Algorithmic aspects of a chip-firing game

van den Heuvel, Jan ORCID: 0000-0003-0897-9148 (2001) Algorithmic aspects of a chip-firing game. Combinatorics, Probability and Computing, 10 (6). pp. 505-529. ISSN 0963-5483

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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.

Item Type:	Article
Official URL:	http://journals.cambridge.org/action/displayJourna...
Additional Information:	© 2001 Cambridge University Press
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	18 Nov 2008 15:10
Last Modified:	11 Dec 2024 22:21
URI:	http://eprints.lse.ac.uk/id/eprint/18470

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