TR-2015-12

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

Lilla Tóthmérész



Abstract

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:

@techreport{egres-15-12,
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}
}


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