TY - GEN
T1 - Deterministic population protocols for exact majority and plurality
AU - Gasieniec, Leszek
AU - Hamilton, David
AU - Martin, Russell
AU - Spirakis, Paul G.
AU - Stachowiak, Grzegorz
N1 - Funding Information:
This work is sponsored in part by the University of Liverpool initiative Networks Sciences and Technologies (NeST) and by the Polish National Science Centre grant DEC-2012/06/M/ST6/00459. The authors wish to thank Yukiko Yamauchi for the valuable referral to [18] about fair composition of self-stabilising algorithms, and for discussions related to the work in this paper. We also wish to thank the anonymous referees and the shepherd of OPODIS 2016 for their help in preparation of the final version of this paper.
Publisher Copyright:
© Leszek Gąsieniec, David Hamilton, Russell Martin, Paul G. Spirakis, and Grzegorz Stachowiak.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - In this paper we study space-efficient deterministic population protocols for several variants of the majority problem including plurality consensus. We focus on space efficient majority protocols in populations with an arbitrary number of colours C represented by k-bit labels, where k = ⌈log C⌉. In particular, we present asymptotically space-optimal (with respect to the adopted k-bit representation of colours) protocols for (1) the absolute majority problem, i.e., a protocol which decides whether a single colour dominates all other colours considered together, and (2) the relative majority problem, also known in the literature as plurality consensus, in which colours declare their volume superiority versus other individual colours. The new population protocols proposed in this paper rely on a dynamic formulation of the majority problem in which the colours originally present in the population can be changed by an external force during the communication process. The considered dynamic formulation is based on the concepts studied in [4] and [24] about stabilizing inputs and composition of population protocols. Also, the protocols presented in this paper use a composition of some known protocols for static and dynamic majority.
AB - In this paper we study space-efficient deterministic population protocols for several variants of the majority problem including plurality consensus. We focus on space efficient majority protocols in populations with an arbitrary number of colours C represented by k-bit labels, where k = ⌈log C⌉. In particular, we present asymptotically space-optimal (with respect to the adopted k-bit representation of colours) protocols for (1) the absolute majority problem, i.e., a protocol which decides whether a single colour dominates all other colours considered together, and (2) the relative majority problem, also known in the literature as plurality consensus, in which colours declare their volume superiority versus other individual colours. The new population protocols proposed in this paper rely on a dynamic formulation of the majority problem in which the colours originally present in the population can be changed by an external force during the communication process. The considered dynamic formulation is based on the concepts studied in [4] and [24] about stabilizing inputs and composition of population protocols. Also, the protocols presented in this paper use a composition of some known protocols for static and dynamic majority.
KW - Deterministic population protocols
KW - Majority
KW - Plurality consenus
UR - http://www.scopus.com/inward/record.url?scp=85018244681&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85018244681&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.OPODIS.2016.14
DO - 10.4230/LIPIcs.OPODIS.2016.14
M3 - Conference contribution
AN - SCOPUS:85018244681
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 14.1-14.14
BT - 20th International Conference on Principles of Distributed Systems, OPODIS 2016
A2 - Jimenez, Ernesto
A2 - Fatourou, Panagiota
A2 - Pedone, Fernando
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 20th International Conference on Principles of Distributed Systems, OPODIS 2016
Y2 - 13 December 2016 through 16 December 2016
ER -