Computing Time Complexity of Population Protocols with Cover Times - The ZebraNet Example

Beauquier, Joffroy; Blanchard, Peva; Burman, Janna; Delaët, Sylvie

doi:10.1007/978-3-642-24550-3_6

Cited by 1 publication

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“…The research of Self-Stabilization (over some fairness assumption) has been explored in [5,7]. An extension with sensors offering a cover-time notion was also studied in [6]. A recent study in [18] also focused on finding the median agent in an extension of the model called Arithmetic Population Protocols.…”

Section: Introductionmentioning

confidence: 99%

Global Versus Local Computations: Fast Computing with Identifiers

Rabie¹

2017

Structural Information and Communication Complexity

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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 CP P L 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.

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Section: Introductionmentioning

confidence: 99%

Global Versus Local Computations: Fast Computing with Identifiers

Rabie¹

2017

Structural Information and Communication Complexity

View full text Add to dashboard Cite

show abstract

Computing Time Complexity of Population Protocols with Cover Times - The ZebraNet Example

Cited by 1 publication

References 13 publications

Global Versus Local Computations: Fast Computing with Identifiers

Global Versus Local Computations: Fast Computing with Identifiers

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