Wei, HaoTing ;
Hon, WingKai ;
Horn, Paul ;
Liao, ChungShou ;
Sadakane, Kunihiko
An O(1)Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity
Abstract
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 vertexweighted 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 primaldual algorithm for maintaining a constantfactor 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 nonuniform and unsplittable demand, and (2) the more general capacitated set cover problem.
BibTeX  Entry
@InProceedings{wei_et_al:LIPIcs:2018:9431,
author = {HaoTing Wei and WingKai Hon and Paul Horn and ChungShou Liao and Kunihiko Sadakane},
title = {{An O(1)Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
pages = {27:127:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770859},
ISSN = {18688969},
year = {2018},
volume = {116},
editor = {Eric Blais and Klaus Jansen and Jos{\'e} D. P. Rolim and David Steurer},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9431},
URN = {urn:nbn:de:0030drops94312},
doi = {10.4230/LIPIcs.APPROXRANDOM.2018.27},
annote = {Keywords: approximation algorithm, dynamic algorithm, primaldual, vertex cover}
}
13.08.2018
Keywords: 

approximation algorithm, dynamic algorithm, primaldual, vertex cover 
Seminar: 

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Issue date: 

2018 
Date of publication: 

13.08.2018 