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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.

We generalize the concept of block reduction for lattice bases from the l 2 {norm to arbitrary norms. This extends the results of Schnorr S87, S94]. We give algorithms for block reduction and apply the resulting enumeration concept to solve subset sum problems. The deterministic algorithm solves all subset sum problems. For up to 66 weights it needs in… (More)

- 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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