Abstract
We consider an extension of the classical bin packing problem, motivated by a frequency allocation problem arising in cellular networks. The problem is as follows: Each object has two attributes, weight and fragility. The goal is to pack objects into bins such that, for every bin, the sum of weights of objects in that bin is no more than the fragility of the most fragile object in that bin.
We look for approximation algorithms for this problem. We provide a 2-approximation to the problem of minimizing the number of bins. We also show a lower bound of 3/2. Unlike in traditional bin packing, this bound holds in the asymptotic case. We then consider the approximation with respect to fragility and provide a 2-approximation algorithm. Our algorithm uses the same number of bins as the optimum but the weight of objects in a bin can exceed the fragility by a factor of 2.
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Bansal, N., Liu, Z., Sankar, A. (2002). Bin-Packing with Fragile Objects. In: Baeza-Yates, R., Montanari, U., Santoro, N. (eds) Foundations of Information Technology in the Era of Network and Mobile Computing. IFIP — The International Federation for Information Processing, vol 96. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35608-2_4
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DOI: https://doi.org/10.1007/978-0-387-35608-2_4
Publisher Name: Springer, Boston, MA
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