Star factorizations of graph products

Bryant, Darryn; El-Zanati, Saad I.; Eynden, Charles Vanden

doi:10.1002/1097-0118(200102)36:2<59::aid-jgt1>3.0.co;2-a

Cited by 6 publications

(1 citation statement)

References 19 publications

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“…One of the famous and well studied graph decompositions in literature is star decomposition [3,4,5]. A decomposition of a graph into stars is a way of expressing the graph as the union of disjoint stars [6]. The problem of star decomposition has several applications including scientific computing, scheduling, load balancing and parallel computing [7], important nodes detection in social networks [8].…”

Section: Introductionmentioning

confidence: 99%

Polynomial Silent Self-Stabilizing p-Star Decomposition†

Haddad

Johnen

Köhler

2019

The Computer Journal

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We present a silent self-stabilizing distributed algorithm computing a maximal $\ p$-star decomposition of the underlying communication network. Under the unfair distributed scheduler, the most general scheduler model, the algorithm converges in at most $12\Delta m + \mathcal{O}(m+n)$ moves, where $m$ is the number of edges, $n$ is the number of nodes and $\Delta $ is the maximum node degree. Regarding the time complexity, we obtain the following results: our algorithm outperforms the previously known best algorithm by a factor of $\Delta $ with respect to the move complexity. While the round complexity for the previous algorithm was unknown, we show a $5\big \lfloor \frac{n}{p+1} \big \rfloor +5$ bound for our algorithm.

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Section: Introductionmentioning

confidence: 99%

Polynomial Silent Self-Stabilizing p-Star Decomposition†

Haddad

Johnen

Köhler

2019

The Computer Journal

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Erratum to: “Star factorizations of graph products”

Bryant¹,

El-Zanati²,

Eynden³

2006

Journal of Graph Theory

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A Self-stabilizing Algorithm for Maximal p-Star Decomposition of General Graphs

Neggazi¹,

Turau²,

Haddad³

et al. 2013

Lecture Notes in Computer Science

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International audienceA p-star is a complete bipartite graph K 1,p with one center node and p leaf nodes. In this paper we propose the first distributed self-stabilizing algorithm for graph decomposition into p-stars. For a graph G and an integer p ≥ 1, this decomposition provides disjoint components of G where each component forms a p-star. We prove convergence and correctness of the algorithm under an unfair distributed daemon. The stabilization time is 2⌊n/(p+1)⌋+2 rounds

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Star factorizations of graph products

Cited by 6 publications

References 19 publications

Polynomial Silent Self-Stabilizing p-Star Decomposition†

Polynomial Silent Self-Stabilizing p-Star Decomposition†

Erratum to: “Star factorizations of graph products”

A Self-stabilizing Algorithm for Maximal p-Star Decomposition of General Graphs

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