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arXiv · 1304.1007

Linear-in-$Δ$ Lower Bounds in the LOCAL Model

Mika Göös·Juho Hirvonen·Jukka Suomela
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Abstract

By prior work, there is a distributed algorithm that finds a maximal fractional matching (maximal edge packing) in $O(Δ)$ rounds, where $Δ$ is the maximum degree of the graph. We show that this is optimal: there is no distributed algorithm that finds a maximal fractional matching in $o(Δ)$ rounds. Our work gives the first linear-in-$Δ$ lower bound for a natural graph problem in the standard model of distributed computing---prior lower bounds for a wide range of graph problems have been at best logarithmic in $Δ$.

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Mika Göös, Juho Hirvonen, Jukka Suomela. 2013-04-03. Linear-in-$Δ$ Lower Bounds in the LOCAL Model. https://doi.org/10.1007/s00446-015-0245-8

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