Consider the following algorithm for bin packing:
- Initially, sort the items by their size.
- Put the largest item in a new bin.
- Fill the bin with small items in ascending order of size, up to the largest item that fits.
- Close the bin. If some items remain, go back to step 1.
There is a very similar algorithm for the dual problem of bin covering, and its approximation ratio for that problem is 3/2. However, I did not find this algorithm discussed in the context of bin packing.
Is anything known about its approximation ratio – how close it is to the optimal solution?