Approximating Barrier Resilience in Wireless Sensor Networks
Barrier coverage in a sensor network has the goal of ensuring that all paths through the surveillance domain joining points in some start region S to some target region T will intersect the coverage region associated with at least one sensor. In this paper, we revisit a notion of redundant barrier coverage known as k-barrier coverage.
We describe two different notions of width, or impermeability, of the barrier provided by the sensors in \(\cal A\) to paths joining two arbitrary regions S to T. The first, what we refer to as the thickness of the barrier, counts the minimum number of sensor region intersections, over all paths from S to T. The second, what we refer to as the resilience of the barrier, counts the minimum number of sensors whose removal permits a path from S to T with no sensor region intersections. Of course, a configuration of sensors with resilience k has thickness at least k and constitutes a k-barrier for S and T.
Our result demonstrates that any (Euclidean) shortest path from S to T that intersects a fixed number of distinct sensors, never intersects any one sensor more than three times. It follows that the resilience of \(\cal A\) (with respect to S and T) is at least one-third the thickness of \(\cal A\) (with respect to S and T). (Furthermore, if points in S and T are moderately separated (relative to the radius of individual sensor coverage) then no shortest path intersects any one sensor more than two times, and hence the resilience of \(\cal A\) is at least one-half the thickness of \(\cal A\).)
A second result, which we are only able to sketch here, shows that the approximation bounds can be tightened (to 1.666 in the case of moderately separated S and T) by exploiting topological properties of simple paths that make double visits to a collection of disks.
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