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We present $O(loglog n)$ round scalable Massively Parallel Computation algorithms for maximal independent set and maximal matching, in trees and more generally graphs of bounded arboricity, as well as for constant coloring trees. Following the standards, by a scalable MPC algorithm, we mean that these algorithms can work on machines that have capacity/memory as small as $n^{delta}$ for any positive constant $delta<1$. Our results improve over the $O(log^2log n)$ round algorithms of Behnezhad et al. [PODC19]. Moreover, our matching algorithm is presumably optimal as its bound matches an $Omega(loglog n)$ conditional lower bound of Ghaffari, Kuhn, and Uitto [FOCS19].
In this paper we study fractional coloring from the angle of distributed computing. Fractional coloring is the linear relaxation of the classical notion of coloring, and has many applications, in particular in scheduling. It was proved by Hasemann, H
Recently, Balliu, Brandt, and Olivetti [FOCS 20] showed the first $omega(log^* n)$ lower bound for the maximal independent set (MIS) problem in trees. In this work we prove lower bounds for a much more relaxed family of distributed symmetry breaking
A distributed proof (also known as local certification, or proof-labeling scheme) is a mechanism to certify that the solution to a graph problem is correct. It takes the form of an assignment of labels to the nodes, that can be checked locally. There
Network decompositions, as introduced by Awerbuch, Luby, Goldberg, and Plotkin [FOCS89], are one of the key algorithmic tools in distributed graph algorithms. We present an improved deterministic distributed algorithm for constructing network decompo
We show that the $(degree+1)$-list coloring problem can be solved deterministically in $O(D cdot log n cdotlog^2Delta)$ rounds in the CONGEST model, where $D$ is the diameter of the graph, $n$ the number of nodes, and $Delta$ the maximum degree. Usin