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A CAT algorithm for the exhaustive generation of ice piles

Published online by Cambridge University Press:  28 February 2011

Paolo Massazza  and
Roberto Radicioni
Paolo Massazza
Affiliation:
Università degli Studi dell'Insubria, Dipartimento di Informatica e Comunicazione, Via Mazzini 5, 21100 Varese, Italy; {paolo.massazza,roberto.radicioni}@uninsubria.it
Roberto Radicioni
Affiliation:
Università degli Studi dell'Insubria, Dipartimento di Informatica e Comunicazione, Via Mazzini 5, 21100 Varese, Italy; {paolo.massazza,roberto.radicioni}@uninsubria.it
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Abstract

We present a CAT (constant amortized time) algorithm for generating those partitions of n that are in the ice pile model$\mbox{IPM}_k$(n), a generalization of the sand pile model$\mbox{SPM}$(n). More precisely, for any fixed integer k, we show that the negative lexicographic ordering naturally identifies a tree structure on the lattice $\mbox{IPM}_k$(n): this lets us design an algorithm which generates all the ice piles of $\mbox{IPM}_k$(n) in amortized time O(1) and in space O($\sqrt n$).

Keywords

Sand pile modelice pile modelinteger partitionsexhaustive generationCAT algorithmsdiscrete dynamical systems
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 44 , Issue 4 , October 2010 , pp. 525 - 543
Copyright
© EDP Sciences, 2011

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