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Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or not obtained the tightest possible values. Recent work has…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-05-27 Hussam Al Daas , Grey Ballard , Laura Grigori , Suraj Kumar , Kathryn Rouse

We fully determine the communication complexity of approximating matrix rank, over any finite field $\mathbb{F}$. We study the most general version of this problem, where $0\leq r<R\leq n$ are given integers, Alice and Bob's inputs are…

Computational Complexity · Computer Science 2024-10-29 Alexander A. Sherstov , Andrey A. Storozhenko

We investigate the power of the most important lower bound technique in randomized communication complexity, which is based on an evaluation of the maximal size of approximately monochromatic rectangles, minimized over all distributions on…

Computational Complexity · Computer Science 2007-05-23 Hartmut Klauck

Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle…

Data Structures and Algorithms · Computer Science 2020-03-03 Grace Dinh , James Demmel

Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with that we can and cannot do with quantum information that goes beyond the abilities of classical information processing…

Quantum Physics · Physics 2009-11-10 Gilles Brassard , Anne Broadbent , Alain Tapp

Quantum communication holds the promise of creating disruptive technologies that will play an essential role in future communication networks. For example, the study of quantum communication complexity has shown that quantum communication…

Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in…

Quantum Physics · Physics 2016-10-07 Thomas Vidick , John Watrous

This paper gives a QMA (Quantum Merlin-Arthur) protocol for 3-SAT with two logarithmic-size quantum proofs (that are not entangled with each other) such that the gap between the completeness and the soundness is Omega(1/n polylog(n)). This…

Quantum Physics · Physics 2021-10-05 Francois Le Gall , Shota Nakagawa , Harumichi Nishimura

Communication complexity quantifies how difficult it is for two distant computers to evaluate a function f(X,Y), where the strings X and Y are distributed to the first and second computer respectively, under the constraint of exchanging as…

Quantum Physics · Physics 2024-07-17 Pierre Botteron , Anne Broadbent , Reda Chhaibi , Ion Nechita , Clément Pellegrini

Communication complexity refers to the minimum rate of public communication required for generating a maximal-rate secret key (SK) in the multiterminal source model of Csiszar and Narayan. Tyagi recently characterized this communication…

Information Theory · Computer Science 2014-01-14 Manuj Mukherjee , Navin Kashyap

We study nondeterministic quantum algorithms for Boolean functions f. Such algorithms have positive acceptance probability on input x iff f(x)=1. In the setting of query complexity, we show that the nondeterministic quantum complexity of a…

Computational Complexity · Computer Science 2007-05-23 Ronald de Wolf

It is known that Mermin-Peres like proofs of quantum contextuality can furnish non-local games with a guaranteed quantum strategy, when classically no such guarantee can exist. This phenomenon, also called quantum pseudo-telepathy, has been…

Quantum Physics · Physics 2023-10-12 Colm Kelleher , Mohammad Roomy , Frédéric Holweck

Suppose that Alice and Bob are given each an infinite string, and they want to decide whether their two strings are in a given relation. How much communication do they need? How can communication be even defined and measured for infinite…

Computational Complexity · Computer Science 2015-01-26 Pierre Guillon , Emmanuel Jeandel

Buhrman showed that an efficient communication protocol implies a reliable XOR game protocol. This idea rederives Linial and Shraibman's lower bounds of communication complexity, which was derived by using factorization norms, with worse…

Information Theory · Computer Science 2017-05-01 Ryuhei Mori

We consider the communication complexity of a number of distributed optimization problems. We start with the problem of solving a linear system. Suppose there is a coordinator together with $s$ servers $P_1, \ldots, P_s$, the $i$-th of…

Data Structures and Algorithms · Computer Science 2019-11-01 Santosh S. Vempala , Ruosong Wang , David P. Woodruff

Consider the "Number in Hand" multiparty communication complexity model, where k players holding inputs x_1,...,x_k in {0,1}^n communicate to compute the value f(x_1,...,x_k) of a function f known to all of them. The main lower bound…

Computational Complexity · Computer Science 2017-10-10 Jan Draisma , Eyal Kushilevitz , Enav Weinreb

The communication complexity of many fundamental problems reduces greatly when the communicating parties share randomness that is independent of the inputs to the communication task. Natural communication processes (say between humans)…

Computational Complexity · Computer Science 2024-01-24 Clément L. Canonne , Venkatesan Guruswami , Raghu Meka , Madhu Sudan

Bell proved that quantum entanglement enables two space-like separated parties to exhibit classically impossible correlations. Even though these correlations are stronger than anything classically achievable, they cannot be harnessed to…

Quantum Physics · Physics 2009-11-11 Gilles Brassard , Harry Buhrman , Noah Linden , Andre A. Methot , Alain Tapp , Falk Unger

We study the effect that the amount of correlation in a bipartite distribution has on the communication complexity of a problem under that distribution. We introduce a new family of complexity measures that interpolates between the two…

Computational Complexity · Computer Science 2015-08-25 Ralph C. Bottesch , Dmitry Gavinsky , Hartmut Klauck

We prove an optimal $\Omega(n)$ lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially optimal multi-pass space lower bounds in the data stream model…

Computational Complexity · Computer Science 2012-07-02 Amit Chakrabarti , Oded Regev