Related papers: Distributed Approximate Maximum Matching and Minim…
We present a simple deterministic distributed $(2+\epsilon)$-approximation algorithm for minimum weight vertex cover, which completes in $O(\log{\Delta}/\epsilon\log\log{\Delta})$ rounds, where $\Delta$ is the maximum degree in the graph,…
We give efficient distributed algorithms for the minimum vertex cover problem in bipartite graphs in the CONGEST model. From K\H{o}nig's theorem, it is well known that in bipartite graphs the size of a minimum vertex cover is equal to the…
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…
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…
In their seminal paper from 2004, Kuhn, Moscibroda, and Wattenhofer (KMW) proved a hardness result for several fundamental graph problems in the LOCAL model: For any (randomized) algorithm, there are input graphs with $n$ nodes and maximum…
In a recent breakthrough result, Balliu et al. [FOCS'19] proved a deterministic $\Omega(\min(\Delta,\log n /\log \log n))$-round and a randomized $\Omega(\min(\Delta,\log \log n/\log \log \log n))$-round lower bound for the complexity of…
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 investigate the distributed complexity of maximal matching and maximal independent set (MIS) in hypergraphs in the LOCAL model. A maximal matching of a hypergraph $H=(V_H,E_H)$ is a maximal disjoint set $M\subseteq E_H$ of hyperedges and…
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…
In this work, we present a fast distributed algorithm for local potential problems: these are graph problems where the task is to find a locally optimal solution where no node can unilaterally improve the utility in its local neighborhood…
We present a deterministic distributed $2$-approximation algorithm for the Minimum Weight Vertex Cover problem in the CONGEST model whose round complexity is $O(\log n \log \Delta / \log^2 \log \Delta)$. This improves over the currently…
We present a massively parallel algorithm, with near-linear memory per machine, that computes a $(2+\varepsilon)$-approximation of minimum-weight vertex cover in $O(\log\log d)$ rounds, where $d$ is the average degree of the input graph.…
We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank $f$. This problem is equivalent to the Minimum Weight Set Cover problem in which the frequency of every…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank $f$. This problem is equivalent to the Minimum Weight Set Cover Problem in which the frequency of every…
We provide CONGEST model algorithms for approximating minimum weighted vertex cover and the maximum weighted matching. For bipartite graphs, we show that a $(1+\varepsilon)$-approximate weighted vertex cover can be computed…
The local minimum degree of a graph is the minimum degree that can be reached by means of local complementation. For any n, there exist graphs of order n which have a local minimum degree at least 0.189n, or at least 0.110n when restricted…
In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…
Optimization problems consist of either maximizing or minimizing an objective function. Instead of looking for a maximum solution (resp. minimum solution), one can find a minimum maximal solution (resp. maximum minimal solution). Such…
In this work, we present an $\Omega\left(\min\{\log \Delta, \sqrt{\log n}\}\right)$ lower bound for Maximal Matching (MM) in $\Delta$-ary trees against randomized algorithms. By a folklore reduction, the same lower bound applies to Maximal…