The Expected Size of the Rule k Dominating Set: I
نویسندگان
چکیده
Dai, Li, and Wu [11] [30] proposed Rule k, a localized approximation algorithm that attempts to find a small connected dominating set in a graph. In this paper we consider the “average case”performance of Rule k for the model of random unit disk graphs constructed from n random points in an `n × `n square. We show that if k ≥ 3 and `n = o(√n), then the expected size of the Rule k dominating set is Θ(`n) as n → ∞. If `n ≤ √ n 10 log n , then expected size of the minimum CDS is also Θ(`n). These results complement results for Rule 1 and Rule 2 obtained in a companion paper [18]. keywords and phrases: dominating set, localized algorithm, approximation algorithm, performance analysis, probabilistic analysis, Rule k, unit disk graph,
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The Expected Size of the Rule k Dominating Set: II
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