Bin packing with “Largest In Bottom” constraint: tighter bounds and generalizations

Gyorgy Dosa (), Zsolt Tuza () and Deshi Ye ()
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Gyorgy Dosa: University of Pannonia
Zsolt Tuza: Hungarian Academy of Sciences
Deshi Ye: Zhejiang University

Journal of Combinatorial Optimization, 2013, vol. 26, issue 3, No 2, 416-436

Abstract: Abstract The (online) bin packing problem with LIB constraint is stated as follows: The items arrive one by one, and must be packed into unit capacity bins, but a bigger item cannot be packed into a bin which already contains a smaller item. The number of used bins has to be minimized as usually. We show that the absolute performance bound of algorithm First Fit is not worse than 2+1/6≈2.1666 for the problem, improving the previous best upper bound 2.5. Moreover, if the item sizes do not exceed 1/d, then we improve the previous best result 2+1/d to 2+1/d(d+2), for any d≥2. (Both previously best results are due to Epstein, Nav. Res. Logist. 56(8):780–786, 2009.) Furthermore, we define a problem with the generalized LIB constraint, where some incoming items cannot be packed into the bins of some already packed items. The (in)compatibility of the incoming item with the items already packed becomes known only at the arrival of the actual item, and is given by an undirected graph (and, as usual in case of online graph problems, we can see only that part of the graph what already arrived). We show that 3 is an upper bound for this general problem if some natural transitivity constraint is satisfied.

Keywords: Bin packing; LIB constraint; Incompatibility graph (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10878-011-9408-0

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