Abstract
This paper presents a mathematical model to geometrically optimize the density of active sensor nodes in a wireless sensor network (WSN) using concentric hexagonal tessellations and the concept of coverage contribution area for randomly deployed nodes in the field of interest (FOI). Some of the WSN applications, such as environmental monitoring, security, surveillance and health care require the target area to be covered a number of times. This number is denoted by a variable $$k$$ and is known as the ‘degree of coverage.’ The problem of achieving required degree of coverage is formulated as $$k$$ -coverage problem. An algorithm has been proposed to generate maximum number of disjoint-independent subsets of sensor nodes as an optimized solution to the $$k$$ -coverage problem, along with maximizing the WSN lifetime. Superiority and efficacy of the technique have been verified by mathematical analysis as well as simulations carried out using MATLAB.
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