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Community detection is considered for a stochastic block model graph of n vertices, with K vertices in the planted community, edge probability p for pairs of vertices both in the community, and edge probability q for other pairs of…
A recent upper bound by Le and Solomon [STOC '23] has established that every $n$-node graph has a $(1+\varepsilon)(2k-1)$-spanner with lightness $O(\varepsilon^{-1} n^{1/k})$. This bound is optimal up to its dependence on $\varepsilon$; the…
One of the best lower bound methods for the quantum communication complexity of a function H (with or without shared entanglement) is the logarithm of the approximate rank of the communication matrix of H. This measure is essentially…
We consider channel coding for Gaussian channels with the recently introduced mean and variance cost constraints. Through matching converse and achievability bounds, we characterize the optimal first- and second-order performance. The main…
Random selection, leader election, and collective coin flipping are fundamental tasks in fault-tolerant distributed computing. We study these problems in the full-information model where despite decades of study, key gaps remain in our…
Dominating broadcasting is a domination-type structure that models a transmission antenna network. In this paper, we study a limited version of this structure, that was proposed as a common framework for both broadcast and classical…
For an input graph $G$, an additive spanner is a sparse subgraph $H$ whose shortest paths match those of $G$ up to small additive error. We prove two new lower bounds in the area of additive spanners: 1) We construct $n$-node graphs $G$ for…
The class $FORMULA[s] \circ \mathcal{G}$ consists of Boolean functions computable by size-$s$ de Morgan formulas whose leaves are any Boolean functions from a class $\mathcal{G}$. We give lower bounds and (SAT, Learning, and PRG) algorithms…
A long-standing open question is which graph class is the most general one permitting constant-time constant-factor approximations for dominating sets. The approximation ratio has been bounded by increasingly general parameters such as…
The two-way capacities of quantum channels determine the ultimate entanglement and secret-key distribution rates achievable by two distant parties that are connected by a noisy transmission line, in absence of quantum repeaters. Since…
The nearest lattice point problem in $\mathbb{R}^n$ is formulated in a distributed network with $n$ nodes. The objective is to minimize the probability that an incorrect lattice point is found, subject to a constraint on inter-node…
Recently, Ezra and Sharir [ES22a] showed an $O(n^{3/2+\sigma})$ space and $O(n^{1/2+\sigma})$ query time data structure for ray shooting among triangles in $\mathbb{R}^3$. This improves the upper bound given by the classical…
We consider distributed online learning protocols that control the exchange of information between local learners in a round-based learning scenario. The learning performance of such a protocol is intuitively optimal if approximately the…
This paper employs the add-and-subtract technique of the auxiliary receiver approach to establish a new upper bound for the distributed hypothesis testing problem. This new bound has fewer assumptions than the upper bound proposed by Rahman…
In this work we focus our attention on distributed optimization problems in the context where the communication time between the server and the workers is non-negligible. We obtain novel methods supporting bidirectional compression (both…
Distributed optimization increasingly plays a central role in economical and sustainable operation of cyber-physical systems. Nevertheless, the complete potential of the technology has not yet been fully exploited in practice due to…
We propose a new algorithm for k-means clustering in a distributed setting, where the data is distributed across many machines, and a coordinator communicates with these machines to calculate the output clustering. Our algorithm guarantees…
This paper studies lower bounds for fundamental optimization problems in the CONGEST model. We show that solving problems exactly in this model can be a hard task, by providing $\tilde{\Omega}(n^2)$ lower bounds for cornerstone problems,…
Given a positive integer $k$, $k$-set agreement is the distributed task in which each process $i\in [n]$ in a group of $n$ processing nodes starts with an input value $x_i$ in the set $\{0,\dots,k\}$, and must output a value $y_i$ such that…
This paper proposes a new method for the K-armed dueling bandit problem, a variation on the regular K-armed bandit problem that offers only relative feedback about pairs of arms. Our approach extends the Upper Confidence Bound algorithm to…