We study a variant of the multi-agent path finding (MAPF) problem in which the group of agents are required to stay connected with a supervising base station throughout the execution. In addition, we consider the problem of covering an area with the same connectivity constraint. We show that both problems are PSPACE-complete on directed and undirected topological graphs while checking the existence of a bounded plan is NP-complete when the bound is given in unary (and PSPACE-hard when the encoding is in binary). Moreover, we identify a realistic class of topological graphs on which the decision problem falls in NLOGSPACE although the bounded versions remain NP-complete for unary encoding.

中文翻译：

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关联代理计划的复杂性

我们研究了多代理程序路径查找（MAPF）问题的一种变体，其中在整个执行过程中，需要一组代理程序与监督基站保持连接。另外，我们考虑用相同连通性约束覆盖区域的问题。我们表明，当有界以一元形式给出时，检查有界计划的存在是否是NP完整，而有向和无向拓扑图上的两个问题都是PSPACE完整的；当以二进制形式给出边界时，检查有界平面的存在是NP完整的。此外，我们确定了决策问题落在NLOGSPACE上的一类现实的拓扑图，尽管有界版本对于一元编码仍保持NP完全性。