时变动态图上的均衡分散
Balanced Dispersion on Time-Varying Dynamic Graphs
AI总结：
本文提出动态图上的 k-balanced dispersion 问题，通过同时约束各节点智能体数的上下界，将移动智能体分散与可移动负载均衡统一起来。
摘要：
我们旨在连接两个问题，即分散和负载均衡。这两个问题在静态图和动态图上都已经得到研究。尽管分散和负载均衡具有某些共同特征，但用于解决负载均衡的工具与用于解决分散的工具显著不同。原因之一是，负载均衡问题主要是在节点作为处理器并在消息传递模型下工作的图上引入和深入研究的，而分散则是移动智能体在图上完成的一项任务。为了将（负载）均衡方面引入分散问题，我们提出，移动智能体通过移动，使自身尽可能均等地分布在图的各个节点上，而不是像负载均衡问题中那样由静止节点共享负载。我们将其称为 k-balanced dispersion（k-均衡分散）问题，并在动态图上对其进行研究。这等价于考虑以智能体形式存在的可移动负载时的负载均衡问题。此前，在静态图上，k-dispersion（k-分散）问题[TAMC 2019]也追求相同目标，其方式是在最终配置中对每个节点上的智能体数量设置上界；然而，其问题定义中缺少对智能体数量的下界，这妨碍了负载均衡方面，因为在最终配置中某些节点可能最终没有任何智能体。我们在 k-balanced dispersion 问题定义中处理了这一部分，从而在这两个领域之间建立了更紧密的联系。
英文摘要：
We aim to connect two problems, namely, dispersion and load balancing. Both problems have already been studied over static as well as dynamic graphs. Though dispersion and load balancing share some common features, the tools used in solving load balancing differ significantly from those used in solving dispersion. One of the reasons is that the load balancing problem is introduced and studied heavily over graphs where nodes are the processors and work under the message passing model, whereas dispersion is a task for mobile agents to achieve on graphs. To bring the (load) balancing aspect in the dispersion problem, we say, mobile agents move to balance themselves as equally as possible across the nodes of the graph, instead of stationary nodes sharing loads in the load balancing problem. We call it the \emph{$k$-balanced dispersion} problem and study it on dynamic graphs. This is equivalent to the load balancing problem considering movable loads in form of the agents. Earlier, on static graphs, the \emph{$k$-dispersion} problem [TAMC 2019] aimed for the same by putting an upper bound on the number of agents on each node in the final configuration; however, the absence of a lower bound on the number of agents in their problem definition hampers the load-balancing aspect, as some nodes may end up with no agents in the final configuration. We take care of this part in our \emph{$k$-balanced dispersion} problem definition and thus produce a stronger connection between the two domains.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
