In this paper, we study discrete swarm algorithms, where mobile robots (or “mobots”) move around interacting in an environment to solve computational problems. This work extends recent work on swarm algorithms in the distributed computing, artificial intelligence, and robotics literatures in that we assume that mobots are computational, that is, they have additional memory and hardware so as to enable computations that are somewhat more sophisticated than finite state automata. We describe efficient swarm algorithms for a number of foundational problems, which are essential prerequisites for coordinated movement, data gathering, and data processing computations, including rectangle ranking, prefix sums and products, permutation routing, and sorting. Each of our algorithms is optimal in at least one complexity measure
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