Single Machine Scheduling with Few Deadlines

Klaus Heeger; Danny Hermelin; Dvir Shabtay

doi:10.4230/LIPIcs.IPEC.2023.24

Single Machine Scheduling with Few Deadlines

Klaus Heeger, Danny Hermelin, Dvir Shabtay

Department of Industrial Engineering and Management

Ben-Gurion University of the Negev

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	American English
Title of host publication	18th International Symposium on Parameterized and Exact Computation, IPEC 2023
Editors	Neeldhara Misra, Magnus Wahlstrom
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959773058
DOIs	https://doi.org/10.4230/LIPIcs.IPEC.2023.24
State	Published - 1 Dec 2023
Event	18th International Symposium on Parameterized and Exact Computation, IPEC 2023 - Amsterdam, Netherlands Duration: 6 Sep 2023 → 8 Sep 2023

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	285

Conference

Conference	18th International Symposium on Parameterized and Exact Computation, IPEC 2023
Country/Territory	Netherlands
City	Amsterdam
Period	6/09/23 → 8/09/23

Keywords

parameterized complexity
pseudopolynomial algorithms
Single-machine scheduling
tardy jobs
weighted completion time

All Science Journal Classification (ASJC) codes

Software

Access to Document

10.4230/LIPIcs.IPEC.2023.24

Cite this

Heeger, K., Hermelin, D., & Shabtay, D. (2023). Single Machine Scheduling with Few Deadlines. In N. Misra, & M. Wahlstrom (Eds.), 18th International Symposium on Parameterized and Exact Computation, IPEC 2023 Article 24 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 285). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.IPEC.2023.24

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title = "Single Machine Scheduling with Few Deadlines",

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.",

keywords = "parameterized complexity, pseudopolynomial algorithms, Single-machine scheduling, tardy jobs, weighted completion time",

author = "Klaus Heeger and Danny Hermelin and Dvir Shabtay",

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doi = "10.4230/LIPIcs.IPEC.2023.24",

language = "American English",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

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booktitle = "18th International Symposium on Parameterized and Exact Computation, IPEC 2023",

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Heeger, K, Hermelin, D & Shabtay, D 2023, Single Machine Scheduling with Few Deadlines. in N Misra & M Wahlstrom (eds), 18th International Symposium on Parameterized and Exact Computation, IPEC 2023., 24, Leibniz International Proceedings in Informatics, LIPIcs, vol. 285, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 18th International Symposium on Parameterized and Exact Computation, IPEC 2023, Amsterdam, Netherlands, 6/09/23. https://doi.org/10.4230/LIPIcs.IPEC.2023.24

Single Machine Scheduling with Few Deadlines. / Heeger, Klaus; Hermelin, Danny ; Shabtay, Dvir.
18th International Symposium on Parameterized and Exact Computation, IPEC 2023. ed. / Neeldhara Misra; Magnus Wahlstrom. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2023. 24 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 285).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Shabtay, Dvir

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N2 - 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.

AB - 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.

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KW - pseudopolynomial algorithms

KW - Single-machine scheduling

KW - tardy jobs

KW - weighted completion time

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M3 - Conference contribution

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BT - 18th International Symposium on Parameterized and Exact Computation, IPEC 2023

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Heeger K, Hermelin D , Shabtay D. Single Machine Scheduling with Few Deadlines. In Misra N, Wahlstrom M, editors, 18th International Symposium on Parameterized and Exact Computation, IPEC 2023. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2023. 24. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.IPEC.2023.24

Single Machine Scheduling with Few Deadlines

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Keywords

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