Global Versus Local Computations: Fast Computing with Identifiers

Mikael Rabie

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

This paper studies what can be computed by using probabilistic local interactions with agents with a very restricted power in polylogarithmic parallel time.
It is known that if agents are only finite state (corresponding to the Population Protocol model by Angluin et al.), then only semilinear predicates over the global input can be computed. In fact, if the population starts with a unique leader, these predicates can even be computed in a polylogarithmic parallel time.
If identifiers are added (corresponding to the Community Protocol model by Guerraoui and Ruppert), then more global predicates over the input multiset can be computed. Local predicates over the input sorted according to the identifiers can also be computed, as long as the identifiers are ordered. The time of some of those predicates might require exponential parallel time.
In this paper, we consider what can be computed with Community Protocol in a polylogarithmic number of parallel interactions. We introduce the class CPPL corresponding to protocols that use O(n log^k n), for some k, expected interactions to compute their predicates, or equivalently a polylogarithmic number of parallel expected interactions.
We provide some computable protocols, some boundaries of the class, using the fact that the population can compute its size. We also prove two impossibility results providing some arguments showing that local computations are no longer easy: the population does not have the time to compare a linear number of consecutive identifiers. The Linearly Local languages, such that the rational language (ab)^*, are not computable.
Original languageEnglish
Title of host publicationStabilization, Safety, and Security of Distributed Systems
Subtitle of host publication18th International Symposium, SSS 2016, Lyon, France, November 7-10, 2016, Proceedings
EditorsBorzoo Bonakdarpour, Franck Petit
Place of PublicationCham
Pages90-105
Number of pages16
ISBN (Electronic)978-3-319-49259-9
DOIs
Publication statusPublished - 19 Jun 2017
MoE publication typeA4 Article in a conference publication
EventInternational Colloquium on Structural Information and Communication Complexity - Porquerolles, France
Duration: 19 Jun 201722 Jun 2017
Conference number: 24

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume10083
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceInternational Colloquium on Structural Information and Communication Complexity
Abbreviated titleSIROCCO
CountryFrance
CityPorquerolles
Period19/06/201722/06/2017

Keywords

  • Population Protocols
  • Community Protocols
  • Identifiers
  • Distributed computing

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