License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/LIPIcs.ESA.2023.93
URN: urn:nbn:de:0030-drops-187466
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18746/
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Schieber, Baruch ; Vahidi, Soroush

Approximating Connected Maximum Cuts via Local Search

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LIPIcs-ESA-2023-93.pdf (0.8 MB)

Abstract

The Connected Max Cut (CMC) problem takes in an undirected graph G(V,E) and finds a subset S ⊆ V such that the induced subgraph G[S] is connected and the number of edges connecting vertices in S to vertices in V⧵S is maximized. This problem is closely related to the Max Leaf Degree (MLD) problem. The input to the MLD problem is an undirected graph G(V,E) and the goal is to find a subtree of G that maximizes the degree (in G) of its leaves. [Gandhi et al. 2018] observed that an α-approximation for the MLD problem induces an ?(α)-approximation for the CMC problem.
We present an ?(log log |V|)-approximation algorithm for the MLD problem via local search. This implies an ?(log log |V|)-approximation algorithm for the CMC problem. Thus, improving (exponentially) the best known ?(log |V|) approximation of the Connected Max Cut problem [Hajiaghayi et al. 2015].

BibTeX - Entry

@InProceedings{schieber_et_al:LIPIcs.ESA.2023.93,
  author =	{Schieber, Baruch and Vahidi, Soroush},
  title =	{{Approximating Connected Maximum Cuts via Local Search}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{93:1--93:17},
  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/2023/18746},
  URN =		{urn:nbn:de:0030-drops-187466},
  doi =		{10.4230/LIPIcs.ESA.2023.93},
  annote =	{Keywords: approximation algorithms, graph theory, max-cut, local search}
}

Keywords: approximation algorithms, graph theory, max-cut, local search
Collection: 31st Annual European Symposium on Algorithms (ESA 2023)
Issue Date: 2023
Date of publication: 30.08.2023

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