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.ITCS.2023.85
URN: urn:nbn:de:0030-drops-175884
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17588/
Go to the corresponding LIPIcs Volume Portal

Manurangsi, Pasin

Improved Inapproximability of VC Dimension and Littlestone’s Dimension via (Unbalanced) Biclique

pdf-format:
LIPIcs-ITCS-2023-85.pdf (0.7 MB)

Abstract

We study the complexity of computing (and approximating) VC Dimension and Littlestone’s Dimension when we are given the concept class explicitly. We give a simple reduction from Maximum (Unbalanced) Biclique problem to approximating VC Dimension and Littlestone’s Dimension. With this connection, we derive a range of hardness of approximation results and running time lower bounds. For example, under the (randomized) Gap-Exponential Time Hypothesis or the Strongish Planted Clique Hypothesis, we show a tight inapproximability result: both dimensions are hard to approximate to within a factor of o(log n) in polynomial-time. These improve upon constant-factor inapproximability results from [Pasin Manurangsi and Aviad Rubinstein, 2017].

BibTeX - Entry

@InProceedings{manurangsi:LIPIcs.ITCS.2023.85,
  author =	{Manurangsi, Pasin},
  title =	{{Improved Inapproximability of VC Dimension and Littlestone’s Dimension via (Unbalanced) Biclique}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{85:1--85:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17588},
  URN =		{urn:nbn:de:0030-drops-175884},
  doi =		{10.4230/LIPIcs.ITCS.2023.85},
  annote =	{Keywords: VC Dimension, Littlestone’s Dimension, Maximum Biclique, Hardness of Approximation, Fine-Grained Complexity}
}

Keywords: VC Dimension, Littlestone’s Dimension, Maximum Biclique, Hardness of Approximation, Fine-Grained Complexity
Collection: 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Issue Date: 2023
Date of publication: 01.02.2023

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI