**14. Conclusion**

20 Will-be-set-by-IN-TECH

Algorithm *n*=40 *n*=80 *n*=120 LBP [4] 12.4 29.1 40.1 Degree-Based [35] 13.8 33.4 45.6 Sampling-Based 13.7 30.3 42.1 Randomized-Sampling 10.1 17.6 30.1

Now that we have seen that sampling works well when compared to the degree based heuristic, the question that remains to be answered is how much faster is the sampling algorithm? Figure 9 compares head-to-head the running time for the degree based heuristic (potentially exponential in *m*) and the linear time sampling algorithm. As can be seen from the figure the running time for the sampling algorithm is about half of the running time for

Finally, we individually study the 1-hop (Table 3) and 2-hop (Table 4) sampling heuristics with comparable algorithms. For the 1-hop algorithms, we also include a randomized-sampling algorithm that makes completely random picks for each target, without considering properties of the equivalence classes. The intention is to ensure that the performance of our sampling-heuristic can be attributed to the selection algorithm. For the 2-hop versions of

**Figure 8.** Comparison of Network Lifetime with 25 Targets

**Figure 9.** Comparison of Running Time with 25 Targets

**Table 3.** Comparison of Network Lifetime for 1-hop algorithms

the degree-based heuristic.

Despite a lot of recent research effort, creating real-world deployable sensor networks remains a difficult task. A key bottleneck is the limited battery life of sensor motes. Hence, energy conservation at every layer of the network stack is critical. Creating realistic theoretical models for problems in this domain that take this into account remains a challenge. Our work addresses energy efficiency at only point in the network stack. However, a holistic approach to energy efficiency design should not only account for energy concerns in each layer of the network stack for problems like routing, medium access etc., but also consider cross-layer issues and interactions.

In this chapter, we present innovative models and heuristics to address the coverage problem in Wireless Sensor Networks. Our work points to the potential of lifetime dependency graphs while serving to highlight the shortcomings of using standard distributed algorithms to this problem. In order to successfully bridge the gap between the theory and practice of wireless sensor networks, there is a clear need for algorithms that are designed keeping the unique constraints of these networks in mind. The improvements in network lifetime obtained by our approach using the dependency graph and heuristics that stem serve to underscore this point.
