O(f) Bi-criteria Approximation for Capacitated Covering with Hard Capacities

We consider capacitated vertex cover with hard capacity constraints (VC-HC) on hypergraphs. In this problem we are given a hypergraph G = ( V , E ) with a maximum edge size f . Each edge is associated with a demand and each vertex is associated with a weight (cost), a capacity, and an available mult...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Algorithmica Jg. 81; H. 5; S. 1800 - 1817
Hauptverfasser: Kao, Mong-Jen, Tu, Hai-Lun, Lee, D. T.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 15.05.2019
Springer Nature B.V
Schlagworte:
Algorithm Analysis and Problem Complexity
Algorithms
Apexes
Approximation
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Graph theory
Mathematical analysis
Mathematics of Computing
Minimum weight
Theory of Computation
Hard capacities
Capacitated covering
Bi-criteria approximation
ISSN:0178-4617, 1432-0541
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We consider capacitated vertex cover with hard capacity constraints (VC-HC) on hypergraphs. In this problem we are given a hypergraph G = ( V , E ) with a maximum edge size f . Each edge is associated with a demand and each vertex is associated with a weight (cost), a capacity, and an available multiplicity. The objective is to find a minimum-weight vertex multiset such that the demands of the edges can be covered by the capacities of the vertices and the multiplicity of each vertex does not exceed its available multiplicity. In this paper we present an O ( f ) bi-criteria approximation for VC-HC that gives a trade-off on the number of augmented multiplicity and the cost of the resulting cover. In particular, we show that, by augmenting the available multiplicity by a factor of k ≥ 2 , a cover with a cost ratio of 1 + 1 k - 1 ( f - 1 ) to the optimal cover for the original instance can be obtained. This improves over the previously best known guarantee, which has a cost ratio of f 2 via augmenting the available multiplicity by a factor of f .
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-018-0506-6