论文信息 - Complexity of the Frobenius problem

Complexity of the Frobenius problem

Consider the Frobenius Problem: Given positive integersa1,...,an withai ≥ 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 ofa1,...,an. In this paper we prove that the Frobenius problem is NP-hard, under Turing reductions.

J. L. Ramírez-Alfonsín

[1] R. Graham,et al. On a linear diophantine problem of Frobenius , 1972 .

[2] Ravi Kannan,et al. Lattice translates of a polytope and the Frobenius problem , 1992, Comb..

[3] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4] Herbert E. Scarf,et al. The Frobenius Problem and Maximal Lattice Free Bodies , 1993, Math. Oper. Res..

[5] Harold Greenberg,et al. Solution to a Linear Diophantine Equation for Nonnegative Integers , 1988, J. Algorithms.

[6] A. Brauer,et al. On a problem of Frobenius. , 1962 .

[7] Öyvind Beyer,et al. On the linear diophantine problem of Frobenius in three variables. , 1978 .

[8] E. Selmer,et al. On the linear diophantine problem of Frobenius. , 1977 .