In this paper, we have considered the coverage problem in wireless sensor network (WSN) on a convex subset of $R^2$. Sensors are dropped from the air randomly on some pre-fixed points, which is known as vertices, of Region of Interest (ROI). We use optimal partition of the ROI, which is actually partition in several regular hexagons. Since sensors are distributed randomly, a sensor may not be placed on the target vertex. For this reason, ROI will not be completely covered by a set of sensors. In practice, few more sensors are deployed on few (randomly chosen) vertices or used actuator (it can carry sensors to the proper vertex) to reduce the uncovered region or area. In one of our previous works, we have developed a strategy as follows: reduce the distance among two adjacent vertices and deployed one sensor on a vertex so that total number of sensors will be same as in existing old method (drop two sensors on some vertices and one sensor on the rest). We have compared the proportion of uncovered region using the commonly used old strategy with our previous one. We have simulated for several values of percentage of extra sensors and observed that our previous strategy is better for low standard deviation (s.d.), but not better for higher s.d. in both two and three-dimension. Inspiring from the above fact, in this paper, we combined above two strategies to find a general one, for deploying sensors in two-dimension. The excess sensors are divides in two parts. One part is used for decrease the side of the regular hexagon and other part is used for using one more sensor on some selected points. We simulate uncovered area and results indicate the optimal choice of these two parts, which change with the standard deviation of randomness.

Coverage problem, random deployment, wireless sensor networks.