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

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

Beteiligte: Wei, Hao-Ting [VerfasserIn]; Hon, Wing-Kai [VerfasserIn]; Horn, Paul [VerfasserIn]; Liao, Chung-Shou [VerfasserIn]; Sadakane, Kunihiko [VerfasserIn]

Erschienen: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2018

Sprache: Englisch

DOI: https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2018.27

Schlagwörter: dynamic algorithm ; primal-dual ; approximation algorithm ; vertex cover

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Beschreibung: 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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