The Complexity of Approximate Optima for Greatest Common Divisor Computations

  title={The Complexity of Approximate Optima for Greatest Common Divisor Computations},
  author={Carsten R{\"o}ssner and Jean-Pierre Seifert},
We study the approximability of the following NP-complete (in their feasibility recognition forms) number theoretic optimization problems: 1. x 2 Z n with minimum max 1in jxij satisfying P n i=1 xiai = gcd(a1; : : : ; an). We present a polynomial-time algorithm which approximates a minimum gcd set for a1; : : : ; an within a factor 1+ln n and prove that this algorithm is best possible in the sense that unless NP DTIME(n O(log log n)), there is no polynomial-time algorithm which approximates a… CONTINUE READING


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