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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…
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…
The focus of this paper is on {\em quantum distributed} computation, where we investigate whether quantum communication can help in {\em speeding up} distributed network algorithms. Our main result is that for certain fundamental network…
Minimum dominating set is a basic local covering problem and a core task in distributed computing. Despite extensive study, in the classic LOCAL model there exist significant gaps between known algorithms and lower bounds. Chang and Li…
The last five years of research on distributed graph algorithms have seen huge leaps of progress, both regarding algorithmic improvements and impossibility results: new strong lower bounds have emerged for many central problems and…
The CONGEST and CONGEST-CLIQUE models have been carefully studied to represent situations where the communication bandwidth between processors in a network is severely limited. Messages of only $O(log(n))$ bits of information each may be…
The computation of the diameter is one of the most central problems in distributed computation. In the standard CONGEST model, in which two adjacent nodes can exchange $O(\log n)$ bits per round (here $n$ denotes the number of nodes of the…
Locally finding a solution to symmetry-breaking tasks such as vertex-coloring, edge-coloring, maximal matching, maximal independent set, etc., is a long-standing challenge in distributed network computing. More recently, it has also become…
We present the first local problem that shows a super-constant separation between the classical randomized LOCAL model of distributed computing and its quantum counterpart. By prior work, such a separation was known only for an artificial…
Very recently, Khoury and Schild [FOCS 2025] showed that any randomized LOCAL algorithm that solves maximal matching requires $\Omega(\min\{\log \Delta, \log_\Delta n\})$ rounds, where $n$ is the number of nodes in the graph and $\Delta$ is…
This paper concerns {\em randomized} leader election in synchronous distributed networks. A distributed leader election algorithm is presented for complete $n$-node networks that runs in O(1) rounds and (with high probability) uses only…
Hybrid networks, i.e., networks that leverage different means of communication, become ever more widespread. To allow theoretical study of such networks, [Augustine et al., SODA'20] introduced the $\mathsf{HYBRID}$ model, which is based on…
Gossip and in particular network coded algebraic gossip have recently attracted attention as a fast, bandwidth-efficient, reliable and distributed way to broadcast or multicast multiple messages. While the algorithms are simple, involved…
Linial's famous color reduction algorithm reduces a given $m$-coloring of a graph with maximum degree $\Delta$ to a $O(\Delta^2\log m)$-coloring, in a single round in the LOCAL model. We show a similar result when nodes are restricted to…
We consider a coded distributed computing problem in a ring-based communication network, where $N$ computing nodes are arranged in a ring topology and each node can only communicate with its neighbors within a constant distance $d$. To…
Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement…
The online-LOCAL and SLOCAL models are extensions of the LOCAL model where nodes are processed in a sequential but potentially adversarial order. So far, the only problem we know of where the global memory of the online-LOCAL model has an…
In this paper, we present a low-diameter decomposition algorithm in the LOCAL model of distributed computing that succeeds with probability $1 - 1/poly(n)$. Specifically, we show how to compute an $\left(\epsilon, O\left(\frac{\log…
We show a lower bound on expected communication cost of interactive entanglement assisted quantum state redistribution protocols and a slightly better lower bound for its special case, quantum state transfer. Our bound implies that the…
In this paper, we study the number of rounds of communication needed to implement certain tasks by local quantum operations and classical communication (LOCC). We find that the class of LOCC operations becomes strictly more powerful as more…