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A note on dual approximation algorithms for class constrained bin packing problems

Published online by Cambridge University Press:  21 October 2008

Eduardo C. Xavier  and
Flàvio Keidi Miyazawa
Eduardo C. Xavier
Affiliation:
Institute of Computing, University of Campinas, UNICAMP, P.O. Box 6176, 13083-970, Campinas, SP, Brazil; ecx@ic.unicamp.br; fkm@ic.unicamp.br
Flàvio Keidi Miyazawa
Affiliation:
Institute of Computing, University of Campinas, UNICAMP, P.O. Box 6176, 13083-970, Campinas, SP, Brazil; ecx@ic.unicamp.br; fkm@ic.unicamp.br
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Abstract

In this paper we present a dual approximation scheme for the class constrained shelf bin packing problem. In this problem, we are given bins of capacity 1, and n items of Q different classes, each item e with class ce and size se. The problem is to pack the items into bins, such that two items of different classes packed in a same bin must be in different shelves. Items in a same shelf are packed consecutively. Moreover, items in consecutive shelves must be separated by shelf divisors of size d. In a shelf bin packing problem, we have to obtain a shelf packing such that the total size of items and shelf divisors in any bin is at most 1. A dual approximation scheme must obtain a shelf packing of all items into N bins, such that, the total size of all items and shelf divisors packed in any bin is at most 1 + ε for a given ε > 0 and N is the number of bins used in an optimum shelf bin packing problem. Shelf divisors are used to avoid contact between items of different classes and can hold a set of items until a maximum given weight. We also present a dual approximation scheme for the class constrained bin packing problem. In this problem, there is no use of shelf divisors, but each bin uses at most C different classes.

Keywords

Bin packingapproximation algorithms.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 2 , April 2009 , pp. 239 - 248
Copyright
© EDP Sciences, 2008

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