Abstract
In this chapter, we introduce the self-stabilizing algorithm model and present several definitive examples that illustrate the simplicity and elegance of this algorithmic paradigm when applied to problems related to dominating sets in graphs. In this paradigm, a distributed computing system or network is modeled by an undirected graph Gā=ā(V, E), where Vā is its set of nodes, or processors, and E is its set of edges, or communication links. Each node has only a local view of the system, namely its immediate neighbors. Thus, it has no knowledge of the network, its size, or how it is structured. Every node executes the same algorithm simultaneously, and in a finite amount of time, often O(n), the system converges, or stabilizes, to a global, stable state, satisfying some desired property. For example, the states of the nodes in the given graph G can define a maximal independent set, a maximal matching, a minimal dominating set, a minimal total dominating set, or even two disjoint minimal dominating sets.
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The author would like to thank the reviewers for the time it took them to carefully read this chapter and for their many suggestions to improve its presentation.
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Hedetniemi, S.T. (2021). Self-Stabilizing Domination Algorithms. In: Haynes, T.W., Hedetniemi, S.T., Henning, M.A. (eds) Structures of Domination in Graphs . Developments in Mathematics, vol 66. Springer, Cham. https://doi.org/10.1007/978-3-030-58892-2_16
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