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Scheduling and fixed-parameter tractability
Publikationstyp
Journal Article
Date Issued
2014-12-01
Sprache
English
Author(s)
TORE-URI
Journal
Volume
154
Issue
1-2
Start Page
533
End Page
562
Citation
Mathematical Programming (2015)
Publisher DOI
ArXiv ID
Publisher
Springer Nature
Fixed-parameter tractability analysis and scheduling are two core domains of combinatorial optimization which led to deep understanding of many important algorithmic questions. However, even though fixed-parameter algorithms are appealing for many reasons, no such algorithms are known for many fundamental scheduling problems. In this paper we present the first fixed-parameter algorithms for classical scheduling problems such as makespan minimization, scheduling with job-dependent cost functions—one important example being weighted flow time—and scheduling with rejection. To this end, we identify crucial parameters that determine the problems’ complexity. In particular, we manage to cope with the problem complexity stemming from numeric input values, such as job processing times, which is usually a core bottleneck in the design of fixed-parameter algorithms. We complement our algorithms with(Formula presented.) (Formula presented.)-hardness results showing that for smaller sets of parameters the respective problems do not allow fixed-parameter algorithms. In particular, our positive and negative results for scheduling with rejection explore a research direction proposed by Dániel Marx.
DDC Class
000: Allgemeines, Wissenschaft