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.2021.29
URN: urn:nbn:de:0030-drops-146103
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Chandrasekaran, Karthekeyan ; Wang, Weihang

?_p-Norm Multiway Cut

LIPIcs-ESA-2021-29.pdf (0.8 MB)


We introduce and study ?_p-norm-multiway-cut: the input here is an undirected graph with non-negative edge weights along with k terminals and the goal is to find a partition of the vertex set into k parts each containing exactly one terminal so as to minimize the ?_p-norm of the cut values of the parts. This is a unified generalization of min-sum multiway cut (when p = 1) and min-max multiway cut (when p = ∞), both of which are well-studied classic problems in the graph partitioning literature. We show that ?_p-norm-multiway-cut is NP-hard for constant number of terminals and is NP-hard in planar graphs. On the algorithmic side, we design an O(log² n)-approximation for all p ≥ 1. We also show an integrality gap of Ω(k^{1-1/p}) for a natural convex program and an O(k^{1-1/p-ε})-inapproximability for any constant ε > 0 assuming the small set expansion hypothesis.

BibTeX - Entry

  author =	{Chandrasekaran, Karthekeyan and Wang, Weihang},
  title =	{{?\underlinep-Norm Multiway Cut}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{29:1--29:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-146103},
  doi =		{10.4230/LIPIcs.ESA.2021.29},
  annote =	{Keywords: multiway cut, approximation algorithms}

Keywords: multiway cut, approximation algorithms
Collection: 29th Annual European Symposium on Algorithms (ESA 2021)
Issue Date: 2021
Date of publication: 31.08.2021

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