# Brief Announcement: Exact Size Counting in Uniform Population Protocols in Nearly Logarithmic Time

LIPICS - Leibniz International Proceedings in Informatics, Sep 2018

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.

This is a preview of a remote PDF: http://drops.dagstuhl.de/opus/volltexte/2018/9835/pdf/LIPIcs-DISC-2018-46.pdf

David Doty, Mahsa Eftekhari, Othon Michail, Paul G. Spirakis, Michail Theofilatos. Brief Announcement: Exact Size Counting in Uniform Population Protocols in Nearly Logarithmic Time, LIPICS - Leibniz International Proceedings in Informatics, 2018, 46:1-46:3, DOI: 10.4230/LIPIcs.DISC.2018.46