Guaranteed, Predictable, Polynomial AGV Time-Pathing

In this paper we present a framework of key algorithms and data-structures for efficiently generating timetables for any number of AGVs from any given positioning on any given graph to accomplish any given demands as long as a few easily satisfiable assumptions are met. Our proposed algorithms provide guaranteed solutions in predictable polynomial running-times, which is fundamental to any real-time application. We also develop an improved geographic reservation algorithm that provides a substantial run-time improvement of the previously best-known algorithm from $O(nm)$ to $O(n)$.