Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Duan, Ran; He, Haoqing; Zhang, Tianyi https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-124487
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A Scaling Algorithm for Weighted f-Factors in General Graphs

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Abstract

We study the maximum weight perfect f-factor problem on any general simple graph G = (V,E,ω) with positive integral edge weights w, and n = |V|, m = |E|. When we have a function f:V → ℕ_+ on vertices, a perfect f-factor is a generalized matching so that every vertex u is matched to exactly f(u) different edges. The previous best results on this problem have running time O(m f(V)) [Gabow 2018] or Õ(W(f(V))^2.373)) [Gabow and Sankowski 2013], where W is the maximum edge weight, and f(V) = ∑_{u ∈ V}f(u). In this paper, we present a scaling algorithm for this problem with running time Õ(mn^{2/3} log W). Previously this bound is only known for bipartite graphs [Gabow and Tarjan 1989]. The advantage is that the running time is independent of f(V), and consequently it breaks the Ω(mn) barrier for large f(V) even for the unweighted f-factor problem in general graphs.

BibTeX - Entry

@InProceedings{duan_et_al:LIPIcs:2020:12448,
  author =	{Ran Duan and Haoqing He and Tianyi Zhang},
  title =	{{A Scaling Algorithm for Weighted f-Factors in General Graphs}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{41:1--41:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12448},
  URN =		{urn:nbn:de:0030-drops-124487},
  doi =		{10.4230/LIPIcs.ICALP.2020.41},
  annote =	{Keywords: Scaling Algorithm, f-Factors, General Graphs}
}

Keywords: Scaling Algorithm, f-Factors, General Graphs
Seminar: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue date: 2020
Date of publication: 29.06.2020


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