Abstract: It is one of the challenging core issues in the research of WSN that coverage and connectivity can be realized by using the least sensor nodes in certain coverage conditions. An algorithm of optimal coverage in the regular region and connectivity was put forward. Target nodes can be distributed into the range of square by the double square, then association mould can be worked out by sensor nodes and target nodes. By the way, in case of the whole coverage region, the least sensor nodes under coverage can be figured out by using expectation value of probability. At last, connectivity probability mould of fringe nodes within the range of outer square and inference procedures were analyzed. The experiment shows that the error between the theoretical value and simulated result is below 5%. The validity of this algorithm is thus verified. The distribution of network resources is decreased so that network coverage and connectivity can be better evaluated.

Key words: Wireless sensor networks( WSN) , Coverage, Connectivity, Algorithm, Nodes