# The expected size of the rule k dominating set

Jennie C. Hansen, Eric Schmutz, Li Sheng

Research output: Contribution to journalArticle

### 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 ln × ln square. We show that if k = 3 and ln = o(vn), then for both versions of Rule k, the expected size of the Rule k dominating set is T(l n2) as n ? 8. It follows that, for ln in a suitable range, the expected size of the Rule k dominating sets are within a constant factor of the optimum. © Springer 2006.

Original language English 409-418 10 Algorithmica 46 3-4 https://doi.org/10.1007/s00453-006-0104-x Published - Nov 2006

### Fingerprint

Dominating Set
Unit Disk Graph
Connected Dominating Set
Random Graphs
Approximation Algorithms
Graph in graph theory
Range of data

### Keywords

• Approximation algorithm
• Dominating set
• Localized algorithm
• Performance analysis
• Probabilistic analysis
• Rule k
• Unit disk graph

### Cite this

Hansen, Jennie C. ; Schmutz, Eric ; Sheng, Li. / The expected size of the rule k dominating set. In: Algorithmica . 2006 ; Vol. 46, No. 3-4. pp. 409-418.
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The expected size of the rule k dominating set. / Hansen, Jennie C.; Schmutz, Eric; Sheng, Li.

In: Algorithmica , Vol. 46, No. 3-4, 11.2006, p. 409-418.

Research output: Contribution to journalArticle

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