グラフ上の最適マルチロボット経路計画：構造と計算複雑性
Optimal Multi-Robot Path Planning on Graphs: Structure and Computational Complexity
4つの目的関数（総到着時間・メイクスパン・総距離・最大距離）間のパレート最適性とNP困難性を3-SAT還元で示し、最適解の計算困難性を明らかにした。
著者: Jingjin Yu, Steven M. LaValle
分類: cs.RO
原文アブストラクト
We study the problem of optimal multi-robot path planning on graphs (MPP) over four distinct minimization objectives: the total arrival time, the makespan (last arrival time), the total distance, and the maximum (single-robot traveled) distance. On the structure side, we show that each pair of these four objectives induces a Pareto front and cannot always be optimized simultaneously. Then, through reductions from 3-SAT, we further establish that computation over each objective is an NP-hard task, providing evidence that solving MPP optimally is generally intractable. Nevertheless, in a related paper, we design complete algorithms and efficient heuristics for optimizing all four objectives, capable of solving MPP optimally or near-optimally for hundreds of robots in challenging setups.
