**3. Problem statement**

The lifetime problem can be stated as follows. Given a monitored region *R*, a set of sensors *S* and a set of targets *T*, find a monitoring schedule for these sensors such that


A related problem is that of monitoring an area of interest. In general, the area and target coverage problems have been shown to be equivalent. [3, 10, 41] provide ways to map an area to a set of points (targets) . In the work presented in the remainder of this dissertation, we focus on the target coverage problem with the implicit understanding that the algorithms and techniques presented can be translated to the area coverage problem by mapping the area to a set of points (virtial targets) with an appropriate granularity.

There are also several other variations of this basic problem. For example the *p*% coverage problem [30] requires only a certain percentage of all targets to be covered. The fault tolerant *k*-coverage version of this problem requires each target to be covered by at least *k* sensors [27, 47]. Also, the basic problem has been modified to include sensors that have adjustable sensing ranges, non uniform sensing shapes and othe heterogeneous sensor network models.
