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Algorithmica

, Volume 65, Issue 2, pp 443–466 | Cite as

Power Domination in Circular-Arc Graphs

  • Chung-Shou Liao
  • D. T. LeeEmail author
Article

Abstract

A set SV is a power dominating set (PDS) of a graph G=(V,E) if every vertex and every edge in G can be observed based on the observation rules of power system monitoring. The power domination problem involves minimizing the cardinality of a PDS of a graph. We consider this combinatorial optimization problem and present a linear time algorithm for finding the minimum PDS of an interval graph if the interval ordering of the graph is provided. In addition, we show that the algorithm, which runs in Θ(nlogn) time, where n is the number of intervals, is asymptotically optimal if the interval ordering is not given. We also show that the results hold for the class of circular-arc graphs.

Keywords

Domination Power domination Interval graphs Circular-arc graphs Algorithm 

Notes

Acknowledgements

We wish to thank Hengchin Yeh, Ching-Chi Lin, G.J. Chang, and the anonymous reviewers for many valuable comments and suggestions, which helped us improve the quality of the presentation of the paper.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Engineering ManagementNational Tsing Hua UniversityHsinchuTaiwan
  2. 2.Department of Computer Science and EngineeringNational Chung Hsing UniversityTaichungTaiwan
  3. 3.Dept. of Computer Science and Information EngineeringNational Taiwan UniversityTaipeiTaiwan
  4. 4.Institute of Information ScienceAcademia SinicaNankang, TaipeiTaiwan

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