@inproceedings{edcd348627c94fbeaf19bc1a148c16f6,
title = "Scheduling and Fixed-Parameter Tractability",
abstract = "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{\textquoteright} 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 w[1]-hardness results showing that for smaller sets of parameters the respective problems do not allow fpt-algorithms. In particular, our positive and negative results for scheduling with rejection explore a research direction proposed by d{\'a}niel marx.",
author = "Matthias Mnich and Andreas Wiese",
year = "2014",
doi = "10.1007/978-3-319-07557-0_32",
language = "English",
isbn = "978-3-319-07556-3",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "381--392",
editor = "Jon Lee and Jens Vygen",
booktitle = "Integer Programming and Combinatorial Optimization",
address = "United States",
}