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arXiv · 2002.08216

Truly Tight-in-$\Delta$ Bounds for Bipartite Maximal Matching and Variants

Sebastian Brandt·Dennis Olivetti
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Abstract

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 the bipartite maximal matching problem on $n$-node graphs in the LOCAL model of distributed computing. Both lower bounds are asymptotically tight as a function of the maximum degree $\Delta$. We provide truly tight bounds in $\Delta$ for the complexity of bipartite maximal matching and many natural variants, up to and including the additive constant. As a by-product, our results yield a considerably simplified version of the proof by Balliu et al. We show that our results can be obtained via bounded automatic round elimination, a version of the recent automatic round elimination technique by Brandt [PODC'19] that is particularly suited for automatization from a practical perspective. In this context, our work can be seen as another step towards the automatization of lower bounds in the LOCAL model.

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Sebastian Brandt, Dennis Olivetti. 2020-02-19. Truly Tight-in-$\Delta$ Bounds for Bipartite Maximal Matching and Variants. https://arxiv.org/abs/2002.08216

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