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Lattice reduction in two dimensions: analyses under realistic probabilistic models
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) (2007).

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The Gaussian algorithm for lattice reduction in dimension 2 is precisely analysed under a class of realistic probabilistic models, which are of interest when applying the Gauss algorithm "inside'' the LLL algorithm. The proofs deal with the underlying dynamical systems and transfer operators. All the main parameters are studied: execution parameters which describe the behaviour of the algorithm itself as well as output parameters, which describe the geometry of reduced bases. 
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     author = {Vall\'ee, Brigitte and Vera, Antonio},
     title = {Lattice reduction in two dimensions: analyses under realistic probabilistic models},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07)},
     year = {2007},
     doi = {10.46298/dmtcs.3549},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3549/}
}
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Vallée, Brigitte; Vera, Antonio. Lattice reduction in two dimensions: analyses under realistic probabilistic models. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) (2007). doi : 10.46298/dmtcs.3549. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3549/

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