Self-Stabilizing Population Protocols With Global Knowledge

Yuichi Sudo,Yonghwan Kim,Masahiro Shibata,Toshimitsu Masuzawa,Junya Nakamura

doi:10.1109/tpds.2021.3076769

Abstract

In the population protocol model, many problems cannot be solved in a self-stabilizing manner. However, global knowledge, such as the number of nodes in a network, sometimes enables the design of a self-stabilizing protocol for such problems. For example, it is known that we can solve the self-stabilizing leader election in complete graphs if and only if every node knows the exact number of nodes. In this article, we investigate the effect of global knowledge on the possibility of self-stabilizing population protocols in arbitrary graphs. Specifically, we clarify the solvability of the leader election problem, the ranking problem, the degree recognition problem, and the neighbor recognition problem by self-stabilizing population protocols with knowledge of the number of nodes and/or the number of edges in a network.

Highlights

IntroductionA network called population consists of a large number of finite-state automata, called agents
WE consider the population protocol (PP) model [2] in this paper
We investigate the solvability of leader election (LE), ranking problem (RK), degree recognition (DR), and neighbor recognition (NR) for arbitrary graphs with the knowledge n and m

Summary

Introduction

A network called population consists of a large number of finite-state automata, called agents. Agents make interactions (i.e., pairwise communication) with each other to update their states. The interactions are opportunistic, i.e., they are unpredictable for the agents. Agents are strongly anonymous: they do not have identifiers, and they cannot distinguish their neighbors in the same states. Two devices can communicate (i.e., interact) with each other only when the corresponding birds come sufficiently close to each other. A population is modeled by a graph G 1⁄4 ðV; EÞ, where V represents the set of agents, and E indicates which pair of agents can interact. In the field of population protocols, many efforts have been devoted to devising protocols for a complete graph, i.e., a population where every pair of agents interacts infinitely often.

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