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In wireless sensor networks, the number of cluster heads and nodes has direct relation to its cost and its performance, such as robust, fault-tolerance, etc. Further more, it is considered at first as wireless sensor networks are designed. The paper simplifies complex connectivity and coverage problem step by step. By means of theoretical analysis, math modeling and geometry proving and making use of geometric theories and the method of mathematics induction, the method of grid plot of sensor field is proposed from the viewpoints of topology. In the end, the analysis formulae of minimum number of cluster heads and nodes are respectively educed in theory under circumstances of full and seamless connectivity and coverage problem in wireless sensor networks. That is, the problems of full and seamless connectivity and coverage are solved that how many clusters total sensor field is plotted and how many nodes are deployed over the field at the fewest, or MCDS (minimum connected dominating set) and MSDS (minimum sensing dominating set).
Date of Conference: 18-18 Dec. 2008