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Breaking the All Subsets Barrier for Min k-Cut

Authors Daniel Lokshtanov, Saket Saurabh , Vaishali Surianarayanan

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Author Details

Daniel Lokshtanov
  • University of California Santa Barbara, CA, USA
Saket Saurabh
  • The Institute of Mathematical Sciences, HBNI, Chennai, India
  • University of Bergen, Norway
Vaishali Surianarayanan
  • University of California Santa Barbara, CA, USA

Funding

  • Lokshtanov, Daniel: NSF award CCF-2008838.
  • Saurabh, Saket: European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant no. 819416), and Swarnajayanti Fellowship grant DST/SJF/MSA01/2017-18.
  • Surianarayanan, Vaishali: NSF award CCF-2008838.

Cite AsGet BibTex

Daniel Lokshtanov, Saket Saurabh, and Vaishali Surianarayanan. Breaking the All Subsets Barrier for Min k-Cut. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 90:1-90:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ICALP.2023.90

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Exact algorithms
  • min k-cut
  • exponential algorithms
  • graph algorithms
  • k-way cut

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