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Approximation preserving reductions for set covering, vertex covering and independent set hierarchies under differential approximation

Ekim, Tinaz; Paschos, Vangelis (2004), Approximation preserving reductions for set covering, vertex covering and independent set hierarchies under differential approximation, International Journal of Computer Mathematics, 81, 5, p. 569-582. http://dx.doi.org/10.1080/00207160410001688592

Type
Article accepté pour publication ou publié
Date
2004
Journal name
International Journal of Computer Mathematics
Volume
81
Number
5
Publisher
Taylor & Francis
Pages
569-582
Publication identifier
Metadata
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Author(s)
Ekim, Tinaz
Paschos, Vangelis
Abstract (EN)
The notion of approximability preserving reductions between different problems deserves special attention in approximability theory. These kinds of reductions allow us polynomial time conversion of some already known 'good' approximation algorithms for some NP-hard problems into ones for some other NP-hard problems. In this context, we consider reductions for set covering and vertex covering hierarchies. Our results are then extended to hitting set and independent set hierarchies. Here, we adopt the differential approximation ratio that has the natural property to be stable under affine transformations of the objective function of a problem.
Subjects / Keywords
Vertex covering; Set covering; Hierarchy; Differential approximation ratio; Approximability preserving reductions