Fig. 5. Twelve different ways of labeling H graph
Counting the number of exposed-terminal sets is equivalent to counting the number of labeled subgraph H (See Table 2). There are
⎟⎟⎠
⎜⎜ ⎞
⎝
⎛ 4
n ways to select four from n elements. Each
has 2
2 4⎟⎟⎠×
⎜⎜ ⎞
⎝
⎛ =12 ways in forming the subgraph H (Figure 5).
Computing Subgraph Probability of Random Geometric Graphs 469
RGGs. We also believe that the techniques developed in the paper can be exploited to conduct quantitative analysis on other fundamental properties of wireless ad hoc networks.
We would like to thank Dr. Jau-Ling Shih for her invaluable help.
Acknowledgements
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INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS Int. J. Commun. Syst.(in press)
Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/dac.848
Energy optimization for chain-based data gathering in wireless sensor networks
Li-Hsing Yen1,*,y, Ming-Zhou Cai2, Yang-Min Cheng2 and Ping-Yuan Yang2
1Department of Computer Science and Information Engineering, National University of Kaohsiung, Taiwan 811, ROC
2Department of Computer Science and Information Engineering, Chung Hua University, Hsinchu, Taiwan 300, ROC
SUMMARY
This paper aims to minimize energy expense for chain-based data gathering schemes, which is essential to prolong the operation lifetime of wireless sensor networks. Energy expense in chain-based data gathering schemes consists of two parts. One corresponds to inter-sensor communications and depends on chain structure. The other corresponds to leader-BS (base station) communications and depends on leader scheduling policy. To optimize inter-sensor communications, the notion of virtual chain is utilized, where an edge may correspond to a multi-hop data propagation path to conserve power. In contrast, an edge in previous work can only be a costly direct communication link. To optimize leader-BS communications, a leader scheduling rule is presented, where the node with the maximum residual power will be selected to be the leader of the chain. In contrast, nodes in previous work act as leaders by turns, resulting in non-uniform energy consumption among sensors. Simulation results show that our strategies are nearly optimal in terms of power conservation. Copyright # 2006 John Wiley & Sons, Ltd.
Received 30 December 2005; Revised 7 June 2006; Accepted 30 June 2006
KEY WORDS: wireless sensor networks; energy consumption; data gathering; logical chain