This invention describes a software method for computers for solving integer programming problems containing systems of linear equations where part of or all of the variables may take only integer values. Said software method consists of 2 main steps. First, the arithmetic binary decision diagrams associated to the equations of the system are constructed. A solution to any of said equations is determined by finding an allowed path through the associated arithmetic binary decision diagram. Then, solutions common to all equation of the system are determined by searching for common paths between the arithmetic binary decision diagrams of the equations. Searching for common paths between said arithmetic binary decision diagrams is done by determining correspondences between the nodes of said arithmetic binary decision diagrams.
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