TY - GEN
T1 - Scheduling lower bounds via and Subset Sum
AU - Abboud, Amir
AU - Bringmann, Karl
AU - Hermelin, Danny
AU - Shabtay, Dvir
N1 - Funding Information:
Funding Karl Bringmann: This work is part of the project TIPEA that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 850979).
Funding Information:
Karl Bringmann: This work is part of the project TIPEA that has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 850979).
Publisher Copyright:
© Amir Abboud, Karl Bringmann, Danny Hermelin, and Dvir Shabtay; licensed under Creative Commons License CC-BY 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020).
PY - 2020/6/1
Y1 - 2020/6/1
N2 - Given N instances (X1, t1), . . ., (XN, tN) 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 Xi has a subset that sums up to the target integer ti. We prove that this problem cannot be solved in time Oe((N · tmax)1−ε), for tmax = maxi ti and any ε > 0, assuming the ∀∃ Strong Exponential Time Hypothesis (∀∃-SETH). We then use this result to exclude Oe(n + Pmax · n1−ε)-time algorithms for several scheduling problems on n jobs with maximum processing time Pmax, assuming ∀∃-SETH. These include classical problems such as 1||P wjUj, the problem of minimizing the total weight of tardy jobs on a single machine, and P2||P Uj, the problem of minimizing the number of tardy jobs on two identical parallel machines.
AB - Given N instances (X1, t1), . . ., (XN, tN) 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 Xi has a subset that sums up to the target integer ti. We prove that this problem cannot be solved in time Oe((N · tmax)1−ε), for tmax = maxi ti and any ε > 0, assuming the ∀∃ Strong Exponential Time Hypothesis (∀∃-SETH). We then use this result to exclude Oe(n + Pmax · n1−ε)-time algorithms for several scheduling problems on n jobs with maximum processing time Pmax, assuming ∀∃-SETH. These include classical problems such as 1||P wjUj, the problem of minimizing the total weight of tardy jobs on a single machine, and P2||P Uj, the problem of minimizing the number of tardy jobs on two identical parallel machines.
KW - Fine grained complexity
KW - SETH
KW - Scheduling
KW - Subset Sum
UR - http://www.scopus.com/inward/record.url?scp=85089338932&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ICALP.2020.4
DO - 10.4230/LIPIcs.ICALP.2020.4
M3 - Conference contribution
AN - SCOPUS:85089338932
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
A2 - Czumaj, Artur
A2 - Dawar, Anuj
A2 - Merelli, Emanuela
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
Y2 - 8 July 2020 through 11 July 2020
ER -