Abstract
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 maximal matchings and maximal independent sets cannot be found in o(Δ + log log n / log log log n) rounds with any randomized algorithm in the LOCAL model of distributed computing. As a corollary, it follows that there is no deterministic algorithm for maximal matchings or maximal independent sets that runs in o(Δ + log n / log log n) rounds; this is an improvement over prior lower bounds also as a function of n.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
