Update and Paging Rules

In this article we study the amortized efficiency of the “move-to-front” and similar rules for dynamically maintaining a linear list. Under the assumption that accessing the i th element from the front of the list takes e(i) time, we show that move-to-front is within a constant factor of optimum among a wide class of list maintenance rules. Other natural heuristics, such as the transpose and frequency count rules, do not share this property. We generalize our results to show that move-to-front is within a constant factor of optimum as long as the access cost is a convex function. We also study paging, a setting in which the access cost is not convex. The paging rule corresponding to move-to-front is the “least recently used“ replacement rule. We analyze the amortized complexity of LRU, showing that its efficiency differs from that of the offline paging rule (Belady’s MlN algorithm) by a factor that depends on the size of fast memory. No on-line paging algorithm has better amortized performance.