License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2022.106
URN: urn:nbn:de:0030-drops-164478
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16447/
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Rubinstein, Aviad ; Zhao, Junyao

Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond 1/2-Approximation

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LIPIcs-ICALP-2022-106.pdf (0.8 MB)

Abstract

In this work we give two new algorithms that use similar techniques for (non-monotone) submodular function maximization subject to a cardinality constraint. The first is an offline fixed-parameter tractable algorithm that guarantees a 0.539-approximation for all non-negative submodular functions. The second algorithm works in the random-order streaming model. It guarantees a (1/2+c)-approximation for symmetric functions, and we complement it by showing that no space-efficient algorithm can beat 1/2 for asymmetric functions. To the best of our knowledge this is the first provable separation between symmetric and asymmetric submodular function maximization.

BibTeX - Entry

@InProceedings{rubinstein_et_al:LIPIcs.ICALP.2022.106,
  author =	{Rubinstein, Aviad and Zhao, Junyao},
  title =	{{Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond 1/2-Approximation}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{106:1--106:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16447},
  URN =		{urn:nbn:de:0030-drops-164478},
  doi =		{10.4230/LIPIcs.ICALP.2022.106},
  annote =	{Keywords: Submodular optimization, Fixed-parameter tractability, Random-order streaming}
}

Keywords: Submodular optimization, Fixed-parameter tractability, Random-order streaming
Collection: 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)
Issue Date: 2022
Date of publication: 28.06.2022

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