Lattice Problem - Shortest Basis Problem

Shortest Basis Problem

Many problems become easier if the input basis consists of short vectors. An algorithm that solves the Shortest Basis Problem (SBP) must, given a lattice basis, output an equivalent basis such that the length of the longest vector in is as short as possible.

The approximation version problem consist of finding a basis whose longest vector is at most times longer than the longest vector in the shortest basis.

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