发表机构
Simon Fraser University（西蒙菲莎大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明目标驻留的匿名多智能体路径发现（AMAPF）中代价和（SoC）最小化是NP难问题，而智能体到达目标后消失的AMAPF对应问题存在多项式时间算法，明确了复杂度边界。
AI 中文摘要
匿名多智能体路径发现（AMAPF）在多个目标下存在多项式时间的网络流算法，包括最大完成时间、总距离，以及当智能体到达目标后消失时的代价和（SoC）。我们表明标准的目标驻留AMAPF存在本质差异。我们首先通过在标准的时间扩展流模型中加入目标驻留约束，构建了代价和最小化问题，并证明该问题的线性规划松弛是不可积的。随后我们通过归约自3-SAT问题，证明目标驻留AMAPF中的代价和最小化问题是NP难的。结合消失变体的多项式时间结果，这确立了由已完成智能体是否驻留在其目标位置所决定的清晰复杂度边界。
英文摘要
Anonymous Multi-Agent Path Finding (AMAPF) admits polynomial-time network-flow algorithms for several objectives, including makespan, total distance, and sum-of-costs (SoC) when agents disappear upon reaching goals. We show that standard goal-staying AMAPF is fundamentally different. We first formulate SoC minimization by augmenting the standard time-expanded flow model with goal-settlement constraints and show that the resulting linear programming relaxation is non-integral. We then prove that minimizing SoC in goal-staying AMAPF is NP-hard via a reduction from 3-SAT. Together with the polynomial-time result for the disappearing variant, this establishes a sharp complexity boundary determined by whether completed agents remain at their goals.
