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218
A Parallel LLL Algorithm
"... The LLL algorithm is a wellknow and widely used lattice basis reduction algorithm. In many applications, its speed is of essential. However, it is very difficult to parallelize the original LLL algorithm. We present a multithreading LLL algorithm based on a recent improved version: an LLL algorith ..."
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Cited by 1 (1 self)
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The LLL algorithm is a wellknow and widely used lattice basis reduction algorithm. In many applications, its speed is of essential. However, it is very difficult to parallelize the original LLL algorithm. We present a multithreading LLL algorithm based on a recent improved version: an LLL
Numerical Properties of the LLL Algorithm
, 2007
"... The LLL algorithm is widely used to solve the integer least squares problems that arise in many engineering applications. As most practitioners did not understand how the LLL algorithm works, they avoided the issue by referring to the method as an integer Gram Schmidt approach (without explaining wh ..."
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Cited by 2 (1 self)
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The LLL algorithm is widely used to solve the integer least squares problems that arise in many engineering applications. As most practitioners did not understand how the LLL algorithm works, they avoided the issue by referring to the method as an integer Gram Schmidt approach (without explaining
Conditioning Properties of the LLL Algorithm
, 2009
"... Although the LLL algorithm 1 was originally developed for lattice basis reduction, the method can also be used 2 to reduce the condition number of a matrix. In this paper, we propose a pivoted LLL algorithm that further improves the conditioning. Our experimental results demonstrate that this pivoti ..."
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Although the LLL algorithm 1 was originally developed for lattice basis reduction, the method can also be used 2 to reduce the condition number of a matrix. In this paper, we propose a pivoted LLL algorithm that further improves the conditioning. Our experimental results demonstrate
Modelling the LLL algorithm by sandpiles
 In Proc. of LATIN, volume 6034 of LNCS
, 2010
"... Abstract The LLL algorithm aims at finding a “reduced ” basis of a Euclidean lattice. The LLL algorithm plays a primary role in many areas of mathematics and computer science. However, its general behaviour is far from being well understood. There are already many experimental observations about the ..."
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Cited by 3 (0 self)
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Abstract The LLL algorithm aims at finding a “reduced ” basis of a Euclidean lattice. The LLL algorithm plays a primary role in many areas of mathematics and computer science. However, its general behaviour is far from being well understood. There are already many experimental observations about
Lattices in Computer Science LLL Algorithm
"... In this lecture1 we describe an approximation algorithm to the Shortest Vector Problem (SVP). This algorithm, developed in 1982 by A. K. Lenstra, H. W. Lenstra, Jr. and L. Lovasz, usually called the LLL algorithm, gives a ( 2 √) 3 n approximation ratio, where n is the dimension of the lattice. In ma ..."
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In this lecture1 we describe an approximation algorithm to the Shortest Vector Problem (SVP). This algorithm, developed in 1982 by A. K. Lenstra, H. W. Lenstra, Jr. and L. Lovasz, usually called the LLL algorithm, gives a ( 2 √) 3 n approximation ratio, where n is the dimension of the lattice
Worstcase complexity of the optimal LLL algorithm
 In Proceedings of LATIN’2000  Punta del Este. LNCS 1776
"... . In this paper, we consider the open problem of the complexity of the LLL algorithm in the case when the approximation parameter t of the algorithm has its extreme value 1. This case is of interest because the output is then the strongest Lovaszreduced basis. Experiments reported by Lagarias and ..."
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Cited by 8 (2 self)
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. In this paper, we consider the open problem of the complexity of the LLL algorithm in the case when the approximation parameter t of the algorithm has its extreme value 1. This case is of interest because the output is then the strongest Lovaszreduced basis. Experiments reported by Lagarias
Improving the Parallel SchnorrEuchner LLL Algorithm
"... Abstract. This paper introduces a number of modifications that allow for significant improvements of parallel LLL reduction. Experiments show that these modifications result in an increase of the speedup by a factor of more than 1.35 for SVP challenge type lattice bases in comparing the new algorit ..."
A Delayed Sizereduction Technique for Speeding Up the LLL Algorithm
"... In this paper, we present a delayed sizereduction technique for speeding up the LLL algorithm. It can significantly speed up the LLL algorithm without sacrificing the quality of the results. Our experiments have shown that for problems of size 80, our algorithm can be twice as fast as the LLL algor ..."
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Cited by 1 (1 self)
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In this paper, we present a delayed sizereduction technique for speeding up the LLL algorithm. It can significantly speed up the LLL algorithm without sacrificing the quality of the results. Our experiments have shown that for problems of size 80, our algorithm can be twice as fast as the LLL
LoopReduction LLL Algorithm and Architecture for LatticeReductionAided MIMO Detection
"... We propose a loopreduction LLL (LRLLL) algorithm for latticereductionaided (LRA) multiinput multioutput (MIMO) detection. The LLL algorithm is an iterative algorithm that contains many check and process operations; however, the traditional LLL algorithm itself possesses a lot of redundant chec ..."
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We propose a loopreduction LLL (LRLLL) algorithm for latticereductionaided (LRA) multiinput multioutput (MIMO) detection. The LLL algorithm is an iterative algorithm that contains many check and process operations; however, the traditional LLL algorithm itself possesses a lot of redundant
On complex LLL algorithm for integer forcing linear receivers
 in Proc. of 2013 Australian Communications Theory Workshop (AusCTW13
, 2013
"... ar ..."
Results 1  10
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