Shortest path with acceleration constraints: complexity and approximation algorithms

Abstract We introduce a variant of the Shortest Path Problem (SPP), in which we impose additional constraints on acceleration over arcs, and call it Bounded Acceleration SPP (BASP). This is inspired by an industrial application: vehicle needs to travel from its current position target one minimum-time, following pre-defined geometric paths connecting positions within facility, while satisfying some speed depending along currently traveled path. characterize complexity BASP, proving NP-hardness. also show that, under hypotheses problem data, admits pseudo-polynomial time-complexity algorithm. Moreover, present approximation algorithm with polynomial respect data original inverse factor $$\epsilon$$ ϵ . Finally, computational experiments evaluate performance proposed