  We design efficient and robust algorithms for the batch posting of rollup
chain calldata on the base layer chain, using tools from operations research.
We relate the costs of posting and delaying, by converting them to the same
units and adding them up. The algorithm that keeps the average and maximum
queued number of batches tolerable enough improves the posting costs of the
trivial algorithm, which posts batches immediately when they are created, by
8%. On the other hand, the algorithm that only cares moderately about the batch
queue length can improve the trivial algorithm posting costs by 29%. Our
findings can be used by layer two projects that post data to the base layer at
some regular rate.
