Practical Applicability of the Metric Approach for a Scheduling Problem

Abstract

A given special case of NP-complete scheduling problem can be approximated by solving a special case of similar problem with the same precedence graph. We construct a metric space over a set of special cases of this problem and consider the statistical relationship between distance between a pair of special cases of the under consideration and the average error of the approximated solution. Sethi, Gabow, Coffman's and Fujii's algorithms for this problem are used. It is shown that the absolute and the relative error of the objective function decreases over the density of a graph with a fixed number of jobs. In general case, relative non-zero error value increases with the number of jobs.