Parallel Online Algorithms for the Bin Packing Problem
Abstract
We study \emph{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 $k$-\emph{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 \emph{advice} on future events, i.e., a number of bits available in advance. We develop \textsc{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 \textsc{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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2019
- DOI:
- 10.48550/arXiv.1910.03249
- arXiv:
- arXiv:1910.03249
- Bibcode:
- 2019arXiv191003249F
- Keywords:
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- Computer Science - Data Structures and Algorithms