Friendly Bin Packing Instances without Integer Round-up Property
Alberto Caprara, Mauro Dell'Amico, José Carlos Díaz Díaz, Manuel Iori and Romeo Rizzi
Abstract
It is well known that the gap between the optimal values of bin packing and fractional bin packing,
if the latter is rounded up to the closest integer, is almost always null. Known counterexamples
to this for integer input values involve fairly large numbers. Specifically, the first one was
derived in 1986 and involved a bin capacity of the order of a billion. Later in 1998 a counterexample
with a bin capacity of the order of a million was found. In this paper we show a large number of
counterexamples with bin capacity of the order of a hundred, showing that the gap may be positive
even for numbers which arise in customary applications. The associated instances are constructed
starting from the Petersen graph and using the fact that it is fractionally, but not integrally,
3-edge colorable.
Bibtex
@ARTICLE{CDDIR14,
AUTHOR = "Caprara, A. and Dell'Amico, M. and D\'iaz D\'iaz, J.C.
and Iori, M. and Rizzi, R.",
TITLE = "Friendly Bin Packing Instances without Integer Round-up Property",
JOURNAL = "Mathematical Programming Series A and B",
YEAR = 2014,
DOI = "10.1007/s10107-014-0791-z"
}