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Lecture Notes in Computer Science
In this paper, we consider the open problem of the complexity of the LLL algorithm in the case when the approximation parameter Ø of the algorithm has its extreme value ½. This case is of interest because the output is then the strongest Lovász-reduced basis. Experiments reported by Lagarias and Odlyzko [LO83] seem to show that the algorithm remain polynomial in average. However no bound better than a naive exponential order one is established for the worstcase complexity of the optimal LLLdoi:10.1007/10719839_35 fatcat:uzqcj2goejeylmnimxabdepdei