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

翻译：本文研究并扩展了移动机器人在图上的分散问题和拜占庭分散问题，这些问题最初由Augustine和Moses Jr. [ICDCN 2018] 以及Molla、Mondal和Moses Jr. [ALGOSENSORS 2020] 提出，现将其推广至节点具有可变容量的图上。我们利用单一引导者（一种更强大的、绝不会以拜占庭方式行事的机器人）的概念，实现了快速拜占庭分散，即使在存在其他强拜占庭机器人时也如此。我们还展示了在无拜占庭机器人时，引导者对于容量化图上分散问题的优势。