TY - GEN

T1 - Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times - A polymatroid optimization approach

AU - Shakhlevich, Natalia V.

AU - Shioura, Akiyoshi

AU - Strusevich, Vitaly A.

N1 - Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-540-87744-8_63

DO - 10.1007/978-3-540-87744-8_63

M3 - Conference contribution

AN - SCOPUS:57749175049

SN - 3540877436

SN - 9783540877431

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 756

EP - 767

BT - Algorithms - ESA 2008 - 16th Annual European Symposium, Proceedings

PB - Springer Verlag

T2 - 16th Annual European Symposium on Algorithms, ESA 2008

Y2 - 15 September 2008 through 17 September 2008

ER -