Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-99-09

August 1999

Algorithmic Aspects of a Chip-Firing Game

Jan van den Heuvel


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 configuration has many interesting properties. In this paper is 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.

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