Fully Dynamic Bin Packing Revisited

Sebastian Berndt, Klaus Jansen, Kim-Manuel Klein


We consider the fully dynamic bin packing problem, where items arrive and depart in an online fashion and repacking of previously packed items is allowed. The goal is, of course, to minimize both the number of bins used as well as the amount of repacking. A recently introduced way of measuring the repacking costs at each timestep is the migration factor, defined as the total size of repacked items divided by the size of an arriving or departing item. Concerning the trade-off between number of bins and migration factor, if we wish to achieve an asymptotic competitive ratio of 1 + epsilon for the number of bins, a relatively simple argument proves a lower bound of Omega(1/epsilon) of the migration factor. We establish a fairly close upper bound of O(1/epsilon^4 log(1/epsilon)) using a new dynamic rounding technique and new ideas to handle small items in a dynamic setting such that no amortization is needed. The running time of our algorithm is polynomial in the number of items n and in 1/epsilon. The previous best trade-off was for an asymptotic competitive ratio of 5/4 for the bins (rather than 1+epsilon) and needed an amortized number of O(log n) repackings (while in our scheme the number of repackings is independent of n and non-amortized).
Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)
EditorsNaveen Garg, Klaus Jansen, Anup Rao, José D. P. Rolim
Number of pages17
Place of PublicationDagstuhl, Germany
PublisherSchloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Publication date14.01.2015
ISBN (Print)978-3-939897-89-7
Publication statusPublished - 14.01.2015
EventApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)
- Princeton University , Princeton, United States
Duration: 24.08.201526.08.2015


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