Fast approximation algorithms for job scheduling with processing set restrictions

• Published in: Theoretical computer science Vol. 411; no. 44-46; pp. 3947 - 3955
• Main Authors: Huo, Yumei, Leung, Joseph Y.-T.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier B.V 25-10-2010; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Approximation; C (programming language); Combinatorics; Combinatorics. Ordered structures; Computer science; control theory; systems; Computer systems performance. Reliability; Constrictions; Exact sciences and technology; Graph theory; Inclusive processing set; Makespan minimization; Mathematical analysis; Mathematics; Miscellaneous; Nested processing set; Nonpreemptive scheduling; NP-hard; Polynomial-time approximation algorithm; Schedules; Scheduling; Sciences and techniques of general use; Software; Theoretical computing; Tree-hierarchical processing set; NP-hard; Makespan minimization; Tree-hierarchical processing set; Nested processing set; Nonpreemptive scheduling; Inclusive processing set; Polynomial-time approximation algorithm; Computer theory; Polynomial approximation; Parallel machines; Minimization; Makespan; Approximation algorithm; Polynomial time; Schedule; Tree; Fast algorithm
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2010.08.008

We consider the problem of scheduling n independent jobs on m parallel machines, where the machines differ in their functionality but not in their processing speeds. Each job has a restricted set of machines to which it can be assigned, called its processing set. Preemption is not allowed. Our goal is to minimize the makespan of the schedule. We study two variants of this problem: (1) the case of tree-hierarchical processing set and (2) the case of nested processing set. We first give a fast algorithm for the case of tree-hierarchical processing set with a worst-case bound of 4/3, which is better than the best known algorithm whose worst-case bound is 2. We then give a more complicated algorithm for the case of nested processing set with a worst-case bound of 5/3, which is better than the best known algorithm whose worst-case bound is 7/4. In both cases, we will give examples achieving the worst-case bounds.