
Lower bounds for maximal matchings and maximal independent sets
There are distributed graph algorithms for finding maximal matchings and...
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Improved Distributed Lower Bounds for MIS and Bounded (Out)Degree Dominating Sets in Trees
Recently, Balliu, Brandt, and Olivetti [FOCS '20] showed the first ω(log...
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Distributed Data Summarization in WellConnected Networks
We study distributed algorithms for some fundamental problems in data su...
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Very fast construction of boundeddegree spanning graphs via the semirandom graph process
Semirandom processes involve an adaptive decisionmaker, whose goal is ...
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A Breezing Proof of the KMW Bound
In their seminal paper from 2004, Kuhn, Moscibroda, and Wattenhofer (KMW...
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Optimal Spanners for Unit Ball Graphs in Doubling Metrics
Resolving an open question from 2006, we prove the existence of lightwe...
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The Communication Complexity of Set Intersection and Multiple Equality Testing
In this paper we explore fundamental problems in randomized communicatio...
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Distributed Lower Bounds for Ruling Sets
Given a graph G = (V,E), an (α, β)ruling set is a subset S ⊆ V such that the distance between any two vertices in S is at least α, and the distance between any vertex in V and the closest vertex in S is at most β. We present lower bounds for distributedly computing ruling sets. The results carry over to one of the most fundamental symmetry breaking problems, maximal independent set (MIS), as MIS is the same as a (2,1)ruling set. More precisely, for the problem of computing a (2, β)ruling set (and hence also any (α, β)ruling set with α > 2) in the LOCAL model of distributed computing, we show the following, where n denotes the number of vertices and Δ the maximum degree. ∙ There is no deterministic algorithm running in o( logΔ/βloglogΔ) + o(√(log n/βloglog n)) rounds, for any β∈ o(√(logΔ/loglogΔ)) + o((log n/loglog n)^1/3). ∙ There is no randomized algorithm running in o( logΔ/βloglogΔ) + o(√(loglog n/βlogloglog n)) rounds, for any β∈ o(√(logΔ/loglogΔ)) + o((loglog n/logloglog n)^1/3). For β > 1, this improves on the previously best lower bound of Ω(log^* n) rounds that follows from the old bounds of Linial [FOCS'87] and Naor [J.Disc.Math.'91] (resp. Ω(1) rounds if β∈ω(log^* n)). For β = 1, i.e., for MIS, our results improve on the previously best lower bound of Ω(log^* n)on trees, as our bounds already hold on trees.
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