This paper addresses the following relay sensor placement problem: given the set of duty sensors in the plane and the upper bound of the transmission range, compute the minimum number of relay sensors such that the induced topology by all sensors is globally connected. This problem is motivated by practically considering the tradeoff among performance, lifetime, and cost when designing sensor networks. In our study, this problem is modelled by a NP-hard network optimization problem namedSteiner Minimum Tree with Minimum number of Steiner Points and bounded edge length (SMT-MSP). In this paper, we propose two approximate algorithms, and conduct detailed performance analysis. The first algorithm has a performance ratio of 3 and the second has a performance ratio of 2.5.

Authors and Affiliations

1. Department of Computer Science, The George Washington University, Washington, DC, 20052, USA

   Xiuzhen Cheng

2. Department of Computer Science, The University of Texas at Dallas, Richardson, TX, 75083, USA

   Ding-Zhu Du

3. Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong

   Lusheng Wang

4. School of Math. and Computer Science, Nanjing Normal University, 122 Ninghai Road, Nanjing, 210097, P.R. China

   Baogang Xu

Corresponding author

Correspondence toXiuzhen Cheng.

Xiuzhen Cheng is an Assistant Professor in the Department of Computer Science at the George Washington University. She received her MS and PhD degrees in Computer Science from the University of Minnesota - Twin Cities in 2000 and 2002, respectively. Her current research interests include Wireless and Mobile Computing, Sensor Networks, Wireless Security, Statistical Pattern Recognition, Approximation Algorithm Design and Analysis, and Computational Medicine. She is an editor for the International Journal on Ad Hoc and Ubiquitous Computing and the International Journal of Sensor Networks. Dr. Cheng is a member of IEEE and ACM. She received the National Science Foundation CAREER Award in 2004.

Ding-Zhu Du received his M.S. degree in 1982 from Institute of Applied Mathematics, Chinese Academy of Sciences, and his Ph.D. degree in 1985 from the University of California at Santa Barbara. He worked at Mathematical Sciences Research Institutea, Berkeley in 1985-86, at MIT in 1986-87, and at Princeton University in 1990-91. He was an associate-professor/professor at Department of Computer Science and Engineering, University of Minnesota in 1991-2005, a professor at City University of Hong Kong in 1998-1999, a research professor at Institute of Applied Mathematics, Chinese Academy of Sciences in 1987-2002, and a Program Director at National Science Foundation of USA in 2002-2005. Currently, he is a professor at Department of Computer Science, University of Texas at Dallas and the Dean of Science at Xi’an Jiaotong University. His research interests include design and analysis of algorithms for combinatorial optimization problems in communication networks and bioinformatics. He has published more than 140 journal papers and 10 written books. He is the editor-in-chief of Journal of Combinatorial Optimization and book series on Network Theory and Applications. He is also in editorial boards of more than 15 journals.

Lusheng Wang received his PhD degree from McMaster University in 1995. He is an associate professor at City University of Hong Kong. His research interests include networks, algorithms and Bioinformatics. He is a member of IEEE and IEEE Computer Society.

Baogang Xu received his PhD degree from Shandong University in 1997. He is a professor at Nanjing Normal University. His research interests include graph theory and algorithms on graphs.

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