eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-10-04
46:1
46:3
10.4230/LIPIcs.DISC.2018.46
article
Brief Announcement: Exact Size Counting in Uniform Population Protocols in Nearly Logarithmic Time
Doty, David
1
Eftekhari, Mahsa
1
Michail, Othon
2
Spirakis, Paul G.
3
Theofilatos, Michail
2
Department of Computer Science, University of California, Davis
Department of Computer Science, University of Liverpool, UK
Department of Computer Science, University of Liverpool, UK and Computer Technology Institute & Press "Diophantus" (CTI), Patras, Greece
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol121-disc2018/LIPIcs.DISC.2018.46/LIPIcs.DISC.2018.46.pdf
population protocol
counting
leader election
polylogarithmic time