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# The Complexity of the Extended GCD Problem

@inproceedings{Havas1999TheCO, title={The Complexity of the Extended GCD Problem}, author={George Havas and Jean-Pierre Seifert}, booktitle={MFCS}, year={1999} }

- Published in MFCS 1999
DOI:10.1007/3-540-48340-3_10

We undertake a thorough complexity study of the following fundamental optimization problem, known as the `p-norm shortest extended GCD multiplier problem: given a1, . . . , an ∈ Z, find an `p-norm shortest gcd multiplier for a1, . . . , an, i.e., a vector x ∈ Z with minimum ( ∑n i=1 |xi|) satisfying ∑n i=1 xiai = gcd(a1, . . . , an). First, we prove that the shortest GCD multiplier problem (in its feasibility recognition form) is NP-complete for every `p-norm with p ∈ N. This gives an… CONTINUE READING