An improved lower bound for on-line bin packing algorithms
Information Processing Letters
On the hardness of approximating minimization problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Approximation algorithms for time constrained scheduling
Information and Computation
Online computation and competitive analysis
Online computation and competitive analysis
On the online bin packing problem
Journal of the ACM (JACM)
Approximation lower bounds in online LIB bin packing and covering
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the 13th Australasian workshop on combinatorial algorithms
Tighter bounds of the First Fit algorithm for the bin-packing problem
Discrete Applied Mathematics
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Multi-dimensional packing with conflicts
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
The tight bound of first fit decreasing bin-packing algorithm is FFD(I) ≤ 11/9OPT(I) + 6/9
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
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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驴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驴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.