Fast computation by population protocols with a leader
Fast algorithms are presented for performing computations in a probabilistic population model. This is a variant of the standard population protocol model, in which finite-state agents interact in pairs under the control of an adversary scheduler, where all pairs are equally likely to be chosen for...
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| Veröffentlicht in: | Distributed computing Jg. 21; H. 3; S. 183 - 199 |
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| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin/Heidelberg
Springer-Verlag
01.09.2008
Springer Nature B.V |
| Schlagworte: | |
| ISSN: | 0178-2770, 1432-0452 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Fast algorithms are presented for performing computations in a probabilistic population model. This is a variant of the standard population protocol model, in which finite-state agents interact in pairs under the control of an adversary scheduler, where all pairs are equally likely to be chosen for each interaction. It is shown that when a unique leader agent is provided in the initial population, the population can simulate a virtual register machine with high probability in which standard arithmetic operations like comparison, addition, subtraction, and multiplication and division by constants can be simulated in
O
(
n
log
5
n
) interactions using a simple register representation or in
O
(
n
log
2
n
) interactions using a more sophisticated representation that requires an extra
O
(
n
log
O
(1)
n
)-interaction initialization step. The central method is the extensive use of epidemics to propagate information from and to the leader, combined with an epidemic-based phase clock used to detect when these epidemics are likely to be complete. Applications include a reduction of the cost of computing a semilinear predicate to
O
(
n
log
5
n
) interactions from the previously best-known bound of
O
(
n
2
log
n
) interactions and simulation of a LOGSPACE Turing machine using
O
(
n
log
2
n
) interactions per step after an initial
O
(
n
log
O
(1)
n
)-interaction startup phase. These bounds on interactions translate into polylogarithmic time per step in a natural parallel model in which each agent participates in an expected
Θ
(1) interactions per time unit. Open problems are discussed, together with simulation results that suggest the possibility of removing the initial-leader assumption. |
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| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23 |
| ISSN: | 0178-2770 1432-0452 |
| DOI: | 10.1007/s00446-008-0067-z |