Optimal deterministic competitive ratio for paging with delay

Determine the optimal deterministic competitive ratio for paging with delay on at least k+2 pages, thereby resolving the gap between the lower bound of 2k+1 and the upper bound of 2k+2 and establishing whether a ratio of 2k+1 is attainable by an online algorithm outside the fixed-threshold class.

Background

The paper studies online paging with delay, in which a cache of size k serves page requests while allowing requests to be delayed at an accumulated delay cost. The authors establish a deterministic upper bound of 2k+2 for a threshold-triggered FIFO algorithm on universes with at least k+2 pages, while the known general lower bound is 2k+1.

The fixed-threshold FIFO upper bound is shown to be tight within that algorithmic class, and fixed-threshold algorithms are further shown to have competitive ratio at least 2k+3/2. Consequently, achieving the lower bound of 2k+1, if possible, would require an algorithm outside the fixed-threshold class. The paper notes that even for k=2 and n=4, the optimal ratio remains unresolved between 5 and 6.