License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.4
URN: urn:nbn:de:0030-drops-124119
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12411/
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Abboud, Amir ; Bringmann, Karl ; Hermelin, Danny ; Shabtay, Dvir

Scheduling Lower Bounds via AND Subset Sum

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LIPIcs-ICALP-2020-4.pdf (0.5 MB)

Abstract

Given N instances (X_1,t_1),…,(X_N,t_N) 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 X_i has a subset that sums up to the target integer t_i. We prove that this problem cannot be solved in time Õ((N ⋅ t_max)^{1-ε}), for t_max = max_i t_i and any ε > 0, assuming the ∀ ∃ Strong Exponential Time Hypothesis (∀∃-SETH). We then use this result to exclude Õ(n+P_max⋅n^{1-ε})-time algorithms for several scheduling problems on n jobs with maximum processing time P_max, assuming ∀∃-SETH. These include classical problems such as 1||∑ w_jU_j, the problem of minimizing the total weight of tardy jobs on a single machine, and P₂||∑ U_j, the problem of minimizing the number of tardy jobs on two identical parallel machines.

BibTeX - Entry

@InProceedings{abboud_et_al:LIPIcs:2020:12411,
  author =	{Amir Abboud and Karl Bringmann and Danny Hermelin and Dvir Shabtay},
  title =	{{Scheduling Lower Bounds via AND Subset Sum}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12411},
  URN =		{urn:nbn:de:0030-drops-124119},
  doi =		{10.4230/LIPIcs.ICALP.2020.4},
  annote =	{Keywords: SETH, fine grained complexity, Subset Sum, scheduling}
}

Keywords: SETH, fine grained complexity, Subset Sum, scheduling
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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