Covering Points of a Digraph with Point-Disjoint Paths and Its Application to Code Optimization

Abstract

A point-disjoint path cover of a directed graph is a collection of point-disjoint paths (some paths possibly having zero length) which covers all the points. A path cover which minimizes the number of paths corresponds to an optimal sequence of the steps of a computer program for efficient coding and documentation. The minimization problem for the general directed graph is hard in the sense of being NP-complete. In the case of cycle-free digraphs, however, the problem is polynomial, for it is shown that it can be reduced to the maximum-matching problem. A heuristic given here for finding a near optimal path cover for the general case is based upon applying the maximum-matching algorithm to the subgraphs of an interval decomposition.