We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in O(Tfeas(n)× log n) time by using our divide-and-conquer technique, where n is the number of jobs and O(T feas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Shakhlevich, N. V., Shioura, A., & Strusevich, V. A. (2008). Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times - A polymatroid optimization approach. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5193 LNCS, pp. 756–767). Springer Verlag. https://doi.org/10.1007/978-3-540-87744-8_63
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