TY - GEN
T1 - Minimizing the Weighted Number of Tardy Jobs Is W[1]-Hard
AU - Heeger, Klaus
AU - Hermelin, Danny
N1 - Publisher Copyright:
© Klaus Heeger and Danny Hermelin; licensed under Creative Commons License CC-BY 4.0.
PY - 2024/9/1
Y1 - 2024/9/1
N2 - 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).
AB - 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).
KW - number of different processing times
KW - number of different weights
KW - single-machine scheduling
UR - http://www.scopus.com/inward/record.url?scp=85203830090&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ESA.2024.68
DO - 10.4230/LIPIcs.ESA.2024.68
M3 - Conference contribution
AN - SCOPUS:85203830090
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 32nd Annual European Symposium on Algorithms, ESA 2024
A2 - Chan, Timothy
A2 - Fischer, Johannes
A2 - Iacono, John
A2 - Herman, Grzegorz
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 32nd Annual European Symposium on Algorithms, ESA 2024
Y2 - 2 September 2024 through 4 September 2024
ER -