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Algorithmic aspects of a chip-firing game

By Jan van den Heuvel

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

Topics: QA Mathematics
Publisher: Cambridge University Press
Year: 2001
DOI identifier: 10.1017/S0963548301004886
OAI identifier: oai:eprints.lse.ac.uk:18470
Provided by: LSE Research Online

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