Scheduling lower bounds via and Subset Sum

Amir Abboud, Karl Bringmann, Danny Hermelin, Dvir Shabtay

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

Abstract

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)1ε), 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 · n1ε)-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.

Original languageEnglish
Title of host publication47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
EditorsArtur Czumaj, Anuj Dawar, Emanuela Merelli
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771382
DOIs
StatePublished - 1 Jun 2020
Event47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 - Virtual, Online, Germany
Duration: 8 Jul 202011 Jul 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume168
ISSN (Print)1868-8969

Conference

Conference47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
Country/TerritoryGermany
CityVirtual, Online
Period8/07/2011/07/20

Keywords

  • Fine grained complexity
  • SETH
  • Scheduling
  • Subset Sum

ASJC Scopus subject areas

  • Software

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