Accession Number:

AD0712070

Title:

INTEGRAL CONVEX POLYHEDRA AND AN APPROACH TO INTEGRALIZATION.

Descriptive Note:

Doctoral thesis,

Corporate Author:

MASSACHUSETTS INST OF TECH CAMBRIDGE PROJECT MAC

Personal Author(s):

Report Date:

1970-08-01

Pagination or Media Count:

172.0

Abstract:

Many combinatorial optimization problems may be formulated as integer linear programming problems, that is, problems of the form given a convex polyhedron P contained in the non-negative orthant of n-dimensional space, find an integer point in P which maximizes or minimizes a given linear objective function. Well known linear programming methods would suffice to solve such a problem if 1 P is an integral convex polyhedron, or 2 P is transformed into the integral convex polyhedron that is the convex hull of the set of integer points in P, a process which is called integralization. This thesis provides some theoretical results concerning integral convex polyhedra and the process of integralization. Necessary and sufficient conditions for a convex polyhedron P to have the integral property are derived in terms of the system of linear inequalities defining P. A number-theoretic method for integralizing two-dimensional convex polyhedra is developed which makes use of a generalization of the division theorem for integers. The method is applicable to a restricted class of higher dimensional polyhedra as well. Author

Subject Categories:

  • Theoretical Mathematics
  • Operations Research

Distribution Statement:

APPROVED FOR PUBLIC RELEASE