Shortest path with acceleration constraints: complexity and approximation algorithms
研究了一种带加速度约束的最短路径问题，证明其NP困难，并提出了伪多项式时间算法和多项式时间近似算法，适用于车辆在设施内沿预定路径行驶的最小时间路径规划。
Abstract We introduce a variant of the Shortest Path Problem (SPP), in which we impose additional constraints on the acceleration over the arcs, and call it Bounded Acceleration SPP (BASP). This variant is inspired by an industrial application: a vehicle needs to travel from its current position to a target one in minimum-time, following pre-defined geometric paths connecting positions within a facility, while satisfying some speed and acceleration constraints depending on the vehicle position along the currently traveled path. We characterize the complexity of BASP, proving its NP-hardness. We also show that, under additional hypotheses on problem data, the problem admits a pseudo-polynomial time-complexity algorithm. Moreover, we present an approximation algorithm with polynomial time-complexity with respect to the data of the original problem and the inverse of the approximation factor $$\epsilon$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϵ</mml:mi> </mml:math> . Finally, we present some computational experiments to evaluate the performance of the proposed approximation algorithm.