What is the run time complexity of integer linear programming (ILP)?

Question

What is the run time complexity of integer linear programming (ILP) problem when, there are N number of variables and R number of constraints? For coding purpose I am using Matlab's intlinprog function. Any reference would be helpful.

Answer 1

Integer programming is NP-Complete as mentioned in this link . Some heuristic methods used in the intlinprog function in Matlab (such as defining min and max value to limit the search space), but they can't change the complexity of the problem at all.

Also, if all values are between -a to a , we have an algorithm which runs in N^2(R*a^2)^{2R+3} . You can find more details here .