Let A be a fixed integer matrix of size m by n and consider all b for which the body is full dimensional. We examine the set of shortest non-zero integral vectors with respect to the family of norms. We show that the number of such shortest vectors is polynomial in the bit size of A, for fixed n. We also show the existence, for any n, of a family of matrices M for which the number of shortest vectors has as a lower bound a polynomial in the bit size of M of the same degree at the polynomial bound.
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Length: 8 pages Date of creation: Jan 1991 Date of revision: Publication status: Published in Mathematics of Operations Research (August 1993), 18(3): 517-522 Handle: RePEc:cwl:cwldpp:965
Find related papers by JEL classification: C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
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