2026-08-11T20:18:37Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:9835 2024-03-06T10:45:02Z ddc:004 open_access

Brief Announcement: Exact Size Counting in Uniform Population Protocols in Nearly Logarithmic Time Doty, David Eftekhari, Mahsa Michail, Othon Spirakis, Paul G. Theofilatos, Michail population protocol counting leader election polylogarithmic time We study population protocols: networks of anonymous agents whose pairwise interactions are chosen uniformly at random. The size counting problem is that of calculating the exact number n of agents in the population, assuming no leader (each agent starts in the same state). We give the first protocol that solves this problem in sublinear time. The protocol converges in O(log n log log n) time and uses O(n^60) states (O(1) + 60 log n bits of memory per agent) with probability 1-O((log log n)/n). The time to converge is also O(log n log log n) in expectation. Crucially, unlike most published protocols with omega(1) states, our protocol is uniform: it uses the same transition algorithm for any population size, so does not need an estimate of the population size to be embedded into the algorithm. Schloss Dagstuhl – Leibniz-Zentrum für Informatik David Doty and Mahsa Eftekhari and Othon Michail and Paul G. Spirakis and Michail Theofilatos 2018 Is Part Of LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.DISC.2018.46 urn:nbn:de:0030-drops-98359 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.46 eng https://creativecommons.org/licenses/by/3.0/legalcode