Resource minimization job scheduling

Abstract

Given a set J of jobs, where each job j is associated with release date rj, deadline dj and processing time pj, our goal is to schedule all jobs using the minimum possible number of machines. Scheduling a job j requires selecting an interval of length pj between its release date and deadline, and assigning it to a machine, with the restriction that each machine executes at most one job at any given time. This is one of the basic settings in the resource-minimization job scheduling, and the classical randomized rounding technique of Raghavan and Thompson provides an O(logn/loglogn)-approximation for it. This result has been recently improved to an O(√log n)-approximation, and moreover an efficient algorithm for scheduling all jobs on O((OPT)2)machines has been shown. We build on this prior work to obtain a constant factor approximation algorithm for the problem. © 2009 Springer.