Proceedings ArticleDOI
A direct sum theorem for corruption and the multiparty NOF communication complexity of set disjointness
Paul Beame,Toniann Pitassi,Nathan Segerlind,Avi Wigderson +3 more
- pp 52-66
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It is proved that corruption, one of the most powerful measures used to analyze 2-party randomized communication complexity, satisfies a strong direct sum property under rectangular distributions.Abstract:
We prove that corruption, one of the most powerful measures used to analyze 2-party randomized communication complexity, satisfies a strong direct sum property under rectangular distributions. This direct sum bound holds even when the error is allowed to be exponentially close to 1. We use this to analyze the complexity of the widely-studied set disjointness problem in the usual "number-on-the-forehead" (NOF) model of multiparty communication complexity.read more
Citations
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Journal ArticleDOI
Lower Bounds for Lovász-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity
TL;DR: It is proved that an $\omega(\log^4 n)$ lower bound for the three-party number-on-the-forehead (NOF) communication complexity of the set-disjointness function implies an $n^{\omega(1)$ size lower boundFor treelike Lovasz-Schrijver systems that refute unsatisfiable formulas in conjunctive normal form (CNFs).
Journal ArticleDOI
A Strong Direct Product Theorem for Corruption and the Multiparty Communication Complexity of Disjointness
TL;DR: It is proved that two-party randomized communication complexity satisfies a strong direct product property, so long as the communication lower bound is proved by a “corruption” or “one-sided discrepancy” method over a rectangular distribution.
Proceedings ArticleDOI
Integrality gaps of 2 - o(1) for Vertex Cover SDPs in the Lovész-Schrijver Hierarchy
TL;DR: It is shown that a large family of LP and SDP based algorithms fail to produce an approximation for Vertex Cover better than 2.36, and an integrality gap of 2 - o(lfloor)for Vertex cover SDPs obtained by tightening the standard LP relaxation with Omega(radiclog n/ log log n) rounds of LS+.
Journal Article
Lower bounds for Lovasz-Schrijver systems and beyond follow from multiparty communication complexity
TL;DR: In this article, it was shown that for all treelike Lovasz-Schrijver systems that refute unsatisfiable formulas in conjunctive normal form (CNFs), the communication complexity of the set-disjointness function implies a lower bound of O(n log 4 n) for the number of parties involved in the problem.
Proceedings ArticleDOI
Direct product theorems for classical communication complexity via subdistribution bounds: extended abstract
TL;DR: The subdistribution bound is introduced, which is a relaxation of the well-studied rectangle or corruption bound in communication complexity, and it is shown that for the communication complexity of Boolean functions with constant error, the subdist distribution bound is the same as the latter measure, up to a constant factor.
References
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Book
Communication Complexity
Eyal Kushilevitz,Noam Nisan +1 more
TL;DR: This chapter surveys the theory of two-party communication complexity and presents results regarding the following models of computation: • Finite automata • Turing machines • Decision trees • Ordered binary decision diagrams • VLSI chips • Networks of threshold gates.
Journal ArticleDOI
The Space Complexity of Approximating the Frequency Moments
TL;DR: In this paper, the authors considered the space complexity of randomized algorithms that approximate the frequency moments of a sequence, where the elements of the sequence are given one by one and cannot be stored.
Proceedings ArticleDOI
The space complexity of approximating the frequency moments
TL;DR: It turns out that the numbers F0;F1 and F2 can be approximated in logarithmic space, whereas the approximation of Fk for k 6 requires n (1) space.
Journal ArticleDOI
A Parallel Repetition Theorem
TL;DR: It is shown that a parallel repetition of any two-prover one-round proof system (MIP(2,1) decreases the probability of error at an exponential rate, and no constructive bound was previously known.
Journal ArticleDOI
An information statistics approach to data stream and communication complexity
TL;DR: This work presents a new method for proving strong lower bounds in communication complexity based on the notion of the conditional information complexity of a function, and shows that it also admits a direct sum theorem.