Minimum Dominating Sets in Scale-Free Network Ensembles

We study the scaling behavior of the size of minimum dominating set (MDS) in scale-free networks, with respect to network size N and power-law exponent γ, while keeping the average degree fixed. We study ensembles generated by three different network construction methods and we use a greedy algorith...

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Bibliographic Details
Published inScientific reports Vol. 3; no. 1; p. 1736
Main Authors Molnár, F., Sreenivasan, S., Szymanski, B. K., Korniss, G.
Format Journal Article
LanguageEnglish
Published London Nature Publishing Group UK 26.04.2013
Nature Publishing Group
Subjects
639/705/1041
639/705/1042
639/705/117
639/766/530/2801
Algorithms
Approximation
Computer science
Humanities and Social Sciences
Integer programming
multidisciplinary
Nodes
Scaling
Science
Sensors
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Summary:We study the scaling behavior of the size of minimum dominating set (MDS) in scale-free networks, with respect to network size N and power-law exponent γ, while keeping the average degree fixed. We study ensembles generated by three different network construction methods and we use a greedy algorithm to approximate the MDS. With a structural cutoff imposed on the maximal degree we find linear scaling of the MDS size with respect to N in all three network classes. Without any cutoff ( k max = N – 1) two of the network classes display a transition at γ ≈ 1.9, with linear scaling above and vanishingly weak dependence below, but in the third network class we find linear scaling irrespective of γ. We find that the partial MDS, which dominates a given z < 1 fraction of nodes, displays essentially the same scaling behavior as the MDS.
ISSN:2045-2322
2045-2322
DOI:10.1038/srep01736