Abstract—Sensing coverage problem is due to random deployment, quick energy depletion of tiny devices and node failure in the field of interest. Sensor coverage reflects the quality of measurement on the real-time application. In this paper, we derive optimal conditions for connectivity and coverage in WSNs. The existing work focuses on the random or uniform sensors distribution and acclimates the geographic greedy routing for data transmission. This paper follows a 2D Gaussian distribution and gives a framework for coverage. A distributed algorithm is proposed in this paper which has three phases: in the first phase, detection of coverage hole based on Hamiltonian cycle, the cycles that are optimal and borders same boundary hole as other cycles are determined in the second phase. In the final phase, restoration method to fill the coverage holes. A simulation result shows that coverage area increase due to Gaussian distribution and presence of a coverage hole is below 0.3%. It also shows that optimal coverage holes cycles bordering same boundary hole reduce packet loss by 30%.

Index Terms—Coverage area problem; 2D gaussian distribution; coverage hole; hamiltonian cycle; geographic greedy routing.