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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 prove 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.
Bibtex entry:
| AUTHOR | = | {T{\'o}thm{\'e}r{\'e}sz, Lilla}, |
| TITLE | = | {Algorithmic aspects of rotor-routing and the notion of linear equivalence}, |
| NOTE | = | {{\tt www.cs.elte.hu/egres}}, |
| INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
| YEAR | = | {2015}, |
| NUMBER | = | {TR-2015-12} |