文章基本信息

标题：An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity
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作者：Hao-Ting Wei ; Wing-Kai Hon ; Paul Horn 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2018
卷号：116
页码：1-14
DOI：10.4230/LIPIcs.APPROX-RANDOM.2018.27
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：approximation algorithm; dynamic algorithm; primal-dual; vertex cover