eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-13
27:1
27:14
10.4230/LIPIcs.APPROX-RANDOM.2018.27
article
An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity
Wei, Hao-Ting
1
Hon, Wing-Kai
2
Horn, Paul
3
Liao, Chung-Shou
1
Sadakane, Kunihiko
4
Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu 30013, Taiwan
Department of Computer Science, National Tsing Hua University, Hsinchu 30013, Taiwan
Department of Mathematics, University of Denver, Denver, USA
Department of Mathematical Informatics, The University of Tokyo, Tokyo, Japan
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol116-approx-random2018/LIPIcs.APPROX-RANDOM.2018.27/LIPIcs.APPROX-RANDOM.2018.27.pdf
approximation algorithm
dynamic algorithm
primal-dual
vertex cover