Parallel Online Algorithms for the Bin Packing Problem
- 85 Downloads
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.
KeywordsOnline algorithms Bin packing Competitive analysis
- 3.Balogh, J., Békési, J., Dósa, G., Epstein, L., Levin, A.: A new and improved algorithm for online bin packing. In: 26th Annual European Symposium on Algorithms (ESA 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2018)Google Scholar
- 4.Balogh, J., Békési, J., Dósa, G., Epstein, L., Levin, A.: A new lower bound for classic online bin packing. arXiv preprint arXiv:1807.05554 (2018). (To appear at 17th Workshop on Approximation and Online Algorithms (WAOA))
- 8.Brown, D.M.: A lower bound for on-line one-dimensional bin packing algorithms. Technical report (1979)Google Scholar
- 10.Fekete, S.P., Grosse-Holz, J., Keldenich, P., Schmidt, A.: Parallel online algorithms for the bin packing problem (2019). arXiv preprint (1910.03249)Google Scholar
- 12.Heydrich, S., van Stee, R.: Beating the harmonic lower bound for online bin packing. In: The 43rd International Colloquium on Automata, Languages, and Programming (ICALP), pp. 41:1–41:14 (2016)Google Scholar
- 14.Kamali, S., Ortiz, A.L.: Better compression through better list update algorithms. In: 2014 Data Compression Conference, pp. 372–381 (2014)Google Scholar