Chip-firing games, potential theory on graphs, and spanning trees

Authors:
Matthew Baker;Farbod Shokrieh
Affiliations:
Georgia Institute of Technology, Atlanta, GA 30332-0160, USA;Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
Venue:
Journal of Combinatorial Theory Series A
Year:
2013

Citing 22
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Abstract

We study the interplay between chip-firing games and potential theory on graphs, characterizing reduced divisors (G-parking functions) on graphs as the solution to an energy (or potential) minimization problem and providing an algorithm to efficiently compute reduced divisors. Applications include an ''efficient bijective'' proof of Kirchhoff@?s matrix-tree theorem and a new algorithm for finding random spanning trees. The running times of our algorithms are analyzed using potential theory, and we show that the bounds thus obtained generalize and improve upon several previous results in the literature.