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((OPT)2) machines has been shown. We build on this prior work to obtain a constant factor approximation algorithm for the problem.
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Chuzhoy, J., Codenotti, P. (2009). Resource Minimization Job Scheduling. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_6
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DOI: https://doi.org/10.1007/978-3-642-03685-9_6
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