The Cyclic-Routing UAV Problem is PSPACE-Complete

TL;DR

This paper proves that the Cyclic-Routing UAV Problem, which involves scheduling UAVs to visit targets within deadlines, is PSPACE-complete even with only one UAV, highlighting its computational complexity.

Contribution

The paper establishes that the CR-UAV problem remains PSPACE-complete for a single UAV, correcting previous claims of NP-completeness.

Findings

CR-UAV problem is PSPACE-complete with multiple UAVs.

Single-UAV case is PSPACE-complete, not NP-complete as previously claimed.

The problem can be modeled using timed automata for complexity analysis.

Abstract

Consider a finite set of targets, with each target assigned a relative deadline, and each pair of targets assigned a fixed transit flight time. Given a flock of identical UAVs, can one ensure that every target is repeatedly visited by some UAV at intervals of duration at most the target's relative deadline? The Cyclic-Routing UAV Problem (CR-UAV) is the question of whether this task has a solution. This problem can straightforwardly be solved in PSPACE by modelling it as a network of timed automata. The special case of there being a single UAV is claimed to be NP-complete in the literature. In this paper, we show that the CR-UAV Problem is in fact PSPACE-complete even in the single-UAV case.