Addition of Recurrent Configurations in Chip Firing Games: Finding Minimal Recurrent Configurations with Markov Chains View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2010

AUTHORS

David Hutchison , Takeo Kanade , Josef Kittler , Jon M. Kleinberg , Friedemann Mattern , John C. Mitchell , Moni Naor , Oscar Nierstrasz , C. Pandu Rangan , Bernhard Steffen , Madhu Sudan , Demetri Terzopoulos , Doug Tygar , Moshe Y. Vardi , Gerhard Weikum , Matthias Schulz

ABSTRACT

Generalizing the Abelian Sandpile Model by Bak, Tang and Wiesenfeld to general undirected graphs, one gets a variation of the Chip Firing Game intoduced by Chung and Ellis in 2002, which still contains most of the nice algebraic properties of the Abelian Sandpile Model. Particularly the group structure of the recurrent configurations is retained. Using a Markov Chain, we show how a pair consisting of one minimal recurrent configuration and one nearly minimal recurrent configuration can be constructed whose sum is the same as the sum of a given pair of recurrent configurations. Computer simulations of this Markov Chain for the Abelian Sandpile Model suggest that the number of steps needed to reach a final pair usually is proportional to the width of the grid, but can become proportional to the square of the width if one chooses particular configurations. More... »

PAGES

209-218

References to SciGraph publications

Book

TITLE

Cellular Automata

ISBN

978-3-642-15978-7
978-3-642-15979-4

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-15979-4_23

DOI

http://dx.doi.org/10.1007/978-3-642-15979-4_23

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1045143527


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