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In this paper, we look at and expand the problems of dispersion and Byzantinedispersion of mobile robots on a graph, introduced by Augustine andMoses~Jr.~[ICDCN~2018] and by Molla, Mondal, and Moses~Jr.~[ALGOSENSORS~2020],respectively, to graphs where nodes have variable capacities. We use the ideaof a single shepherd, a more powerful robot that will never act in a Byzantinemanner, to achieve fast Byzantine dispersion, even when other robots may bestrong Byzantine in nature. We also show the benefit of a shepherd fordispersion on capacitated graphs when no Byzantine robots are present.

Dispersion, Capacitated Nodes, and the Power of a Trusted Shepherd