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Algorithmica

, Volume 46, Issue 3–4, pp 409–418 | Cite as

The Expected Size of the Rule k Dominating Set

  • Jennie C. Hansen
  • Eric Schmutz
  • Li Sheng
Article

Abstract

Dai, Li, and Wu 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 two closely related versions of Rule k for the model of random unit disk graphs constructed from n random points in an \(\ell_n\times \ell_n\) square. We show that if \(k\geq 3\) and \(\ell_{n}=o(\sqrt{n}),\) then for both versions of Rule k, the expected size of the Rule k dominating set is \(\Theta(\ell_{n}^{2})\) as \(n\rightarrow\infty.\) It follows that, for \(\ell_{n}\) in a suitable range, the expected size of the Rule k dominating sets are within a constant factor of the optimum.

Keywords

Wireless Network Channel Assignment Expected Size Unit Disk Graph Random Geometric Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Actuarial Mathematics and Statistics Department, Herriot-Watt UniversityEdinburgh EH14 4ASScotland
  2. 2.Department of Mathematics, Drexel UniversityPhiladelphia, PA 19104USA

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