Partitioning of sequentially ordered systems using linear programming

A variation of the partitioning problem is solved using linear programming techniques. In this class of problems, the optimal partition of objects must follow an a priori sequential ordering of objects. We examine a program segmentation application of this problem and formulate this sequential partitioning problem as an integer programming problem. The integer programming model of the problem possesses special structure such that the extreme points of its LP relaxation are integer and can be solved using LP techniques. We present computational results for randomly generated problems. We show how the LP approach can handle various side conditions and clustering criteria that arise across different problem types.