z-Approximations

Hassin, Refael; Khuller, Samir

doi:10.1006/jagm.2001.1187

Cited by 57 publications

(61 citation statements)

References 35 publications

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“…For this special case of the COLOR SAVING PROBLEM with a single weight there are approximation algorithms that guarantee at least 1 [8] of the maximum possible saving. It has been observed in [10] that the same bounds also apply to the more general problem of packingsets in an independent system. (Only [14] specifically uses the structure of the node coloring problem in a graph.)…”

Section: Introductionmentioning

confidence: 75%

The maximum saving partition problem

Hassin¹,

Monnot²

2005

Operations Research Letters

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Section: Introductionmentioning

confidence: 75%

The maximum saving partition problem

Hassin¹,

Monnot²

2005

Operations Research Letters

Self Cite

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“…Worst solution for minimum graph-coloring consists of giving to each vertex of the input graph an unused color ( [11,12,14,15]). For probabilistic coloring, the value ω(G) of such solution is equal to v i ∈V p i .…”

Section: Differential Approximationmentioning

confidence: 99%

Probabilistic graph-coloring in bipartite and split graphs

et al. 2007

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“…The approximation ratio of a solution for complementary set cover can be thought of as comparing the "distance" of a solution for set cover from the worst possible solution (i.e., the one that uses n sets to cover the elements) to the distance of the best solution of the worst possible one. This yields an alternative performance measure for the analysis of approximation algorithms; such measures have been considered for many combinatorial optimization problems in the context of differential approximation algorithms [10,9] or z-approximations [16] (see also [3,4]). Duh and Fürer [11] also consider the application of their algorithm on instances of complementary set cover in which the collection of sets is not given explicitly.…”

Section: Introductionmentioning

confidence: 99%

An Improved Approximation Bound for Spanning Star Forest and Color Saving

Athanassopoulos

Caragiannis

Kaklamanis

et al. 2009

Mathematical Foundations of Computer Science 2009

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Abstract. We present a simple algorithm for the maximum spanning star forest problem. We take advantage of the fact that the problem is a special case of complementary set cover and we adapt an algorithm of Duh and Fürer in order to solve it. We prove that this algorithm computes 193/240 ≈ 0.804-approximate spanning star forests; this result improves a previous lower bound of 0.71 by Chen et al. Although the algorithm is purely combinatorial, our analysis defines a linear program that uses a parameter f and which is feasible for values of the parameter f not smaller than the approximation ratio of the algorithm. The analysis is tight and, interestingly, it also applies to complementary versions of set cover such as color saving; it yields the same approximation guarantee of 193/240 that marginally improves the previously known upper bound of Duh and Fürer. We also show that, in general, a natural class of local search algorithms do not provide better than 1/2-approximate spanning star forests.

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z-Approximations

Cited by 57 publications

References 35 publications

The maximum saving partition problem

The maximum saving partition problem

Probabilistic graph-coloring in bipartite and split graphs

An Improved Approximation Bound for Spanning Star Forest and Color Saving

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