# An Efficient Distributed Coverage Hole Detection Protocol for Wireless Sensor Networks
## 4 Proposed Hole Detection Protocol
### Determination of CP
However, in all three protocols, the average hole detection time is increased with the increase in the number of holes, which is obvious. The average energy consumption in the three protocols is simulated for different numbers of coverage holes with a fixed number of nodes deployed over the monitoring region, which is fixed at 1000. As shown in Figure 13, it is found that the average energy consumption in these three protocols increases with the increase in the number of holes. However, the average energy consumption in DCHD is less than LVP and the vector method, which is due to the participation of less nodes to detect a coverage hole. Since, our protocol can save more power to detect the same number of holes as compared to other protocols, it can increase the network lifetime. \[X_{1}:\frac{x_{i}+x_{j}}{2}+\frac{y_{j}-y_{i}}{2d_{ij}}\sqrt{(4R_{s}^{2}-d_{ij} ^{2})},Y_{1}:\frac{y_{i}+y_{j}}{2}-\frac{x_{j}-x_{i}}{2d_{ij}}\sqrt{(4R_{s}^{2} -d_{ij}^{2})} \tag{1}\]2 Comparison of DCHD in terms of the average number of nodes to detect a hole. The control packet overhead of our protocol is compared to LVP and the vector method for different numbers of nodes, as shown in \[X_{1}:\frac{x_{i}+x_{j}}{2}+\frac{y_{j}-y_{i}}{2d_{ij}}\sqrt{(4R_{s}^{2}-d_{ij} ^{2})},Y_{1}:\frac{y_{i}+y_{j}}{2}-\frac{x_{j}-x_{i}}{2d_{ij}}\sqrt{(4R_{s}^{2} -d_{ij}^{2})} \tag{1}\]3 It is observed that our protocol outperforms LVP and the vector method when the number of coverage holes is less. From the simulation result, we find that there is no control packet overhead when the number of sensors is from 100 to 300. However, when the number of sensors is more than 300, the density of the sensors increases, and a greater number of redundant sensors in the network can increase the number of control packets. \[X_{1}:\frac{x_{i}+x_{j}}{2}+\frac{y_{j}-y_{i}}{2d_{ij}}\sqrt{(4R_{s}^{2}-d_{ij} ^{2})},Y_{1}:\frac{y_{i}+y_{j}}{2}-\frac{x_{j}-x_{i}}{2d_{ij}}\sqrt{(4R_{s}^{2} -d_{ij}^{2})} \tag{1}\]4 Comparison of DCHD with other protocols in terms of the average hole detection time. \[X_{1}:\frac{x_{i}+x_{j}}{2}+\frac{y_{j}-y_{i}}{2d_{ij}}\sqrt{(4R_{s}^{2}-d_{ij} ^{2})},Y_{1}:\frac{y_{i}+y_{j}}{2}-\frac{x_{j}-x_{i}}{2d_{ij}}\sqrt{(4R_{s}^{2} -d_{ij}^{2})} \tag{1}\]5 Comparison of DCHD with other protocols in terms of the average energy consumption. ## 6 Conclusion and Future Work

In this paper, a distributed coverage hole detection scheme is proposed in which the sensors can store location information of their one-hop neighbors to detect the presence of a coverage hole without the help of the sink. Prior to the detection of the holes, the construction of the holes is done using simple geometric methods to find the points of intersection and to check whether those points are covered or not. Algorithms are developed to join the critical points of intersection and, finally, to construct the hole. Using local information of the nodes, the global view of the coverage hole detection can be done. Besides, our protocol can formulate the bounded or unbounded coverage holes to predict the nature of the holes, which is a unique contribution in this work. Using covered or uncovered arcs, our protocol can also find the shape of the coverage hole. The interesting contribution in our work is that it can be applicable to detect the coverage holes irrespective of any shape or size of the monitoring region. Though we develop here the protocol for a rectangular monitoring region, our work with the same algorithm can be extended to the monitoring region of any shape and size, which is very practical in wireless sensor networks. Hence, our algorithms can be more useful and beneficial as compared to similar hole detection protocols. We feel that the proposed algorithm can find holes in the simplest way and with less time complexity and is therefore quite suitable for the memory and energy constraints of sensors. In our future work, we plan to design coverage hole detection algorithms for any irregular monitoring region.