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We generalize the Gauss algorithm for the reduction of two–dimensional lattices from the l 2-norm to arbitrary norms and extend Vallée's analysis [J. Algorithms 12 (1991), 556-572] to the generalized algorithm.

- Michael Kaib
- FCT
- 1991

- Michael Kaib
- ANTS
- 1994

We propose a fast variant of the Gaussian algorithm for the reduction of two{ dimensional lattices for the l 1 ?; l 2 ? and l 1 ?norm. The algorithm runs in at most O(n M(B) log B) bit operations for the l 1 ?norm and in O(n logn M(B) log B) bit operations for the l 1 ? and l 2 ?norm on input vectors a; b 2 Z Z n with norm at most 2 B where M(B) is a time… (More)

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