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Sub-Linear Time Aggregation in Probabilistic Population Protocol Model
Ryota EGUCHI Taisuke IZUMI
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2019/09/01
Online ISSN: 1745-1337
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: Distributed algorithms
population protocol model, sub-linear time algorithm, aggregation problem,
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A passively mobile system is an abstract notion of mobile ad-hoc networks. It is a collection of agents with computing devices. Agents move in a region, but the algorithm cannot control their physical behavior (i.e., how they move). The population protocol model is one of the promising models in which the computation proceeds by the pairwise communication between two agents. The communicating agents update their states by a specified transition function (algorithm). In this paper, we consider a general form of the aggregation problem with a base station. The base station is a special agent having the computational power more powerful than others. In the aggregation problem, the base station has to sum up for inputs distributed to other agents. We propose an algorithm that solves the aggregation problem in sub-linear parallel time using a relatively small number of states per agent. More precisely, our algorithm solves the aggregation problem with input domain X in O(√n log2 n) parallel time and O(|X|2) states per agent (except for the base station) with high probability.