The Complexity of the Extended GCD Problem

  title={The Complexity of the Extended GCD Problem},
  author={George Havas and Jean-Pierre Seifert},
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


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