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Algorithmica

, Volume 81, Issue 5, pp 1800–1817 | Cite as

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

  • Mong-Jen KaoEmail author
  • Hai-Lun Tu
  • D. T. Lee
Article
  • 42 Downloads

Abstract

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 \(k \ge 2\), a cover with a cost ratio of \(\left( 1+\frac{1}{k-1}\right) (f-1)\) 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.

Keywords

Capacitated covering Hard capacities Bi-criteria approximation 

Notes

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer Science and Information EngineeringNational Chung-Cheng UniversityChiayiTaiwan
  2. 2.Department of Computer Science and Information EngineeringNational Taiwan UniversityTaipeiTaiwan
  3. 3.Institute of Information ScienceAcademia SinicaTaipeiTaiwan

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