A new sufficient condition for 1-coverage to imply connectivity

An effective approach for energy conservation in wireless sensor networks is scheduling sleep intervals for extraneous nodes while the remaining nodes stay active to provide continuous service. For the sensor network to operate successfully the active nodes must maintain both sensing coverage and network connectivity, It proved before if the communication range of nodes is at least twice the sensing range, complete coverage of a convex area implies connectivity among the working set of nodes. In this paper we consider a rectangular region A = a * b, such that R
S
≤ a, R
S
≤ b, where R
S
is the sensing range of nodes. and put a constraint on minimum allowed distance between nodes( R
S
). according to this constraint we present a new lower bound for communication range relative to sensing range of sensors( √2 + √3 * R
S
) that complete coverage of considered area implies connectivity among the working set of nodes; also we present a new distribution method , that satisfy our constraint.