Polynomial algorithms for linear programming over the algebraic numbers

Authors:
Ilan Adler;Peter A. Beling
Affiliations:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, CA;Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, CA
Venue:
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Year:
1992

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Abstract

We derive an algorithm based on the ellipsoid method that solves linear programs whose coefficients are real algebraic numbers. By defining the encoding size of an algebraic number to be the bit size of the coefficients of its minimal polynomial, we prove the algorithm runs in time polynomial in the dimension of the problem, the encoding size of the input coefficients, and the degree of any algebraic extension which contains the input coefficients. This bound holds even if all input and arithmetic is performed symbolically, using rational numbers only.