  We consider the NP-hard problem of minimizing a separable concave quadratic
function over the integral points in a polyhedron, and we denote by D the
largest absolute value of the subdeterminants of the constraint matrix. In this
paper we give an algorithm that finds an epsilon-approximate solution for this
problem by solving a number of integer linear programs whose constraint
matrices have subdeterminants bounded by D in absolute value. The number of
these integer linear programs is polynomial in the dimension n, in D and in
1/epsilon, provided that the number k of variables that appear nonlinearly in
the objective is fixed. As a corollary, we obtain the first polynomial-time
approximation algorithm for separable concave integer quadratic programming
with D at most two and k fixed. In the totally unimodular case D=1, we give an
improved algorithm that only needs to solve a number of linear programs that is
polynomial in 1/epsilon and is independent on n, provided that k is fixed.

Optimization and Control;Computational Complexity