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# Modelling the LLL Algorithm by Sandpiles

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## Modelling the LLL Algorithm by Sandpiles

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### N of dimensions. We first consider the global variable α, study its distribution,

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5 10 15 20 0.05

0.1 0.15 0.2 0.25 0.3

5 10 15 20

0.2 0.4 0.6 0.8 1

### (1) The distribution of the parameter α for n = 5 ( • ); n = 10 (); n = 15 (N); n = 20 ()

5 10 15 20

2 4 6 8 10

1 1.5 2 2.5 3 3.5 4 4.5 5

0 5 10 15 20

hyi

hxi

### (right, with X = 5), for n = 5 ( • ); n = 10 (); n = 15 (N); n = 20 ()

5 10 15 20

0.05 0.1 0.15 0.2 0.25 0.3 0.35

5 10 15 20

5e-6 1e-5 1.5e-5

hyi

hxi

### with X = 5 and x = 1 ( • ); 2 ( ); 3 ( N ); 4 ( ); 5 ( H )

0 5 10 15

5000 10000 15000 20000 25000

5 10 15 20

5 10 15 20

5 10 15

0.1 0.2 0.3 0.4 0.5 0.6

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### l’algorithme LLL, PhD Thesis, Universiy of Caen (2009)

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