An improved algorithm for online rectangle filling

We consider the problem of scheduling resource allocation where a change in allocation results in a changeover penalty of one time slot. We assume that we are sending packets over a wireless channel of uncertain and varying capacity. In each time slot, a bandwidth of at most the current capacity can be allocated, but changing the capacity has a cost, which is modeled as an empty time slot. Only the current bandwidth and the bandwidth of the immediately following slot are known. We give an online algorithm with competitive ratio 1.753 for this problem, improving over the previous upper bound of 1.848. The main new idea of our algorithm is that it attempts to avoid cases where a single time slot with a nonzero allocation is immediately followed by an empty time slot. Additionally, we improve the lower bound for this problem to 1.6959, and give a better randomized lower bound. Our results significantly narrow the gap between the best known upper and lower bounds.