A new self-stabilizing algorithm for maximal p-star decomposition of general graphs

• Published in: Information processing letters Vol. 115; no. 11; pp. 892 - 898
• Main Authors: Neggazi, Brahim, Haddad, Mohammed, Kheddouci, Hamamache
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2015; Elsevier Sequoia S.A; Elsevier
• Subjects: Algorithms; Computer Science; Data Structures and Algorithms; Decomposition; Distributed systems; Distributed, Parallel, and Cluster Computing; Fault tolerence; Generalized matching; Graph algorithms; Graph decomposition; Information processing; Polynomials; Self-stabilization; Studies; Uniform stars; Self-stabilization; Uniform stars; Graph decomposition; Distributed systems; Graph algorithms; Fault tolerence; Generalized matching
• ISSN: 0020-0190; 1872-6119
• DOI: 10.1016/j.ipl.2015.05.010

•We address the decomposition of graphs into stars in a distributed way.•We propose a new self-stabilizing algorithm for decomposing arbitrary graphs into stars having same size.•The proposed algorithm has polynomial moves complexity.•Formal proofs for correctness and convergence are provided. A p-star is a complete bipartite graph K1,p with one center node and p leaves. In this paper, we propose a polynomial self-stabilizing algorithm for maximal graph decomposition into p-stars. Given an arbitrary graph G and a positive integer p⩾1, this decomposition provides disjoint components of G, such that each component induces a p-star in G. Under the unfair distributed scheduler, the algorithm converges within O(Δ2m) moves where m is the number of edges and Δ is maximum node degree in the graph G.