Complexity of the Frobenius problem

Abstract

Consider the Frobenius Problem: Given positive integersa 1,...,a n witha i ≥ 2 and such that their greatest common divisor is one, find the largest natural number that is not expressible as a non-negative integer combination ofa 1,...,a n. In this paper we prove that the Frobenius problem is NP-hard, under Turing reductions.

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Ramírez-Alfonsín, J.L. Complexity of the Frobenius problem. Combinatorica 16, 143–147 (1996). https://doi.org/10.1007/BF01300131

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Mathematics Subject Classification (1991)

  • 68 Q 15
  • 90 C 10