Related papers: Tight bounds on the randomized communication compl…
We introduce the \emph{local information cost} (LIC), which quantifies the amount of information that nodes in a network need to learn when solving a graph problem. We show that the local information cost presents a natural lower bound on…
We prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed…
Consensus is one of the most thoroughly studied problems in distributed computing, yet there are still complexity gaps that have not been bridged for decades. In particular, in the classical message-passing setting with processes' crashes,…
Given a boolean n by n matrix A we consider arithmetic circuits for computing the transformation x->Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative…
We consider the problem of shared randomness-assisted multiple access channel (MAC) simulation for product inputs and characterize the one-shot communication cost region via almost-matching inner and outer bounds in terms of the smooth…
A common scenario in distributed computing involves a client who asks a server to perform a computation on a remote computer. An important problem is to determine the minimum amount of communication needed to specify the desired…
The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. At the end of the first section I examine tree-balancing. In the second section I summarize the…
The problems discussed in this paper are motivated by general ratio consensus algorithms, introduced by Kempe, Dobra, and Gehrke (2003) in a simple form as the push-sum algorithm, later extended by B\'en\'ezit et al. (2010) under the name…
In a $k$-party communication problem, the $k$ players with inputs $x_1, x_2, \ldots, x_k$, respectively, want to evaluate a function $f(x_1, x_2, \ldots, x_k)$ using as little communication as possible. We consider the message-passing…
A parallel algorithm has perfect strong scaling if its running time on P processors is linear in 1/P, including all communication costs. Distributed-memory parallel algorithms for matrix multiplication with perfect strong scaling have only…
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…
In this short note, we initiate the study of the Linear Isomorphism Testing Problem in the setting of communication complexity, a natural linear algebraic generalization of the classical Equality problem. Given Boolean functions $f, g :…
This paper considers distributed nonconvex optimization with the cost functions being distributed over agents. Noting that information compression is a key tool to reduce the heavy communication load for distributed algorithms as agents…
Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
We show lower bounds of $\Omega(\sqrt{n})$ and $\Omega(n^{1/4})$ on the randomized and quantum communication complexity, respectively, of all $n$-variable read-once Boolean formulas. Our results complement the recent lower bound of…
In this work we revisit the Boolean Hidden Matching communication problem, which was the first communication problem in the one-way model to demonstrate an exponential classical-quantum communication separation. In this problem, Alice's…
We study the tradeoff between the statistical error and communication cost of distributed statistical estimation problems in high dimensions. In the distributed sparse Gaussian mean estimation problem, each of the $m$ machines receives $n$…
Given a correlation generated by a (possibly quantum) communication network, we study the amount of shared randomness required to generate it. We develop a novel upper bound for approximating distributions generated by arbitrary networks…
We study the communication complexity of a direct sum of independent copies of the equality predicate. We prove that the probabilistic communication complexity of this problem is equal to O(N); computational complexity of the proposed…
In a multiparty message-passing model of communication, there are $k$ players. Each player has a private input, and they communicate by sending messages to one another over private channels. While this model has been used extensively in…