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The Bounded Acceleration Shortest Path problem: complexity and solution algorithms
arXiv - CS - Data Structures and Algorithms Pub Date : 2021-03-04 , DOI: arxiv-2103.02914
Stefano Ardizzoni, Luca Consolini, Mattia Laurini, Marco Locatelli

The purpose of this work is to introduce and characterize the Bounded Acceleration Shortest Path (BASP) problem, a generalization of the Shortest Path (SP) problem. This problem is associated to a graph: the nodes represent positions of a mobile vehicle and the arcs are associated to pre-assigned geometric paths that connect these positions. BASP consists in finding the minimum-time path between two nodes. Differently from SP, we require that the vehicle satisfy bounds on maximum and minimum acceleration and speed, that depend on the vehicle position on the currently traveled arc. We prove that BASP is NP-hard and define solution algorithm that achieves polynomial time-complexity under some additional hypotheses on problem data.

中文翻译:

有界加速最短路径问题:复杂度和求解算法

这项工作的目的是介绍和表征有界加速最短路径(BASP)问题,这是最短路径(SP)问题的概括。该问题与图形相关:节点代表移动车辆的位置,弧线与连接这些位置的预先指定的几何路径相关。BASP在于找到两个节点之间的最短时间路径。与SP不同,我们要求车辆满足最大和最小加速度和速度的界限,这取决于当前行驶弧线上的车辆位置。我们证明BASP是NP难解的,并定义了在问题数据的一些其他假设下实现多项式时间复杂性的求解算法。
更新日期:2021-03-05
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