A New Competitive Analysis of Randomized Caching

We provide new competitive upper bounds on the performance of the memoryless, randomized caching algorithm RAND. Our bounds are expressed in terms of the inherent hit rate α of the sequence of memory references, which is the highest possible hit rate that any algorithm can achieve on the sequence for a cache of a given size. Our results show that RAND is (1−αe−1/α)/(1−α)-competitive on any reference sequence with inherent hit rate α. Since our new competitive bound does not scale up with the size k of the cache, it beats the putative Ω(lg k) lower bound on the competitiveness of randomized caching algorithms.