  Suppose one wants to monitor a domain with sensors each sensing small
ball-shaped regions, but the domain is hazardous enough that one cannot control
the placement of the sensors. A prohibitively large number of randomly placed
sensors would be required to obtain static coverage. Instead, one can use fewer
sensors by providing only mobile coverage, a generalization of the static setup
wherein every possible intruder is detected by the moving sensors in a bounded
amount of time. Here, we use topology in order to implement algorithms
certifying mobile coverage that use only local data to solve the global
problem. Our algorithms do not require knowledge of the sensors' locations. We
experimentally study the statistics of mobile coverage in two dynamical
scenarios. We allow the sensors to move independently (billiard dynamics and
Brownian motion), or to locally coordinate their dynamics (collective animal
motion models). Our detailed simulations show, for example, that collective
motion enhances performance: The expected time until the mobile sensor network
achieves mobile coverage is lower for the D'Orsogna collective motion model
than for the billiard motion model. Further, we show that even when the
probability of static coverage is low, all possible evaders can nevertheless be
detected relatively quickly by mobile sensors.
