# The Best Two-Phase Algorithm for Bin Stretching

@article{Bhm2016TheBT, title={The Best Two-Phase Algorithm for Bin Stretching}, author={Martin B{\"o}hm and Jir{\'i} Sgall and Rob van Stee and Pavel Vesel{\'y}}, journal={ArXiv}, year={2016}, volume={abs/1601.08111} }

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. We also show that this approach cannot give better…

## 2 Citations

A two-phase algorithm for bin stretching with stretching factor 1.5

- Computer ScienceJ. Comb. Optim.
- 2017

This work gives an algorithm for Online Bin Stretching with a stretching factor of 1.5 for any number of bins and uses amortization over the bins with the help of two weight functions.

Online bin stretching with three bins

- Computer ScienceJ. Sched.
- 2017

An algorithm for online bin stretching is given with a stretching factor of 11/8 = 1.375 for three bins and a lower bound of 19/14 for four and five bins that were discovered using a computer search.

## References

SHOWING 1-10 OF 18 REFERENCES

Online bin stretching with three bins

- Computer ScienceJ. Sched.
- 2017

An algorithm for online bin stretching is given with a stretching factor of 11/8 = 1.375 for three bins and a lower bound of 19/14 for four and five bins that were discovered using a computer search.

Better Algorithms for Online Bin Stretching

- Computer ScienceWAOA
- 2014

Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as the optimal packing, but is allowed to slightly overpack the bins. The goal…

Semi-Online Bin Stretching with Bunch Techniques

- Computer Science
- 2013

An algorithm with stretching factor 26/17 is presented improving the best known algorithm by Kellerer and Kotov with a stretching factor 11/7 with the goal of assigning items online tom bins while minimizing the stretching factor.

Computing Lower Bounds for Semi-Online Optimization Problems: Application to the Bin Stretching

- Computer Science
- 2013

Game theory techniques are used to automatically compute improved lower bounds on the competitive ratio for the bin stretching problem and it is shown that this technique can be generalized to compute lower bounds for any online or semi-online packing or scheduling problem.

Improved lower bounds for the online bin stretching problem

- Computer Science, Mathematics4OR
- 2017

Game theory techniques are used to automatically compute improved lower bounds on the competitive ratio for the bin stretching problem and this technique can be generalized to compute lower bounds for any online or semi-online packing or scheduling problem.

Preemptive Online Scheduling: Optimal Algorithms for All Speeds

- Computer ScienceAlgorithmica
- 2008

Our main result is an optimal online algorithm for preemptive scheduling on uniformly related machines with the objective to minimize makespan. The algorithm is deterministic, yet it is optimal even…