Integer solutions for systems of linear inequalities, equations,
and congruences are considered along with the construction and
theoretical analysis of integer programming algorithms. The
complexity of algorithms is analyzed dependent upon two parameters:
the dimension, and the maximal modulus of the coefficients
describing the conditions of the problem. The analysis is based on
a thorough treatment of the qualitative and quantitative aspects of
integer programming, in particular on bounds obtained by the author
for the number of extreme points. This permits progress in many
cases in which the traditional approach - which regards complexity
as a function only of the length of the input-leads to a negative
result.
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