Time-space trade-offs in population protocols for the majority problem

Berenbrink, Petra; Elsässer, Robert; Friedetzky, Tom; Kaaser, Dominik; Kling, Peter; Radzik, Tomasz

doi:10.1007/s00446-020-00385-0

Cited by 22 publications

(27 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As we only double once all contributions are small, each agent can always store the new value. This idea of alternating cancelling and doubling phases has been used extensively in the population protocol literature [5,9,10,22]. detect → ′ detect is the transfer function.…”

Section: Daf Decides All Homogeneous Threshold Predicates On Bounded-degree Graphsmentioning

confidence: 99%

Decision Power of Weak Asynchronous Models of Distributed Computing

Czerner

Guttenberg

Helfrich

et al. 2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

View full text Add to dashboard Cite

Esparza and Reiter have recently conducted a systematic comparative study of models of distributed computing consisting of a network of identical finite-state automata that cooperate to decide if the underlying graph of the network satisfies a given property.The study classifies models according to four criteria, and shows that twenty-four initially possible combinations collapse into seven equivalence classes with respect to their decision power, i.e. the properties that the automata of each class can decide. However, Esparza and Reiter only show (proper) inclusions between the classes, and so do not characterise their decision power. In this paper we do so for labelling properties, i.e. properties that depend only on the labels of the nodes, but not on the structure of the graph. In particular, majority (whether more nodes carry label than ) is a labelling property. Our results show that only one of the seven equivalence classes identified by Esparza and Reiter can decide majority for arbitrary networks. We then study the expressive power of the classes on bounded-degree networks, and show that three classes can. In particular, we present an algorithm for majority that works for all bounded-degree networks under adversarial schedulers, i.e. even if the scheduler must only satisfy that every node makes a move infinitely often, and prove that no such algorithm can work for arbitrary networks.

show abstract

Section: Daf Decides All Homogeneous Threshold Predicates On Bounded-degree Graphsmentioning

confidence: 99%

Decision Power of Weak Asynchronous Models of Distributed Computing

Czerner

Guttenberg

Helfrich

et al. 2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

View full text Add to dashboard Cite

show abstract

“….bias means that all minority would be eliminated once we reach hour ⌈log 2 1 ⌉ ≤ . This would give an (log )-state, (log 2 )-time majority algorithm, essentially equivalent to [3,9]. The main idea of our algorithm is to use these rules with a faster clock using only (1) time per hour.…”

Section: Algorithmmentioning

confidence: 99%

“…Our protocol is both monotone and output dominant (see full paper or [3] for discussion of these definitions), so by the Ω(log ) state lower bound of [3], our protocol is both time and space optimal for the class of monotone, output-dominant stable protocols. Like most known majority protocols using more than constant space (the only exceptions being in [9]), our protocol is nonuniform in the sense that agents are assumed to have an estimate of the value ⌈log ⌉ embedded in the transition function and state space. It is possible to modify our main protocol to make it uniform, retaining the (log ) time bound, but increasing the state complexity to (log log log ) in expectation and with high probability.…”

Section: Introductionmentioning

confidence: 99%

Brief Announcement: A Time and Space Optimal Stable Population Protocol Solving Exact Majority

Doty

Eftekhari

Gąsieniec

et al. 2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

View full text Add to dashboard Cite

We study population protocols, a model of distributed computing where agents exchange information in pairwise interactions, but have no control over their schedule of interaction partners. The well-studied majority problem is that of determining in an initial population of agents, each with one of two opinions or , whether there are more , more , or a tie. A stable protocol solves this problem with probability 1 by eventually entering a configuration in which all agents agree on a correct consensus decision of A, B, or T, from which the consensus cannot change. We describe a protocol that solves this problem using (log ) states (log log + (1) bits of memory) and optimal expected time (log ). The number of states (log ) is known to be optimal for the class of polylogarithmic time stable protocols that are "output dominant" and "monotone". These are two natural constraints satisfied by our protocol, making it simultaneously time-and state-optimal for that class. Our protocol is nonuniform: the transition function has the value ⌈log ⌉ encoded in it. We show that the protocol can be modified to be uniform, while increasing the state complexity to Θ(log log log ).

show abstract

“…In the population protocol model, researchers studied various fundamental problems such as leader election problems [1,11,15,18], counting problems [7,8,9], majority problems [5,10,17], etc. In [2,6,13,14], researchers proposed efficient protocols for such fundamental problems with limited communication graphs.…”

Section: Related Workmentioning

confidence: 99%

Population Protocols for Graph Class Identification Problems

Yasumi¹,

Ooshita²,

Inoue³

2021

Preprint

View full text Add to dashboard Cite

In this paper, we focus on graph class identification problems in the population protocol model. A graph class identification problem aims to decide whether a given communication graph is in the desired class (e.g. whether the given communication graph is a ring graph). Angluin et al. proposed graph class identification protocols with directed graphs and designated initial states under global fairness [Angluin et al., DCOSS2005]. We consider graph class identification problems for undirected graphs on various assumptions such as initial states of agents, fairness of the execution, and initial knowledge of agents. In particular, we focus on lines, rings, k-regular graphs, stars, trees, and bipartite graphs. With designated initial states, we propose graph class identification protocols for k-regular graphs, and trees under global fairness, and propose a graph class identification protocol for stars under weak fairness. Moreover, we show that, even if agents know the number of agents n, there is no graph class identification protocol for lines, rings, k-regular graphs, trees, or bipartite graphs under weak fairness. On the other hand, with arbitrary initial states, we show that there is no graph class identification protocol for lines, rings, k-regular graphs, stars, trees, or bipartite graphs.

show abstract

Time-space trade-offs in population protocols for the majority problem

Cited by 22 publications

References 19 publications

Decision Power of Weak Asynchronous Models of Distributed Computing

Decision Power of Weak Asynchronous Models of Distributed Computing

Brief Announcement: A Time and Space Optimal Stable Population Protocol Solving Exact Majority

Population Protocols for Graph Class Identification Problems

Contact Info

Product

Resources

About