Swarm Search of Expanding Regions in Grids: Lower Bounds

In this chapter we examine the dynamic generalization of the Cooperative Cleaners problem presented in Altshuler et al., Swarm intelligent systems (2006), [10] and in the previous chapters of this book, involving a swarm of collaborative drones that are required to search a dynamically expanding region on the \( \mathbf{Z}^{2}\) grid (whose “pixels” that were visited by the drones can become “un-searched” after a certain period of time). The goal of the swarm’s members is to “clean” the spreading contamination in as little time as possible. In this work we present a collaborative swarm search algorithm, as well as several upper bounds on the completion time it takes a swarm of k drones, of various velocities.

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