Deterministic Self-Stabilizing BFS Construction in Constant Space

Fuente: arXiv
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Main Authors: Blin, Lélia, Petit, Franck, Tixeuil, Sébastien
Format: Preprint
Published: 2025
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author Blin, Lélia
Petit, Franck
Tixeuil, Sébastien
author_facet Blin, Lélia
Petit, Franck
Tixeuil, Sébastien
contents In this paper, we resolve a long-standing question in self-stabilization by demonstrating that it is indeed possible to construct a spanning tree in a semi-uniform network using constant memory per node. We introduce a self-stabilizing synchronous algorithm that builds a breadth-first search (BFS) spanning tree with only $O(1)$ bits of memory per node, converging in $2^ε$ time units, where $ε$ denotes the eccentricity of the distinguish node. Crucially, our approach operates without any prior knowledge of global network parameters such as maximum degree, diameter, or total node count. In contrast to traditional self-stabilizing methods, such as pointer-to-neighbor communication or distance-to-root computation, that are unsuitable under strict memory constraints, our solution employs an innovative constant-space token dissemination mechanism. This mechanism effectively eliminates cycles and rectifies deviations in the BFS structure, ensuring both correctness and memory efficiency. The proposed algorithm not only meets the stringent requirements of memory-constrained distributed systems but also opens new avenues for research in self-stabilizing protocols under severe resource limitations.
format Preprint
id arxiv_https___arxiv_org_abs_2505_06596
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Deterministic Self-Stabilizing BFS Construction in Constant Space
Blin, Lélia
Petit, Franck
Tixeuil, Sébastien
Distributed, Parallel, and Cluster Computing
In this paper, we resolve a long-standing question in self-stabilization by demonstrating that it is indeed possible to construct a spanning tree in a semi-uniform network using constant memory per node. We introduce a self-stabilizing synchronous algorithm that builds a breadth-first search (BFS) spanning tree with only $O(1)$ bits of memory per node, converging in $2^ε$ time units, where $ε$ denotes the eccentricity of the distinguish node. Crucially, our approach operates without any prior knowledge of global network parameters such as maximum degree, diameter, or total node count. In contrast to traditional self-stabilizing methods, such as pointer-to-neighbor communication or distance-to-root computation, that are unsuitable under strict memory constraints, our solution employs an innovative constant-space token dissemination mechanism. This mechanism effectively eliminates cycles and rectifies deviations in the BFS structure, ensuring both correctness and memory efficiency. The proposed algorithm not only meets the stringent requirements of memory-constrained distributed systems but also opens new avenues for research in self-stabilizing protocols under severe resource limitations.
title Deterministic Self-Stabilizing BFS Construction in Constant Space
topic Distributed, Parallel, and Cluster Computing
url https://arxiv.org/abs/2505.06596