Minimizing the Weighted Number of Tardy Jobs Is W[1]-Hard

Klaus Heeger, Danny Hermelin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider the 1 || P wjUj problem, the problem of minimizing the weighted number of tardy jobs on a single machine. This problem is one of the most basic and fundamental problems in scheduling theory, with several different applications both in theory and practice. Using a reduction from the Multicolored Clique problem, we prove that 1 || P wjUj is W[1]-hard with respect to the number p# of different processing times in the input, as well as with respect to the number w# of different weights in the input. This, along with previous work, provides a complete picture for 1 || P wjUj from the perspective of parameterized complexity, as well as almost tight complexity bounds for the problem under the Exponential Time Hypothesis (ETH).

Original languageEnglish
Title of host publication32nd Annual European Symposium on Algorithms, ESA 2024
EditorsTimothy Chan, Johannes Fischer, John Iacono, Grzegorz Herman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959773386
DOIs
StatePublished - 1 Sep 2024
Event32nd Annual European Symposium on Algorithms, ESA 2024 - London, United Kingdom
Duration: 2 Sep 20244 Sep 2024

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume308
ISSN (Print)1868-8969

Conference

Conference32nd Annual European Symposium on Algorithms, ESA 2024
Country/TerritoryUnited Kingdom
CityLondon
Period2/09/244/09/24

Keywords

  • number of different processing times
  • number of different weights
  • single-machine scheduling

ASJC Scopus subject areas

  • Software

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