2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/32204This paper is concerned with online caching algorithms for the (n,k)-companion cache, defined by Brehob et. al. In this model the cache is composed of two components: a k-way set-associative cache and a companion fully-associative cache of size n. We show that the deterministic competitive ratio for this problem is (n+1)(k+1)-1, and the randomized competitive ratio is O(\log n \log k) and Ω(\log n +\log k).17 pages, 1 figure. Preliminary version in ESA '02. To be published in Theoretical Computer Science AData Structures and Algorithmstext