License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.27
URN: urn:nbn:de:0030-drops-94312
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9431/
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Wei, Hao-Ting ; Hon, Wing-Kai ; Horn, Paul ; Liao, Chung-Shou ; Sadakane, Kunihiko

An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity

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Abstract

This study considers the soft capacitated vertex cover problem in a dynamic setting. This problem generalizes the dynamic model of the vertex cover problem, which has been intensively studied in recent years. Given a dynamically changing vertex-weighted graph G=(V,E), which allows edge insertions and edge deletions, the goal is to design a data structure that maintains an approximate minimum vertex cover while satisfying the capacity constraint of each vertex. That is, when picking a copy of a vertex v in the cover, the number of v's incident edges covered by the copy is up to a given capacity of v. We extend Bhattacharya et al.'s work [SODA'15 and ICALP'15] to obtain a deterministic primal-dual algorithm for maintaining a constant-factor approximate minimum capacitated vertex cover with O(log n / epsilon) amortized update time, where n is the number of vertices in the graph. The algorithm can be extended to (1) a more general model in which each edge is associated with a non-uniform and unsplittable demand, and (2) the more general capacitated set cover problem.

BibTeX - Entry

@InProceedings{wei_et_al:LIPIcs:2018:9431,
  author =	{Hao-Ting Wei and Wing-Kai Hon and Paul Horn and Chung-Shou Liao and Kunihiko Sadakane},
  title =	{{An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity}},
  booktitle =	{Approximation, Randomization, and Combinatorial  Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Eric Blais and Klaus Jansen and Jos{\'e} D. P. Rolim and David Steurer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9431},
  URN =		{urn:nbn:de:0030-drops-94312},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.27},
  annote =	{Keywords: approximation algorithm, dynamic algorithm, primal-dual, vertex cover}
}

Keywords: approximation algorithm, dynamic algorithm, primal-dual, vertex cover
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)
Issue Date: 2018
Date of publication: 13.08.2018

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