Coordinating agents through hazardous environments, such as aid-delivering drones navigating conflict zones or field robots traversing deployment areas filled with obstacles, poses fundamental planning challenges. We introduce and analyze the computational complexity of a new multi-agent path planning problem that captures this setting. A group of identical agents begins at a common start location and must navigate a graph-based environment to reach a common target. The graph contains hazards that eliminate agents upon contact but then enter a known cooldown period before reactivating. In this discrete-time, fully-observable, deterministic setting, the planning task is to compute a movement schedule that maximizes the number of agents reaching the target. We first prove that, despite the exponentially large space of feasible plans, optimal plans require only polynomially-many steps, establishing membership in NP. We then show that the problem is NP-hard even when the environment graph is a tree. On the positive side, we present a polynomial-time algorithm for graphs consisting of vertex-disjoint paths from start to target. Our results establish a rich computational landscape for this problem, identifying both intractable and tractable fragments.

翻译：摘要：在危险环境中协调智能体（例如穿越冲突区域运送救援物资的无人机，或穿行于布满障碍物的部署区域的场域机器人）会引发基础性的规划挑战。我们引入并分析了一种捕捉此类场景的新型多智能体路径规划问题的计算复杂度。一组相同智能体从共同起始位置出发，需在基于图的环境中导航以抵达共同目标点。该图中存在危险源，智能体接触即被消灭，但随后危险源会进入已知冷却期后方可重新激活。在此离散时间、完全可观测、确定性的设定下，规划任务旨在计算最大化抵达目标点智能体数量的移动调度方案。我们首先证明：尽管可行策略空间呈指数级增长，但最优策略仅需多项式步数即可完成，从而确立该问题属于NP类。继而证明：即便环境图为树形结构，该问题仍为NP难问题。在积极方面，我们针对由起点到目标点构成顶点不相交路径的图结构提出了多项式时间算法。我们的研究结果揭示了该问题丰富的计算特性，既包含难解片段也涵盖易解片段。