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.2023.90
URN: urn:nbn:de:0030-drops-181422
URL: https://drops.dagstuhl.de/opus/volltexte/2023/18142/
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Lokshtanov, Daniel ; Saurabh, Saket ; Surianarayanan, Vaishali

Breaking the All Subsets Barrier for Min k-Cut

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LIPIcs-ICALP-2023-90.pdf (1 MB)


Abstract

In the Min k-Cut problem, the input is a graph G and an integer k. The task is to find a partition of the vertex set of G into k parts, while minimizing the number of edges that go between different parts of the partition. The problem is NP-complete, and admits a simple 3ⁿ⋅n^𝒪(1) time dynamic programming algorithm, which can be improved to a 2ⁿ⋅n^𝒪(1) time algorithm using the fast subset convolution framework by Björklund et al. [STOC'07]. In this paper we give an algorithm for Min k-Cut with running time 𝒪((2-ε)ⁿ), for ε > 10^{-50}. This is the first algorithm for Min k-Cut with running time 𝒪(cⁿ) for c < 2.

BibTeX - Entry

@InProceedings{lokshtanov_et_al:LIPIcs.ICALP.2023.90,
  author =	{Lokshtanov, Daniel and Saurabh, Saket and Surianarayanan, Vaishali},
  title =	{{Breaking the All Subsets Barrier for Min k-Cut}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{90:1--90:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18142},
  URN =		{urn:nbn:de:0030-drops-181422},
  doi =		{10.4230/LIPIcs.ICALP.2023.90},
  annote =	{Keywords: Exact algorithms, min k-cut, exponential algorithms, graph algorithms, k-way cut}
}

Keywords: Exact algorithms, min k-cut, exponential algorithms, graph algorithms, k-way cut
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023


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