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：我们考虑多智能体路径规划（MAPF）设定：智能体已被分配计划，但在执行过程中部分智能体出现延迟。针对这类延迟，我们不从头重新规划，而是提出延迟引入方法——即额外延迟若干智能体，使剩余计划得以安全执行。我们证明：寻找最小额外延迟数量是APX-难问题，即对于某个$\varepsilon>0$，寻找$(1+\varepsilon)$-近似解是NP-难的。然而在实际应用中，通过基于冲突的搜索算法，我们能在极大规模智能体场景中找到最优延迟引入方案，其规划时间和计划最终长度与最先进的重新规划启发式方法相当，有时甚至更优。