New classes of fast lower bounds for bin packing problems. Fekete, S. P. & Schepers, J. Mathematical Programming, 91(1):11--31, October, 2001.
Paper doi abstract bibtex Abstract. The bin packing problem is one of the classical NP-hard optimization problems. In this paper, we present a simple generic approach for obtaining new fast lower bounds, based on dual feasible functions. Worst-case analysis as well as computational results show that one of our classes clearly outperforms the previous best “economical” lower bound for the bin packing problem by Martello and Toth, which can be understood as a special case. In particular, we prove an asymptotic worst-case performance of 3/4 for a bound that can be computed in linear time for items sorted by size. In addition, our approach provides a general framework for establishing new bounds.
@article{fekete_new_2001,
title = {New classes of fast lower bounds for bin packing problems},
volume = {91},
url = {http://dx.doi.org/10.1007/s101070100243},
doi = {10.1007/s101070100243},
abstract = {Abstract. The bin packing problem is one of the classical NP-hard optimization problems. In this paper, we present a simple generic
approach for obtaining new fast lower bounds, based on dual feasible functions. Worst-case analysis as well as computational
results show that one of our classes clearly outperforms the previous best “economical” lower bound for the bin packing problem
by Martello and Toth, which can be understood as a special case. In particular, we prove an asymptotic worst-case performance
of 3/4 for a bound that can be computed in linear time for items sorted by size. In addition, our approach provides a general
framework for establishing new bounds.},
number = {1},
urldate = {2010-04-02TZ},
journal = {Mathematical Programming},
author = {Fekete, Sándor P. and Schepers, Jörg},
month = oct,
year = {2001},
pages = {11--31}
}
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