TY - JOUR
T1 - Scheduling lower bounds via AND subset sum.
AU - Abboud, Amir
AU - Bringmann, Karl
AU - Hermelin, Danny
AU - Shabtay, Dvir
N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2022
Y1 - 2022
N2 - Given N instances of Subset Sum, the AND Subset Sum problem asks to determine whether all of these instances are yes-instances; that is, whether each set of integers has a subset that sums up to the target integer . We prove that this problem cannot be solved in time , for and any , assuming the ∀∃ Strong Exponential Time Hypothesis (∀∃-SETH). We then use this result to exclude -time algorithms for several scheduling problems on n jobs with maximum processing time , assuming ∀∃-SETH. These include classical problems such as , the problem of minimizing the total weight of tardy jobs on a single machine, and , the problem of minimizing the number of tardy jobs on two identical parallel machines.
AB - Given N instances of Subset Sum, the AND Subset Sum problem asks to determine whether all of these instances are yes-instances; that is, whether each set of integers has a subset that sums up to the target integer . We prove that this problem cannot be solved in time , for and any , assuming the ∀∃ Strong Exponential Time Hypothesis (∀∃-SETH). We then use this result to exclude -time algorithms for several scheduling problems on n jobs with maximum processing time , assuming ∀∃-SETH. These include classical problems such as , the problem of minimizing the total weight of tardy jobs on a single machine, and , the problem of minimizing the number of tardy jobs on two identical parallel machines.
U2 - 10.1016/j.jcss.2022.01.005
DO - 10.1016/j.jcss.2022.01.005
M3 - Article
VL - 127
SP - 29
EP - 40
JO - Journal of Computer and System Sciences
JF - Journal of Computer and System Sciences
ER -