Lower Bounds for Maximal Matchings and Maximal Independent Sets

Alkida Balliu, Sebastian Brandt, Juho Hirvonen, Dennis Olivetti, Mikael Rabie, Jukka Suomela

Tutkimustuotos: LehtiartikkeliArticleScientificvertaisarvioitu

Abstrakti

There are distributed graph algorithms for finding maximal matchings and maximal independent sets in O(Δ + log* n) communication rounds; here, n is the number of nodes and Δ is the maximum degree. The lower bound by Linial (1987, 1992) shows that the dependency on n is optimal: These problems cannot be solved in o(log* n) rounds even if Δ = 2. However, the dependency on Δ is a long-standing open question, and there is currently an exponential gap between the upper and lower bounds.

We prove that the upper bounds are tight. We show that any algorithm that finds a maximal matching or maximal independent set with probability at least 1-1/n requires Ω (min { Δ, log log n / log log log n}) rounds in the LOCAL model of distributed computing. As a corollary, it follows that any deterministic algorithm that finds a maximal matching or maximal independent set requires Ω (min {Δ, log n / log log n}) rounds; this is an improvement over prior lower bounds also as a function of n.
AlkuperäiskieliEnglanti
Artikkeli39
Sivut1-30
Sivumäärä30
JulkaisuJournal of the ACM
Vuosikerta68
Numero5
DOI - pysyväislinkit
TilaJulkaistu - lokak. 2021
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

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