In this paper, we consider the coverage problem in wireless sensor network (WSN) on a convex subset of $R^2$. In real life, sensors are dropped randomly from the air on some pre-fixed points, which is known as vertices, of Region of Interest (ROI). We use optimal partition of the region in several regular hexagons. Since sensors are distributed randomly, a sensor may not properly be placed on the vertex. For this reason, ROI will not be completely covered by these sensors. In practice, few more sensors are deployed on some randomly chosen vertices or used actuator (it can carry sensors to the proper vertex) to reduce the uncovered region. In one of our previous work, we have developed a strategy as follows: reduce the distance among two adjacent vertices and deployed one sensor on a vertex. We have compared the proportion of uncovered region using the common strategy with our previous one. We have simulated for several values of percentage of extra sensors in two-dimension in that paper. We have observed that our strategy is better for low standard deviation, but not better for higher standard deviation in both two and three-dimension. In this paper, we combined above two strategies, for deploying the 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. Simulated results indicate the optimal choice of these two parts, which change with the standard deviation of randomness.

Coverage problem, random deployment, wireless sensor networks.