Related papers: Tight bounds on the randomized communication compl…
We give a tight lower bound of Omega(\sqrt{n}) for the randomized one-way communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since there is a quantum one-way communication complexity protocol of O(\log n) qubits for…
We study space-bounded communication complexity for unitary implementation in distributed quantum processors, where we restrict the number of qubits per processor to ensure practical relevance and technical non-triviality. We model…
We give lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, comparison sorting, and the Fast…
We present a linear program for the one-way version of the partition bound (denoted $\mathsf{prt}^1_\varepsilon(f)$). We show that it characterizes one-way randomized communication complexity $\mathsf{R}_\varepsilon^1(f)$ with shared…
We show that for any Boolean function f on {0,1}^n, the bounded-error quantum communication complexity of XOR functions $f\circ \oplus$ satisfies that $Q_\epsilon(f\circ \oplus) = O(2^d (\log\|\hat f\|_{1,\epsilon} + \log…
The communication cost of algorithms (also known as I/O-complexity) is shown to be closely related to the expansion properties of the corresponding computation graphs. We demonstrate this on Strassen's and other fast matrix multiplication…
In this article, we focus on the communication costs of three symmetric matrix computations: i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) ii) adding the result of the multiplication of a matrix with…
We establish novel connections between magic in quantum circuits and communication complexity. In particular, we show that functions computable with low magic have low communication cost. Our first result shows that the $\mathsf{D}\|$…
We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower…
We investigate the randomized and quantum communication complexity of the Hamming Distance problem, which is to determine if the Hamming distance between two n-bit strings is no less than a threshold d. We prove a quantum lower bound of…
This work addresses two problems in the context of two-party communication complexity of functions. First, it concludes the line of research, which can be viewed as demonstrating qualitative advantage of quantum communication in the three…
We consider the class of functions whose value depends only on the intersection of the input X_1,X_2, ..., X_t; that is, for each F in this class there is an f_F: 2^{[n]} \to {0,1}, such that F(X_1,X_2, ..., X_t) = f_F(X_1 \cap X_2 \cap ...…
We characterize the communication complexity of the following distributed estimation problem. Alice and Bob observe infinitely many iid copies of $\rho$-correlated unit-variance (Gaussian or $\pm1$ binary) random variables, with unknown…
Communication is a major factor determining the performance of algorithms on current computing systems; it is therefore valuable to provide tight lower bounds on the communication complexity of computations. This paper presents a lower…
Information theoretically secure multi-party computation (MPC) is a central primitive of modern cryptography. However, relatively little is known about the communication complexity of this primitive. In this work, we develop powerful…
We show how to efficiently simulate the sending of a message M to a receiver who has partial information about the message, so that the expected number of bits communicated in the simulation is close to the amount of additional information…
During the last two decades, a small set of distributed computing models for networks have emerged, among which LOCAL, CONGEST, and Broadcast Congested Clique (BCC) play a prominent role. We consider hybrid models resulting from combining…
This paper discusses and analyzes various models of binary correlated sources, which may be relevant in several distributed communication scenarios. These models are statistically characterized in terms of joint Probability Mass Function…
In this paper we obtain some bounds on communication complexity of Gap Hamming Distance problem ($\mathsf{GHD}^n_{L, U}$): Alice and Bob are given binary string of length $n$ and they are guaranteed that Hamming distance between their…
We study the maximum $k$-set coverage problem in the following distributed setting. A collection of sets $S_1,\ldots,S_m$ over a universe $[n]$ is partitioned across $p$ machines and the goal is to find $k$ sets whose union covers the most…