We consider a Multi-Agent Path Finding (MAPF) setting where agents have been assigned a plan, but during its execution some agents are delayed. Instead of replanning from scratch when such a delay occurs, we propose delay introduction, whereby we delay some additional agents so that the remainder of the plan can be executed safely. We show that finding the minimum number of additional delays is APX-Hard, i.e., it is NP-Hard to find a $(1+\varepsilon)$-approximation for some $\varepsilon>0$. However, in practice we can find optimal delay-introductions using Conflict-Based Search for very large numbers of agents, and both planning time and the resulting length of the plan are comparable, and sometimes outperform the state-of-the-art heuristics for replanning.

翻译：我们考虑一种多智能体路径规划（MAPF）场景，其中智能体已被分配一个计划，但在执行过程中部分智能体出现延迟。我们并非在发生此类延迟时从头开始重新规划，而是提出一种延迟引入方法，即额外延迟部分智能体，以确保剩余计划能够安全执行。我们证明，寻找最小数量的额外延迟是APX-难问题，即对于某个$\varepsilon>0$，找到一个$(1+\varepsilon)$-近似解是NP-难的。然而在实践中，我们能够使用基于冲突的搜索方法为极大规模智能体寻找到最优的延迟引入方案，并且其规划时间与计划最终长度与当前最先进的重新规划启发式方法相当，有时甚至更优。