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 w-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 dániel marx.
|Title of host publication||Integer Programming and Combinatorial Optimization|
|Subtitle of host publication||17th International Conference, IPCO 2014 Bonn, Germany, June 23-25, 2014 Proceedings|
|Editors||Jon Lee, Jens Vygen|
|Publication status||Published - 2014|
|Series||Lecture Notes in Computer Science|
Mnich, M., & Wiese, A. (2014). Scheduling and Fixed-Parameter Tractability. In J. Lee, & J. Vygen (Eds.), Integer Programming and Combinatorial Optimization: 17th International Conference, IPCO 2014 Bonn, Germany, June 23-25, 2014 Proceedings (pp. 381-392). Springer. Lecture Notes in Computer Science, Vol.. 8494 https://doi.org/10.1007/978-3-319-07557-0_32