Approximation Algorithms for Average Stretch Scheduling

We study the basic problem of preemptive scheduling of a stream of jobs on a single processor. Consider an on-line stream of jobs, and let the ith job arrive at time r(i) and have processing time p(i). If C(i) is the completion time of job i, then the flow time of i is C(i) − r(i) and the stretch of i is the ratio of its flow time to its processing time; that is, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{C(i) - r(i)}}{{p(i)}}$$\end{document}. Flow time measures the time that a job is in the system regardless of the service it requests; the stretch measure relies on the intuition that a job that requires a long service time must be prepared to wait longer than jobs that require small service times.