Related papers: Multiparty Communication Complexity of Disjointnes…
We initiate a study of a relaxed version of the standard Erdos-Renyi random graph model, where each edge may depend on a few other edges. We call such graphs "dependent random graphs". Our main result in this direction is a thorough…
We give the first exponential separation between quantum and classical multi-party communication complexity in the (non-interactive) one-way and simultaneous message passing settings. For every k, we demonstrate a relational communication…
For a constant $\epsilon$, we prove a poly(N) lower bound on the (randomized) communication complexity of $\epsilon$-Nash equilibrium in two-player NxN games. For n-player binary-action games we prove an exp(n) lower bound for the…
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,…
The multiplayer promise set disjointness is one of the most widely used problems from communication complexity in applications. In this problem there are $k$ players with subsets $S^1, \ldots, S^k$, each drawn from $\{1, 2, \ldots, n\}$,…
We study shared randomness in the context of multi-party number-in-hand communication protocols in the simultaneous message passing model. We show that with three or more players, shared randomness exhibits new interesting properties that…
Quantum entanglement cannot be used to achieve direct communication between remote parties, but it can reduce the communication needed for some problems. Let each of k parties hold some partial input data to some fixed k-variable function…
We study the approximation of halfspaces $h:\{0,1\}^n\to\{0,1\}$ in the infinity norm by polynomials and rational functions of any given degree. Our main result is an explicit construction of the "hardest" halfspace, for which we prove…
We study the communication complexity of a number of graph properties where the edges of the graph $G$ are distributed between Alice and Bob (i.e., each receives some of the edges as input). Our main results are: * An Omega(n) lower bound…
The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the…
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…
Building on the techniques behind the recent progress on the 3-term arithmetic progression problem [KM'23], Kelley, Lovett, and Meka [KLM'24] constructed the first explicit 3-player function $f:[N]^3 \rightarrow \{0,1\}$ that demonstrates a…
An open problem that is widely regarded as one of the most important in quantum query complexity is to resolve the quantum query complexity of the k-distinctness function on inputs of size N. While the case of k=2 (also called Element…
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…
We study the multiparty communication complexity of high dimensional permutations, in the Number On the Forehead (NOF) model. This model is due to Chandra, Furst and Lipton (CFL) who also gave a nontrivial protocol for the Exactly-n problem…
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…
There are distributed graph algorithms for finding maximal matchings and maximal independent sets in $O(\Delta + \log^* n)$ communication rounds; here $n$ is the number of nodes and $\Delta$ is the maximum degree. The lower bound by Linial…
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 give the first super-polynomial separation in the power of bounded-depth boolean formulas vs. circuits. Specifically, we consider the problem Distance $k(n)$ Connectivity, which asks whether two specified nodes in a graph of size $n$ are…
We show that any randomised Monte Carlo distributed algorithm for the Lov\'asz local lemma requires $\Omega(\log \log n)$ communication rounds, assuming that it finds a correct assignment with high probability. Our result holds even in the…