OnlineMin: A Fast Strongly Competitive Randomized Paging Algorithm

Abstract

Abstract. In the field of online algorithms paging is one of the most studied problems. For randomized paging algorithms a tight bound of H k on the competitive ratio has been known for decades, yet existing algorithms matching this bound have high running times. We present the first randomized paging approach that both has optimal competitiveness and selects victim pages in subquadratic time. In fact, if k pages fit in internal memory the best previous solution required O(k 2 ) time per request and O(k) space, whereas our approach takes also O(k) space, but only O(log k) time in the worst case per page request.

Improved Space Bounds for Strongly Competitive Randomized Paging Algorithms

“…Nonetheless, Equitable is interesting due to its O(log k) runtime and the elegant potential definition. Moreover, the priority-based selection process in [8] gives an alternate approach to analyzing the Equitable distribution by employing elementary combinatorics.…”

“…In [8] we defined a priority based selection process on L which is guaranteed to construct a valid configuration. Assume that pages in the support have pairwise distinct priorities.…”

“…This solved the open question in [7] that there exist H k -competitive paging algorithms using O(k) space. In [8] we proposed an algorithm, denoted OnlineMIN, which further improved Equitable2 by reducing its runtime for processing a page from O(k 2 ) to O(log k/ log log k) while maintaining its space requirements.…”

Engineering Efficient Paging Algorithms

“…If the fraction of revealed requests is 1 − O(1/k), our implementation yields an amortized runtime of O(1) per request with very small constant factors. We show on real-world input traces 2 that, for the particular case of RDM, the new implementation outperforms the treebased approach in Brodal et al [2013]. Moreover, we compare the runtime of RDM with LRU and FIFO and show that the runtimes of RDM and LRU are comparable, albeit slower than FIFO.…”

“…In this work, we focus on the runtime of paging algorithms that, together with the cache misses, is an important factor in practice. We propose a compressed representation of the layer partition in Brodal et al [2013] and Koutsoupias and Papadimitriou [2000]. Based on this and on the fact that typically most requests are to so-called revealed pages (pages that are for sure in the cache of an optimal algorithm), we engineer a fast implementation of the ONOPT class.…”