Sensor networks are particularly applicable to the tracking of objects in
motion. For such applications, it may not necessary that the whole region be
covered by sensors as long as the uncovered region is not too large. This
notion has been formalized by Balasubramanian et.al. as the problem of
κ-weak coverage. This model of coverage provides guarantees about the
regions in which the objects may move undetected. In this paper, we analyse the
theoretical aspects of the problem and provide guarantees about the lifetime
achievable. We introduce a number of practical algorithms and analyse their
significance. The main contribution is a novel linear programming based
algorithm which provides near-optimal lifetime. Through extensive
experimentation, we analyse the performance of these algorithms based on
several parameters defined