A self-stabilizing 2-minimal dominating set algorithm based on loop composition in networks of girth at least 7

Syohei Maruyama; Yuichi Sudo; Sayaka Kamei; Hirotsugu Kakugawa

doi:10.1109/IPDPS53621.2022.00114

2022 IEEE International Parallel and Distributed Processing Symposium (IPDPS)

A self-stabilizing 2-minimal dominating set algorithm based on loop composition in networks of girth at least 7

Year: 2022, Pages: 1140-1150

DOI Bookmark: 10.1109/IPDPS53621.2022.00114

Authors

Syohei Maruyama, Fujitsu Ltd.,Japan
Yuichi Sudo, Hosei University,Japan
Sayaka Kamei, Hiroshima University,Japan
Hirotsugu Kakugawa, Ryukoku University,Japan

Abstract

We propose a silent self-stabilizing asynchronous distributed algorithm to find a 2-minimal dominating set (2-MDS) in networks of girth at least 7. Given a graph

G = (V, E)

$G=(V, E)$ , a 2-MDS of

G

$G$ is a minimal dominating set

D \subseteq V

$D\subseteq V$ such that

D ∖ {p_{i}, p_{j}} \cup {p_{z}}

$D\backslash \{p_{i},p_{j}\}\cup\{p_{z}\}$ is not a dominating set for any nodes

p_{i}, p_{j} \in L (p_{i} \neq p_{j})

$p_{i},p_{j}\in L (p_{i}\neq p_{j})$ and

p_{z} / \in D

$p_{z}\ /{\!\!\!\in} D$ . The girth is the length of the shortest cycles in the graph. We assume that the processes have unique identifiers. The proposed algorithm constructs a 2-MDS in the networks of girth at least 7 under the weakly fair distributed daemon. The time complexity is

O (n H)

$O(nH)$ rounds, and the space complexity is

O (\log n)

$O(\log n)$ bits per process, where

n

$n$ is the number of processes and

H

$H$ is the diameter of the network.

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A self-stabilizing 2-minimal dominating set algorithm based on loop composition in networks of girth at least 7

Authors

Abstract

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