Resource Minimization Job Scheduling

Authors:
Julia Chuzhoy;Paolo Codenotti
Affiliations:
Supported in part by NSF CAREER award CCF-0844872, Toyota Technological Institute, Chicago 60637;Department of Computer Science, University of Chicago, Chicago 60637
Venue:
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Year:
2009

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Abstract

Given a set J of jobs, where each job j is associated with release date r j , deadline d j and processing time p j , our goal is to schedule all jobs using the minimum possible number of machines. Scheduling a job j requires selecting an interval of length p j 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 $O(\sqrt{\log n})$-approximation, and moreover an efficient algorithm for scheduling all jobs on $O(({\rm \sc OPT})^2)$ machines has been shown. We build on this prior work to obtain a constant factor approximation algorithm for the problem.