Das Lovasz Local Lemma (LLL) ist eine der wichtigsten probabilistischen Methoden. Es wird angewendet um zu beweisen, dass bestimmte Ereignisse mit einer positiven Wahrscheinlichkeit eintreten können.[7] Da diese Wahrscheinlichkeit oft sehr klein ist, liefert das LLL keine effizienten Algorithmen. J.Beck hat als erster eine Methode entwickelt, um aus dem Existenzbeweis der LLL einen Polynomialze...

Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with provable output quality. One early improvement of the LLL algorithm was LLL with deep insertions (DeepLLL). The output of this version of LLL has higher quality in...

We modify the concept of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lovász [LLL82] towards a faster reduction algorithm. We organize LLL-reduction in segments of the basis. Our SLLL-bases approximate the successive minima of the lattice in nearly the same way as LLL-bases. For integer lattices of dimension n given by a basis of length 2, SLLL-reduction runs in O(n) bit ope...

The Lovász Local Lemma (LLL) is a powerful tool that can be used to prove that an object having none of a set of bad properties exists, using the probabilistic method. In many applications of the LLL it is also desirable to explicitly construct the combinatorial object. Recently it was shown that this is possible using a randomized algorithm in the full asymmetric LLL setting [R. Moser and G. T...

BACKGROUND Considering promising results in animal models and patients, therapeutic use of MSCs for immune disease is likely to undergo continued evaluation. Low-lever laser (LLL) has been widely applied to retard the inflammatory reaction. LLL treatment can potentially be applied in anti-inflammatory therapy followed by stem cell therapy. AIM OF THE STUDY The purpose of this study was to inv...

OBJECTIVE To quantitatively assess and compare the quality of life (QoL) of women with a self-reported diagnosis of lower limb lymphedema (LLL), to women with lower limb swelling (LLS), and to women without LLL or LLS following treatment for endometrial cancer. METHODS 1399 participants in the Australian National Endometrial Cancer Study were sent a follow-up questionnaire 3-5 years after dia...

BACKGROUND Lower limb lymphedema (LLL) is a chronic and incapacitating condition afflicting patients who undergo lymphadenectomy for gynecologic cancer. This study aimed to identify risk factors for LLL and to develop a prediction model for its occurrence. METHODS Pelvic lymphadenectomy (PLA) with or without para-aortic lymphadenectomy (PALA) was performed on 366 patients with gynecologic mal...

Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with provable output quality. One early improvement of the LLL algorithm was LLL with deep insertions (DeepLLL). The output of this version of LLL has higher quality in...