Before revision:  We give the first online, polynomial-time deterministic algorithm for this problem, with  competitive ratio of O(\log |F| \cdot (\log |C| + \log \log |F|)).
After revision:  We give the first online, polynomial-time deterministic algorithm for this problem, with a competitive ratio of O(\log |F| \cdot (\log |C| + \log \log |F|)).