Related papers: Lifting Theorems Meet Information Complexity: Know…
Lifting theorems are one of the most powerful tools for proving communication lower bounds, with numerous downstream applications in proof complexity, monotone circuit lower bounds, data structures, and combinatorial optimization. However,…
We investigate the power of the most important lower bound technique in randomized communication complexity, which is based on an evaluation of the maximal size of approximately monochromatic rectangles, minimized over all distributions on…
Determining the randomized (or distributional) communication complexity of disjointness is a central problem in communication complexity, having roots in the foundational work of Babai, Frankl, and Simon in the 1980s and culminating in the…
Lifting theorems are theorems that relate the query complexity of a function $f:\{0,1\}^{n}\to\{0,1\}$ to the communication complexity of the composed function $f \circ g^{n}$, for some "gadget" $g:\{0,1\}^{b}\times\{0,1\}^{b}\to\{0,1\}$.…
Information-theoretic methods have proven to be a very powerful tool in communication complexity, in particular giving an elegant proof of the linear lower bound for the two-party disjointness function, and tight lower bounds on…
Three decades of research in communication complexity have led to the invention of a number of techniques to lower bound randomized communication complexity. The majority of these techniques involve properties of large submatrices…
The set disjointness problem is one of the most fundamental and well-studied problems in communication complexity. In this problem Alice and Bob hold sets $S, T \subseteq [n]$, respectively, and the goal is to decide if $S \cap T =…
We introduce new models and new information theoretic measures for the study of communication complexity in the natural peer-to-peer, multi-party, number-in-hand setting. We prove a number of properties of our new models and measures, and…
Lifting theorems are theorems that bound the communication complexity of a composed function $f\circ g^{n}$ in terms of the query complexity of $f$ and the communication complexity of $g$. Such theorems constitute a powerful generalization…
We revisit the direct sum questions in communication complexity which asks whether the resource needed to solve $n$ communication problems together is (approximately) the sum of resources needed to solve these problems separately. Our work…
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…
We show that a large fraction of the data-structure lower bounds known today in fact follow by reduction from the communication complexity of lopsided (asymmetric) set disjointness. This includes lower bounds for: * high-dimensional…
This paper studies the complexity of distributed construction of purely additive spanners in the CONGEST model. We describe algorithms for building such spanners in several cases. Because of the need to simultaneously make decisions at far…
The disjointness problem - where Alice and Bob are given two subsets of $\{1, \dots, n\}$ and they have to check if their sets intersect - is a central problem in the world of communication complexity. While both deterministic and…
Consider the "Number in Hand" multiparty communication complexity model, where k players holding inputs x_1,...,x_k in {0,1}^n communicate to compute the value f(x_1,...,x_k) of a function f known to all of them. The main lower bound…
We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression,…
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 develop an information-theoretic framework for bounding the supremum of stochastic processes, offering a simpler and sharper alternative to classical chaining and slicing arguments for generalization bounds. The key idea is a lifting…
We obtain a lower bound of n^Omega(1) on the k-party randomized communication complexity of the Disjointness function in the `Number on the Forehead' model of multiparty communication when k is a constant. For k=o(loglog n), the bounds…
We give lower bounds on the communication complexity of graph problems in the multi-party blackboard model. In this model, the edges of an $n$-vertex input graph are partitioned among $k$ parties, who communicate solely by writing messages…