**11. Dealing with the exponential space**

In this section, we present our approach of dealing with the exponential solution space of possible cover sets. The next section utilizes these ideas to develop heuristics for maximizing the lifetime of the network. Even though the total number of cover sets for the network may be exponential in the number of sensors, for any given cover set, there are several other sets that are very *similar* to this set. We begin by attempting to define this notion of similarity by expressing it as an equivalence relation.

*Definition 1:* Let be an equivalence relation defined on the set of all sensor covers such that *Ci Cj* if and only if *Ci* and *Cj* share the same bottleneck sensor *sbot*.
