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I have a linear program over real variables for which it can be shown that all the vertices of the polytope describing its feasible region are integral.

Obviously I can just solve this using a standard linear programming solver. However I would like to know if I can take advantage of the known integral nature of the feasible solution set in some way. Is there an algorithm that can use this information to improve its efficiency or stability when solving integral linear programs?

I am trying to solve very small problems of just a few hundred terms on an embedded system. Even micro-optimizations of a few percent would be very helpful in my situation.

Richard Forrest
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  • Are the constants in the linear program integers too? If all the numbers involved are integers, and you know that the result is going to be an integer, it's possible that some computations can be done with integer arithmetic instead of floating-point arithmetic. But note that, although you know the vertices in the feasible region are integral, you have to be careful if some vertices out of the feasible region are not integral and are explored by intermediate steps of the solving algorithm. – Stef Apr 28 '22 at 09:32
  • Alternatively, perhaps you can do all your computations using limited-precision fixed-point arithmetic. As long as you make sure that the accumulated error cannot exceed 0.5, the errors won't affect your solution since you'll round to the nearest integer in the end. – Stef Apr 28 '22 at 09:34

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