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A Better Theoretical Bound to Approximate Connected Dominating Set in Unit Disk Graph

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Wireless Algorithms, Systems, and Applications (WASA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5258))

Abstract

Connected Dominating Set is widely used as virtual backbone in wireless Ad-hoc and sensor networks to improve the performance of transmission and routing protocols. Based on special characteristics of Ad-hoc and sensor networks, we usually use unit disk graph to represent the corresponding geometrical structures, where each node has a unit transmission range and two nodes are said to be adjacent if the distance between them is less than 1. Since every Maximal Independent Set (MIS) is a dominating set and it is easy to construct, we can firstly find a MIS and then connect it into a Connected Dominating Set (CDS). Therefore, the ratio to compare the size of a MIS with a minimum CDS becomes a theoretical upper bound for approximation algorithms to compute CDS. In our paper, with the help of Voronoi diagram and Euler’s formula, we improved this upper bound, so that improved the approximations based on this relation.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, China

    Xianyue Li

  2. Department of Computer Science, University of Texas at Dallas, USA

    Xiaofeng Gao & Weili Wu

Authors
  1. Xianyue Li
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  2. Xiaofeng Gao
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  3. Weili Wu
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1413, 30303, Atlanta, GA, USA

    Yingshu Li

  2. Department of Computer Science, University of Texas at Dallas, EE/CS Building, TX 75083, Richardson, USA

    Dung T. Huynh  & Ding-Zhu Du  & 

  3. Department of Computer Science and Engineering, University of Texas at Arlington, P.O. Box 19015, TX 76019, Arlington, USA

    Sajal K. Das

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© 2008 Springer-Verlag Berlin Heidelberg

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Li, X., Gao, X., Wu, W. (2008). A Better Theoretical Bound to Approximate Connected Dominating Set in Unit Disk Graph. In: Li, Y., Huynh, D.T., Das, S.K., Du, DZ. (eds) Wireless Algorithms, Systems, and Applications. WASA 2008. Lecture Notes in Computer Science, vol 5258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88582-5_18

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  • DOI: https://doi.org/10.1007/978-3-540-88582-5_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88581-8

  • Online ISBN: 978-3-540-88582-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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