A note on dual approximation algorithms for class constrained bin packing problems
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 239-248.

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 c e and size s e . 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.

DOI : https://doi.org/10.1051/ita:2008027
Classification : 68W25
Mots clés : bin packing, approximation algorithms
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     title = {A note on dual approximation algorithms for class constrained bin packing problems},
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Xavier, Eduardo C.; Miyazawa, Flàvio Keidi. A note on dual approximation algorithms for class constrained bin packing problems. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 239-248. doi : 10.1051/ita:2008027. http://www.numdam.org/articles/10.1051/ita:2008027/

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