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Chapter and Conference Paper
The Complexity of Somewhat Approximation Resistant Predicates
A boolean predicate f:{0,1} k → {0,1} is said to be somewhat approximation resistant if for some constant ...
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Chapter and Conference Paper
Linear Programming Hierarchies Suffice for Directed Steiner Tree
We demonstrate that ℓ rounds of the Sherali-Adams hierarchy and 2ℓ rounds of the Lovász-Schrijver hierarchy suffice to reduce the integrality gap of a natural LP relaxation for Directed Steiner Tree in ℓ-layer...
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Chapter and Conference Paper
Sampling-Based Proofs of Almost-Periodicity Results and Algorithmic Applications
We give new and simple combinatorial proofs of almost-periodicity results for sumsets of sets with small doubling in the spirit of Croot and Sisask [7], whose almost-periodicity lemma has had far-reaching implica...
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Chapter and Conference Paper
Optimal Strong Parallel Repetition for Projection Games on Low Threshold Rank Graphs
Given a two-player one-round game G with value val(G) = (1 − η), how quickly does the value decay under parallel repetition? If G is a projection game, then it is known that we can guarantee val(G ...
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Chapter
Convex Relaxations and Integrality Gaps
We discuss the effectiveness of linear and semidefinite relaxations in approximating the optimum for combinatorial optimization problems. Various hierarchies of these relaxations, such as the ones defined by L...
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Chapter and Conference Paper
SDP Gaps for 2-to-1 and Other Label-Cover Variants
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-to-1 Label-Cover; (ii) 2-to-2 ...
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Chapter and Conference Paper
Improved Pseudorandom Generators for Depth 2 Circuits
We prove the existence of a poly(n,m)-time computable pseudorandom generator which “1/poly(n,m)-fools” DNFs with n variables and m terms, and has seed length O(log2 nm ·loglognm). Previously, the ...
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Chapter and Conference Paper
Time Space Tradeoffs for Attacks against One-Way Functions and PRGs
We study time space tradeoffs in the complexity of attacks against one-way functions and pseudorandom generators.
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Chapter and Conference Paper
Optimal Sherali-Adams Gaps from Pairwise Independence
This work considers the problem of approximating fixed predicate constraint satisfaction problems (MAX k-CSP(P)). We show that if the set of assignments accepted by P contains the support of a balanced pairwise i...