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.FSTTCS.2022.6
URN: urn:nbn:de:0030-drops-173986
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17398/
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Beideman, Calvin ; Chandrasekaran, Karthekeyan ; Chekuri, Chandra ; Xu, Chao

Approximate Representation of Symmetric Submodular Functions via Hypergraph Cut Functions

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LIPIcs-FSTTCS-2022-6.pdf (0.6 MB)

Abstract

Submodular functions are fundamental to combinatorial optimization. Many interesting problems can be formulated as special cases of problems involving submodular functions. In this work, we consider the problem of approximating symmetric submodular functions everywhere using hypergraph cut functions. Devanur, Dughmi, Schwartz, Sharma, and Singh [Devanur et al., 2013] showed that symmetric submodular functions over n-element ground sets cannot be approximated within (n/8)-factor using a graph cut function and raised the question of approximating them using hypergraph cut functions. Our main result is that there exist symmetric submodular functions over n-element ground sets that cannot be approximated within a o(n^{1/3}/log² n)-factor using a hypergraph cut function. On the positive side, we show that symmetrized concave linear functions and symmetrized rank functions of uniform matroids and partition matroids can be constant-approximated using hypergraph cut functions.

BibTeX - Entry

@InProceedings{beideman_et_al:LIPIcs.FSTTCS.2022.6,
  author =	{Beideman, Calvin and Chandrasekaran, Karthekeyan and Chekuri, Chandra and Xu, Chao},
  title =	{{Approximate Representation of Symmetric Submodular Functions via Hypergraph Cut Functions}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17398},
  URN =		{urn:nbn:de:0030-drops-173986},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.6},
  annote =	{Keywords: Submodular Functions, Hypergraphs, Approximation, Representation}
}

Keywords: Submodular Functions, Hypergraphs, Approximation, Representation
Collection: 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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