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Table 2 Probabilities estimated by comparing PLLL with LLL, DEEP, SLLL, and VLLL

From: Experimental quality evaluation of lattice basis reduction methods for decorrelating low-dimensional integer least squares problems

Measures

Methods

LLL

DEEP

SLLL

VLLL

O(B)

PBetter

0.908

0.785

0.847

0.991

 

PWorse

0.003

0.125

0.088

0.009

θ(B)

PBetter

0.731

0.547

0.666

0.830

 

PWorse

0.192

0.314

0.238

0.169

â„“ 1(B)

PBetter

0.305

0.024

0.183

0.562

 

PWorse

0.019

0.076

0.026

0.015

r(B)

PBetter

0.774

0.361

0.584

0.882

 

PWorse

0.134

0.512

0.316

0.118

κ B

PBetter

0.845

0.808

0.796

0.951

 

PWorse

0.097

0.102

0.139

0.049

  1. O(B), θ(B), ℓ 1(B), r(B), and κ B correspond to the quality measures described in Section 3. PBetter, the probability with which PLLL performs better; PWorse, the probability with which LLL, DEEP, SLLL, and VLLL perform better than PLLL. Otherwise, PLLL produces the same results as the other reduction methods.