A linear algorithm for integer programming in the plane

Authors:
F. Eisenbrand;Sören Laue
Affiliations:
Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123, Saarbrücken, Germany
Venue:
Mathematical Programming: Series A and B
Year:
2005

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Abstract

We show that a 2-variable integer program, defined by m constraints involving coefficients with at most φ bits, can be solved with O(m+φ) arithmetic operations on rational numbers of size O(φ).