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Set disjointness is a central problem in communication complexity. Here Alice and Bob each receive a subset of an n-element universe, and they need to decide whether their inputs intersect or not. The communication complexity of this…
We consider the learning and communication complexity of subsequence containment. In the learning problem, we seek to learn a classifier that positively labels a binary string $x$ if it contains a fixed binary string $y$ as a subsequence.…
The Collision problem is to decide whether a given list of numbers $(x_1,\ldots,x_n)\in[n]^n$ is $1$-to-$1$ or $2$-to-$1$ when promised one of them is the case. We show an $n^{\Omega(1)}$ randomised communication lower bound for the natural…
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…
We establish a connection between non-deterministic communication complexity and instance complexity, a measure of information based on algorithmic entropy. Let $\overline{x}$, $\overline{y}$ and $Y_1(\overline{x})$ be respectively the…
We study the one-way two-party communication complexity of Maximum Matching in the semi-robust setting where the edges of a maximum matching are randomly partitioned between Alice and Bob, but all remaining edges of the input graph are…
In the communication problem $\mathbf{UR}$ (universal relation) [KRW95], Alice and Bob respectively receive $x$ and $y$ in $\{0,1\}^n$ with the promise that $x\neq y$. The last player to receive a message must output an index $i$ such that…
In the communication problem $\mathbf{UR}$ (universal relation) [KRW95], Alice and Bob respectively receive $x, y \in\{0,1\}^n$ with the promise that $x\neq y$. The last player to receive a message must output an index $i$ such that…
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…
We introduce a simple model illustrating the role of context in communication and the challenge posed by uncertainty of knowledge of context. We consider a variant of distributional communication complexity where Alice gets some information…
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…
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 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…
In communication complexity the input of a function $f:X\times Y\rightarrow Z$ is distributed between two players Alice and Bob. If Alice knows only $x\in X$ and Bob only $y\in Y$, how much information must Alice and Bob share to be able to…
We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared…
Two parties observing correlated random variables seek to run an interactive communication protocol. How many bits must they exchange to simulate the protocol, namely to produce a view with a joint distribution within a fixed statistical…
Pointer-chasing is a central problem in two-party communication complexity: given input size $n$ and a parameter $k$, the two players Alice and Bob are given functions $N_A, N_B: [n] \rightarrow [n]$, respectively, and their goal is to…
The Gap-Hamming-Distance problem arose in the context of proving space lower bounds for a number of key problems in the data stream model. In this problem, Alice and Bob have to decide whether the Hamming distance between their $n$-bit…
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 give improved separations for the query complexity analogue of the log-approximate-rank conjecture i.e. we show that there are a plethora of total Boolean functions on $n$ input bits, each of which has approximate Fourier sparsity at…