Algorithmic aspects of rotor-routing and the notion of linear equivalence

摘要

We define the analogue of linear equivalence of graph divisors for the rotor-router model, and use it to prove polynomial time computability of some problems related to rotor routing. Using the connection between linear equivalence for chip-firing and for rotor routing, we give a simple proof for the fact that the number of rotor-router unicycle-orbits equals the order of the Picard group. We also show that the rotor-router action of the Picard group on the set of spanning in-arborescences can be interpreted in terms of the linear equivalence. (C) 2017 Elsevier B.V. All rights reserved.