Abstract
We study parallel online algorithms: For some fixed integer k, a collective of k parallel processes that perform online decisions on the same sequence of events forms a k-copy algorithm. For any given time and input sequence, the overall performance is determined by the best of the k individual total results. Problems of this type have been considered for online makespan minimization; they are also related to optimization with advice on future events, i.e., a number of bits available in advance.
We develop Predictive Harmonic\(_3\) (PH3), a relatively simple family of k-copy algorithms for the online Bin Packing Problem, whose joint competitive factor converges to 1.5 for increasing k. In particular, we show that \(k=6\) suffices to guarantee a factor of 1.5714 for PH3, which is better than 1.57829, the performance of the best known 1-copy algorithm Advanced Harmonic, while \(k=11\) suffices to achieve a factor of 1.5406, beating the known lower bound of 1.54278 for a single online algorithm. In the context of online optimization with advice, our approach implies that 4 bits suffice to achieve a factor better than this bound of 1.54278, which is considerably less than the previous bound of 15 bits.
A full version is available on arxiv.org [10].
Phillip Keldenich was partially supported by DFG grant FE407/17-2 as part of the Research Group FOR 1800, “Controlling Concurrent Change”.
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Notes
- 1.
The intuition of this value is that at least 1/2 of each 1/3-sub-bin must be filled to guarantee a packing density of 2/3. Therefore, for \(|I_L|\) bins, we have to fill up a total capacity of \(\frac{|I_L|}{6}\) with small items.
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Fekete, S.P., Grosse-Holz, J., Keldenich, P., Schmidt, A. (2020). Parallel Online Algorithms for the Bin Packing Problem. In: Bampis, E., Megow, N. (eds) Approximation and Online Algorithms. WAOA 2019. Lecture Notes in Computer Science(), vol 11926. Springer, Cham. https://doi.org/10.1007/978-3-030-39479-0_8
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