  This 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 \Omega(\log n +\log k).
