A two-phase algorithm for bin stretching with stretching factor 1.5
- 135 Downloads
Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin.We give an algorithm for Online Bin Stretching with a stretching factor of 1.5 for any number of bins. We build on previous algorithms and use a two-phase approach. However, our analysis is technically more complicated and uses amortization over the bins with the help of two weight functions.
KeywordsOnline algorithms Bin packing Scheduling
The authors thank Emese Bittner for useful discussions during her visit to Charles University. We also thank to referees for many useful comments.
- Azar Y, Regev O.(1998)On-line bin-stretching. In: Proceedings of randomization and approximation techniques in computer science (RANDOM). Springer, pp 71–81Google Scholar
- Böhm M, Sgall J, van Stee R, Veselý P (2015) Better algorithms for online bin stretching. In: Proceedings of the 12th workshop on approximation and online algorithms (WAOA 2014), Lecture Notes in Computer Science 8952. Springer, pp 23–34Google Scholar
- Böhm M, Sgall J, van Stee R, Veselý P (2016) Online bin stretching with three bins. arXiv preprint arXiv:1404.5569v3
- Gabay M, Brauner N, Kotov V (2013) Computing lower bounds for semi-online optimization problems: application to the bin stretching problem. HAL preprint hal-00921663, version 2Google Scholar
- Gabay M, Brauner N, Kotov V (2015) Improved lower bounds for the online bin stretching problem. HAL preprint hal-00921663, version 3Google Scholar
- Gabay M, Kotov V, Brauner N (2013) Semi-online bin stretching with bunch techniques. HAL preprint hal-00869858Google Scholar
- Johnson D (1973) Near-optimal bin packing algorithms. Massachusetts Institute of Technology Technical Report MAC TR-109, Project MAC, Cambridge, MassachusettsGoogle Scholar
- Pruhs K, Sgall J, Torng E (2004) Online scheduling. In: Leung JY-T (ed) Handbook of scheduling: algorithms, models, and performance analysis, chapter 15. CRC Press, Boca Raton, pp 15-1–15-41Google Scholar
- Ullman J (1971) The performance of a memory allocation algorithm. Technical Report 100Google Scholar