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This notion of reduction is most useful to use for fast algorithms as such a basis can be found in polynomial time (see LLL reduction).
Let δ∈(14,1)\delta\in\left(\frac14,1\right)δ∈(41,1). A basis{bi}i=1d\left\{b_i\right\}_{i=1}^d{bi}i=1dis δ\deltaδ- LLL-reduced if it is size reduced and satisfy the Lovász condition, i.e.