Algorithm Integral: given a Request Sequence, The

algorithm executes a marking strategy similar to Fractional. At any point in time the algorithm keeps track of the moves Fractional would do assuming a cache of capacity M ? d d?1 S. If there is a request to a page p not in cache, the algorithm determines the total amount O F i of old pages from C i that Fractional does not have in cache when all requests to the-pages of p are served. Let O I i be the total amount of old pages that Integral does not have in cache. Integral chooses b(O F i ?O I i)=S i c pages uniformly at random from among the unmarked (i.e. old) pages in C i that are in cache and loads p. We can show that the expected cost incurred by Integral is at most d times the cost incurred by Fractional. Algorithm Integral may need more space than Fractional run on a cache of size M ? d