When an object needs to be found in a random environment by a team of searchers, we obtain a formula for the total number of searchers needed if at least $k$ of them must find the object by some large time $S$. We then compute the energy consumed by the $N$ searchers if they are all stopped as soon as $k$ are successful, and we show that the energy consumed decreases as $N$ increases. We also consider the case in which the successful ones stop but the unsuccessful ones continue until a time-out or until they are destroyed by some other “natural” cause, and in this case we see that the energy consumed increases with $N$ as one might expect. The transform-based analysis used assumes that the searchers’ motion is described by diffusion processes, that the search space is infinite and homogeneous, that searchers can be destroyed or become permanently lost as they proceed, and that a time-out mechanism is used so that any searcher that exceeds this time-out and has not succeeded in its quest will be removed and replaced by a new searcher that behaves stochastically and independently of its predecessor.

• Received 20 December 2012

DOI:https://doi.org/10.1103/PhysRevE.87.032125