An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity
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.
approximation algorithm
dynamic algorithm
primal-dual
vertex cover
Theory of computation~Dynamic graph algorithms
27:1-27:14
Regular Paper
https://arxiv.org/abs/1802.05623
Hao-Ting
Wei
Hao-Ting Wei
Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu 30013, Taiwan
Wing-Kai
Hon
Wing-Kai Hon
Department of Computer Science, National Tsing Hua University, Hsinchu 30013, Taiwan
Paul
Horn
Paul Horn
Department of Mathematics, University of Denver, Denver, USA
Supported by NSA Young Investigator Grant H98230-15-1-0258, and Simons Collaboration Grant #525039.
Chung-Shou
Liao
Chung-Shou Liao
Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu 30013, Taiwan
Supported by MOST Taiwan under Grants MOST105-2628-E-007-010-MY3 and MOST105-2221-E-007-085-MY3.
Kunihiko
Sadakane
Kunihiko Sadakane
Department of Mathematical Informatics, The University of Tokyo, Tokyo, Japan
10.4230/LIPIcs.APPROX-RANDOM.2018.27
Hao-Ting Wei, Wing-Kai Hon, Paul Horn, Chung-Shou Liao, and Kunihiko Sadakane
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode