, 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


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.


Wireless Network Channel Assignment Expected Size Unit Disk Graph Random Geometric Graph 
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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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