Distributed Voting/Ranking With Optimal Number of States per Node

Salehkaleybar, Saber; Sharifnassab, Arsalan; Golestani, S. Jamaloddin

doi:10.1109/tsipn.2015.2477777

Cited by 14 publications

(34 citation statements)

References 27 publications

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“…The Plurality Problem (also known as Plurality Consensus Problem in Distributed Computing), is an extensively studied problem in many areas of distributed computing, such as population protocols [1,8,9,21,24], fixed-volume Chemical Reaction Networks [13,27], asynchronous Gossip protocols [5,6,10,15,16], Statistical Physics [12] and Mathematical Biology [7,11,20,26].…”

Section: Related Workmentioning

confidence: 99%

“…In the context of the Plurality Problem, for k = 2, the protocols of [9,21] require 4 states per node, and in [21], they showed that the problem cannot be solved with 3 states. For general k, the protocol of [24] uses O(2 k−1 · k) states per node, and the only lower bound known has been so far the trivial Ω(k), as each node/agent needs at least k distinct states to specify its own opinion (which is from a set of size k). Under the crucial assumption that agents initially agree on a representation of the input values as distinct integers, [17] provides an elegant solution to the Plurality Problem which employs O(k 6 ) states only.…”

Section: Related Workmentioning

confidence: 99%

“…This is crucially the case when correctness is required to be deterministic (i.e. the probability of failure should be 0) [21,24].…”

Section: Model and Basic Definitionsmentioning

confidence: 99%

“…However, the state complexity of the problem for general k has so far remained elusive: a clever protocol by Salehkaleybar et al [24], called DMVR, shows how to solve the problem with O(k2 k ) states per person. They conjectured the DMVR protocol to be optimal: "We conjecture that the DMVR protocol is an optimal solution for majority voting problem, i.e.…”

Section: Introductionmentioning

confidence: 99%

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On the Necessary Memory to Compute the Plurality in Multi-agent Systems

Natale

Ramezani

2019

Lecture Notes in Computer Science

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We consider the Relative-Majority Problem (also known as Plurality), in which, given a multi-agent system where each agent is initially provided an input value out of a set of k possible ones, each agent is required to eventually compute the input value with the highest frequency in the initial configuration. We consider the problem in the general Population Protocols model in which, given an underlying undirected connected graph whose nodes represent the agents, edges are selected by a globally fair scheduler. The state complexity that is required for solving the Plurality Problem (i.e., the minimum number of memory states that each agent needs to have in order to solve the problem), has been a long-standing open problem. The best protocol so far for the general multi-valued case requires polynomial memory: Salehkaleybar et al. (2015) devised a protocol that solves the problem by employing O(k2 k ) states per agent, and they conjectured their upper bound to be optimal. On the other hand, under the strong assumption that agents initially agree on a total ordering of the initial input values, G ֒ asieniec et al. (2017), provided an elegant logarithmic-memory plurality protocol. In this work, we refute Salehkaleybar et al.'s conjecture, by providing a plurality protocol which employs O(k 11 ) states per agent. Central to our result is an ordering protocol which allows to leverage on the plurality protocol by G ֒ asieniec et al., of independent interest. We also provide a Ω(k 2 )-state lower bound on the necessary memory to solve the problem, proving that the Plurality Problem cannot be solved within the mere memory necessary to encode the output.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…This is crucially the case when correctness is required to be deterministic (i.e. the probability of failure should be 0) [21,24].…”

Section: Model and Basic Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Necessary Memory to Compute the Plurality in Multi-agent Systems

Natale

Ramezani

2019

Lecture Notes in Computer Science

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“…Consequently, the algorithm termination is embedded within it. Hence, the algorithm becomes more efficient in terms of message complexity compared with previous works [7,10]. We call this algorithm 'binary voting with SPRT' (BiSPRT) algorithm.…”

Section: Introductionmentioning

confidence: 99%

Distributed binary majority voting via exponential distribution

Salehkaleybar¹,

Golestani²

2016

IET signal process.

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In the binary majority voting problem, each node initially chooses between two alternative choices. The goal is to design a distributed algorithm that informs nodes which choice is in majority. In this study, the authors formulate this problem as a hypothesis testing problem and propose fixed-size and sequential solutions using classical and Bayesian approaches. In the sequential version, the proposed mechanism enables nodes to test which choice is in majority, successively in time. Hence, termination of the algorithm is embedded within it, contrary to the existing approaches which require a monitoring algorithm to indicate the termination. This property makes the algorithm more efficient in terms of message complexity. Furthermore, the authors show that the proposed solution is resilient to Byzantine attacks if network connectivity is F + 1 in the presence of F adversarial nodes. Thus, the proposed algorithm is more robust compared with the previous works which are vulnerable to the existence of adversarial nodes.

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