Computing Lower Bounds for Online Optimization Problems: Application to the Bin~Stretching Problem

We use game theory techniques to automatically compute improved lower bounds on the competitive ratio for the bin stretching problem. Using these techniques, we raise the best lower bound for this problem to 19/14. We explain the technique and show that it can be generalized to compute lower bounds for any online or semi-online packing or scheduling problem. We also present a first lower bound, with value 7/6, on the expected competitive ratio of randomized algorithms for the bin stretching problem.