On greedy construction of connected dominating sets in wireless networks

Since no fixed infrastructure and no centralized management present in wireless networks, a Connected Dominating Set (CDS) of the graph representing the network is widely used as a virtual backbone. Constructing a minimum CDS is NP-hard. In ∗Department of Computer Science, Georgia State University, Atlanta, GA, 30303. Email: {yli}@cs.gsu.edu. †Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, 55455. Email: {mythai,fwang,dzd}@cs.umn.edu. Support in part by National Science Foundation under grant CCR-0242520. ‡Department of Computer and Information Science, National Chiao-Tung University, Hsin-Chu, Taiwan. Email: [email protected]. §Department of Computer Science, Illinois Institute of Technology, Chicago, IL, 60616. Email: [email protected]. this paper, we propose a new greedy algorithm, called S-MIS, with the help of Steiner tree that can construct a CDS within a factor of 5.8 + ln 4 from the optimal solution. We also introduce the distributed version of this algorithm. A simulation is conducted to compare S-MIS with its variation which is rS-MIS. The simulation shows that the sizes of the CDSs generated by S-MIS and rS-MIS are almost the same.