2026-07-21T12:57:57Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:9431 2024-03-06T10:44:22Z ddc:004 open_access

An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity Wei, Hao-Ting Hon, Wing-Kai Horn, Paul Liao, Chung-Shou Sadakane, Kunihiko approximation algorithm dynamic algorithm primal-dual vertex cover 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Hao-Ting Wei and Wing-Kai Hon and Paul Horn and Chung-Shou Liao and Kunihiko Sadakane 2018 Is Part Of LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX-RANDOM.2018.27 urn:nbn:de:0030-drops-94312 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.27 eng https://creativecommons.org/licenses/by/3.0/legalcode