randomized twoparty communication where the probability of acceptance must be at least α(n) on yesinputs and at most β(n) on noinputs, for some functions α(n)> β(n). Our main result is a complete characterization of the privatecoin communica ..."
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Cited by 3 (3 self)
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We study setdisjointness in a generalized model of randomized twoparty communication where the probability of acceptance must be at least α(n) on yesinputs and at most β(n) on noinputs, for some functions α(n)> β(n). Our main result is a complete characterization of the privatecoin communication complexity of setdisjointness for all functions α and β, and a nearcomplete characterization for publiccoin protocols. In particular, we obtain a simple proof of a theorem of Braverman and Moitra (STOC 2013), who studied the case where α = 1/2+(n) and β = 1/2 − (n). The following contributions play a crucial role in our characterization and are interesting in their own right. (1) We introduce two communication analogues of the classical complexity class that captures small boundederror computations: we define a “restricted ” class SBP (which lies between MA and AM) and an “unrestricted ” class USBP. The distinction between them is analogous to the distinction between the wellknown communication classes PP and UPP. (2) We show that the SBP communication complexity is precisely captured by the classical corruption lower bound method. This sharpens a theorem of Klauck (CCC 2003). (3) We use information complexity arguments to prove a linear lower bound on the USBP complexity of setdisjointness. 1