Add to ORKGWe study the weighted version of the classic online paging problem where there is a weight (cost) for fetching each page into the cache. We design a randomized O(log k)-competitive online algorithm for this problem, where k is the cache size. This is the first randomized o(k)-competitive algorithm and its competitive ratio matches the known lower bound for the problem, up to constant factors. More generally, we design an O(log(k/(k - h + 1)))-competitive online algorithm for the version of the problem where the online algorithm has cache size k and it is compared to an optimal offline solution with cache size h = k. Our solution is based on a two-step approach. We first obtain an O(log k)-competitive fractional algorithm based on an online ...