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Single Machine Scheduling with Few Deadlines

Authors Klaus Heeger , Danny Hermelin , Dvir Shabtay

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Author Details

Klaus Heeger
  • Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Danny Hermelin
  • Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Dvir Shabtay
  • Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel

Funding

Supported by the ISF, grant No. 1070/20.

Cite AsGet BibTex

Klaus Heeger, Danny Hermelin, and Dvir Shabtay. Single Machine Scheduling with Few Deadlines. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.IPEC.2023.24

Abstract

We study single-machine scheduling problems with few deadlines. We focus on two classical objectives, namely minimizing the weighted number of tardy jobs and the total weighted completion time. For both problems, we give a pseudopolynomial-time algorithm for a constant number of different deadlines. This algorithm is complemented with an ETH-based, almost tight lower bound. Furthermore, we study the case where the number of jobs with a nontrivial deadline is taken as parameter. For this case, the complexity of our two problems differ: Minimizing the total number of tardy jobs becomes fixed-parameter tractable, while minimizing the total weighted completion time is W[1]-hard.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
  • Theory of computation → W hierarchy
  • Theory of computation → Dynamic programming
  • Theory of computation → Scheduling algorithms
Keywords
  • Single-machine scheduling
  • weighted completion time
  • tardy jobs
  • pseudopolynomial algorithms
  • parameterized complexity

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