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Comments on Integer Hulls of Two Linear Constraints

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  • R. G. Jeroslow

    (University of Minnesota, Minneapolis, Minnesota)

Abstract

This paper establishes an intrinsic complexity for the integer-programming problem that goes well beyond the computational complexities of linear programming. To this end, it describes a procedure with the following property: given any two independent linear constraints in two dimensions and any number N however large, the procedure determines two other linear constraints (with integer coefficients) arbitrarily “close” to the given constraints such that the two new constraints have at least N faces in their integer hull. It is possible for the integer-programming optimum to occur at any extreme point of this hull, and the number of extreme points is one less than the number of faces. In contrast, the linear-programming problem consisting of two inequalities in the plane is a triviality. The paper has an expository style and illustrates its highly geometrical arguments with figures.

Suggested Citation

  • R. G. Jeroslow, 1971. "Comments on Integer Hulls of Two Linear Constraints," Operations Research, INFORMS, vol. 19(4), pages 1061-1069, August.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:4:p:1061-1069
    DOI: 10.1287/opre.19.4.1061
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