An improved algorithm for online rectangle filling

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.
Our results significantly narrow the gap between the best known
upper and lower bound.