Maximizing the number of unused bins
Paschos, Vangelis; Monnot, Jérôme; Demange, Marc (2001), Maximizing the number of unused bins, Foundations of Computing and Decision Sciences, 26, 2, p. 169-186
TypeArticle accepté pour publication ou publié
Journal nameFoundations of Computing and Decision Sciences
Publishing House of Poznan University of Technology
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Abstract (EN)We analyze the approximation behavior of some of the best-known polynomial-time approximation algorithms for bin-packing under an approximation criterion, called differential ratio, informally the ratio (n — where n is the size of the input list, is the size of the solution provided by an approximation algorithm and Beta(I) is the size of the optimal one. This measure has originally been introduced by Ausiello, D'Atri and Protasi and more recently revisited, in a more systematic way, by the first and the third authors of the present paper. Under the differential ratio, bin-packing has a natural formulation as the problem of maximizing the number of unused bins. We first show that two basic fit bin-packing algorithms, the first-fit and the best-fit, admit differential approximation ratios 1/2. Next, we show that slightly improved versions of them achieve ratios 2/3. Refining our analysis we show that the famous first-fit-decreasing and best-fit decreasing algorithms achieve differential approximation ratio 3/4: Finally, we show that first-fit-decreasing achieves asymptotic differential approximation ratio 7/9.
Subjects / KeywordsUnused Bins; bin packing; approximation algorithms
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The hypocoloring problem: complexity and approximability results when the chromatic number is small de Werra, Dominique; Demange, Marc; Monnot, Jérôme; Paschos, Vangelis (2004) Communication / Conférence