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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.27
An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity

Authors: Hao-Ting Wei, Wing-Kai Hon, Paul Horn, Chung-Shou Liao, and Kunihiko Sadakane

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

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.
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Hao-Ting Wei, Wing-Kai Hon, Paul Horn, Chung-Shou Liao, and Kunihiko Sadakane. An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{wei_et_al:LIPIcs.APPROX-RANDOM.2018.27,
  author =	{Wei, Hao-Ting and Hon, Wing-Kai and Horn, Paul and Liao, Chung-Shou and Sadakane, Kunihiko},
  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 =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.27},
  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}
}
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