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.ESA.2023.32
URN: urn:nbn:de:0030-drops-186854
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18685/
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Carlson, Charlie ; Jafarov, Jafar ; Makarychev, Konstantin ; Makarychev, Yury ; Shan, Liren

Approximation Algorithm for Norm Multiway Cut

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LIPIcs-ESA-2023-32.pdf (0.6 MB)

Abstract

We consider variants of the classic Multiway Cut problem. Multiway Cut asks to partition a graph G into k parts so as to separate k given terminals. Recently, Chandrasekaran and Wang (ESA 2021) introduced ?_p-norm Multiway Cut, a generalization of the problem, in which the goal is to minimize the ?_p norm of the edge boundaries of k parts. We provide an O(log^{1/2} nlog^{1/2+1/p} k) approximation algorithm for this problem, improving upon the approximation guarantee of O(log^{3/2} n log^{1/2} k) due to Chandrasekaran and Wang.
We also introduce and study Norm Multiway Cut, a further generalization of Multiway Cut. We assume that we are given access to an oracle, which answers certain queries about the norm. We present an O(log^{1/2} n log^{7/2} k) approximation algorithm with a weaker oracle and an O(log^{1/2} n log^{5/2} k) approximation algorithm with a stronger oracle. Additionally, we show that without any oracle access, there is no n^{1/4-ε} approximation algorithm for every ε > 0 assuming the Hypergraph Dense-vs-Random Conjecture.

BibTeX - Entry

@InProceedings{carlson_et_al:LIPIcs.ESA.2023.32,
  author =	{Carlson, Charlie and Jafarov, Jafar and Makarychev, Konstantin and Makarychev, Yury and Shan, Liren},
  title =	{{Approximation Algorithm for Norm Multiway Cut}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{32:1--32:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18685},
  URN =		{urn:nbn:de:0030-drops-186854},
  doi =		{10.4230/LIPIcs.ESA.2023.32},
  annote =	{Keywords: Multiway cut, Approximation algorithms}
}

Keywords: Multiway cut, Approximation algorithms
Collection: 31st Annual European Symposium on Algorithms (ESA 2023)
Issue Date: 2023
Date of publication: 30.08.2023

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