Algorithmic Aspects of a Chip-Firing Game

Authors:
Jan Van Den Heuvel
Affiliations:
Centre for Discrete and Applicable Mathematics, Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, UK/ (e-mail: jan@maths.lse.ac.uk)
Venue:
Combinatorics, Probability and Computing
Year:
2001

Citing 8
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Abstract

Algorithmic aspects of a chip-firing game on a graph introduced by Biggs are studied. This variant of the chip-firing game, called the dollar game, has the properties that every starting configuration leads to a so-called critical configuration. The set of critical configurations has many interesting properties. In this paper it is proved that the number of steps needed to reach a critical configuration is polynomial in the number of edges of the graph and the number of chips in the starting configuration, but not necessarily in the size of the input. An alternative algorithm is also described and analysed.