| Issue |
RAIRO-Theor. Inf. Appl.
Volume 44, Number 4, October-December 2010
|
|
|---|---|---|
| Page(s) | 525 - 543 | |
| DOI | https://doi.org/10.1051/ita/2011004 | |
| Published online | 28 February 2011 | |
A CAT algorithm for the exhaustive generation of ice piles
Università degli Studi dell'Insubria,
Dipartimento di Informatica e Comunicazione,
Via Mazzini 5, 21100 Varese, Italy; {paolo.massazza,roberto.radicioni}@uninsubria.it
Received:
7
February
2009
Accepted:
13
January
2011
We present a CAT (constant amortized time) algorithm for generating those partitions of n that are in the
ice pile model
(n),
a generalization of the
sand pile model
(n).
More precisely, for any fixed integer k, we show that
the negative lexicographic ordering naturally identifies a tree structure on the lattice
(n):
this lets us design an algorithm which generates all the ice piles of
(n)
in amortized time
O(1)
and in space
O(
).
Mathematics Subject Classification: 05A17 / 68R99
Key words: Sand pile model / ice pile model / integer partitions / exhaustive generation / CAT algorithms / discrete dynamical systems
© EDP Sciences, 2011
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