Scheduling and fixed-parameter tractability

• 成果类型: Article
• 署名作者: Mnich, Matthias; Wiese, Andreas
• 署名单位: Max Planck Society
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-014-0830-9
• 发表日期: 2015
• 页码: 533-562
• 关键词: approximation algorithms; bin-packing; complexity; number; jobs

摘要

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 -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 Daniel Marx.