2018/02/15 by Hao-Ting Wei, Wei, Hao-Ting, Wing-Kai Hon +7
Computer Science · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #cs.DS
paper · pdf · doi:10.48550/arxiv.1802.05623
arxiv created 2018/02/20 · arxiv updated 2018/02/21
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 / ε) 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 nonuniform and unsplittable demand, and (2) the more general capacitated set cover problem.