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Communication complexity, which quantifies the minimum communication required for distributed computation, offers a natural setting for investigating the capabilities and limitations of quantum mechanics in information processing. We…
This paper focuses on bounding the total communication complexity of collapsing protocols for multiparty pointer jumping problem ($MPJ_k^n$). Brody and Chakrabati in \cite{bc08} proved that in such setting one of the players must…
We propose a linear algebraic method, rooted in the spectral properties of graphs, that can be used to prove lower bounds in communication complexity. Our proof technique effectively marries spectral bounds with information-theoretic…
We consider the communication complexity of finding an approximate maximum matching in a graph in a multi-party message-passing communication model. The maximum matching problem is one of the most fundamental graph combinatorial problems,…
In secure multiparty computation (MPC), mutually distrusting users collaborate to compute a function of their private data without revealing any additional information about their data to other users. While it is known that information…
We study the relationship between various one-way communication complexity measures of a composed function with the analogous decision tree complexity of the outer function. We consider two gadgets: the AND function on 2 inputs, and the…
We consider the standard two-party communication model. The central problem studied in this article is how much one can save in information complexity by allowing an error of $\epsilon$. For arbitrary functions, we obtain lower bounds and…
We study the CHAIN communication problem introduced by Cormode et al. [ICALP 2019]. It is a generalization of the well-studied INDEX problem. For $k\geq 1$, in CHAIN$_{n,k}$, there are $k$ instances of INDEX, all with the same answer. They…
Recently, there has been an increasing interest in designing distributed convex optimization algorithms under the setting where the data matrix is partitioned on features. Algorithms under this setting sometimes have many advantages over…
Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement…
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,…
In this paper, we show a direct product theorm in the model of two-party bounded-round public-coin randomized communication complexity. For a relation f subset of X times Y times Z (X,Y,Z are finite sets), let R^{(t), pub}_e (f) denote the…
We show a communication complexity lower bound for finding a correlated equilibrium of a two-player game. More precisely, we define a two-player $N \times N$ game called the 2-cycle game and show that the randomized communication complexity…
We study the communication complexity of truthful combinatorial auctions, and in particular the case where valuations are either subadditive or single-minded, which we denote with $\mathsf{SubAdd}\cup\mathsf{SingleM}$. We show that for…
We study an extension of the standard two-party communication model in which Alice and Bob hold probability distributions $p$ and $q$ over domains $X$ and $Y$, respectively. Their goal is to estimate \[ \mathbb{E}_{x \sim p,\, y \sim…
Quantum versus classical separation plays a central role in understanding the advantages of quantum computation. In this paper, we present the first exponential separation between quantum and bounded-error randomized communication…
A novel long-lived distributed problem, called Team Formation (TF), is introduced together with a message- and time-efficient randomized algorithm. The problem is defined over the asynchronous model with a complete communication graph,…
We prove lower bounds for the direct sum problem for two-party bounded error randomised multiple-round communication protocols. Our proofs use the notion of information cost of a protocol, as defined by Chakrabarti, Shi, Wirth and Yao and…
We characterize the communication complexity of truthful mechanisms. Our departure point is the well known taxation principle. The taxation principle asserts that every truthful mechanism can be interpreted as follows: every player is…
We show a near optimal direct-sum theorem for the two-party randomized communication complexity. Let $f\subseteq X \times Y\times Z$ be a relation, $\varepsilon> 0$ and $k$ be an integer. We show,…