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In this work, we introduce an online model for communication complexity. Analogous to how online algorithms receive their input piece-by-piece, our model presents one of the players, Bob, his input piece-by-piece, and has the players Alice…
The question of how much communication is required between collaborating parties to compute a function of their data is of fundamental importance in the fields of theoretical computer science and information theory. In this work, the focus…
Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…
We derive information-theoretic converses (i.e., lower bounds) for the minimum time required by any algorithm for distributed function computation over a network of point-to-point channels with finite capacity, where each node of the…
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…
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 study the exact solution of the two-body problem on a tight-binding one-dimensional lattice, with pairwise interaction potentials which have an arbitrary but finite range. We show how to obtain the full spectrum, the bound and scattering…
We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r + r)$ on the communication required for…
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 define the Streaming Communication model that combines the main aspects of communication complexity and streaming. We consider two agents that want to compute some function that depends on inputs that are distributed to each agent. The…
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…
One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix--the minimum rank of a matrix which is entrywise close to the…
We show that almost all known lower bound methods for communication complexity are also lower bounds for the information complexity. In particular, we define a relaxed version of the partition bound of Jain and Klauck and prove that it…
We consider the process consisting of preparation, transmission through a quantum channel, and subsequent measurement of quantum states. The communication complexity of the channel is the minimal amount of classical communication required…
We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in…
Sketching is widely used in randomized linear algebra for low-rank matrix approximation, column subset selection, and many other problems, and it has gained significant traction in machine learning applications. However, sketching large…
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…
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…
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…
In this paper, we give simple optimal lower bounds on the one-way two-party communication complexity of approximate Maximum Matching and Minimum Vertex Cover with deletions. In our model, Alice holds a set of edges and sends a single…