An O(log k)-competitive algorithm for generalized caching

In the generalized caching problem, we have a set of pages and a cache of size k. Each page p has a size wpe1 and fetching cost cp for loading the page into the cache. At any point in time, the sum of the sizes of the pages stored in the cache cannot exceed k. The input consists of a sequence of page requests. If a page is not present in the cache at the time it is requested, it has to be loaded into the cache incurring a cost of cp. We give a randomized O(log k)-competitive online algorithm for the generalized caching problem, improving the previous bound of O(log2 k) by Bansal, Buchbinder, and Naor (STOC'08). This improved bound is tight and of the same order as the known bounds for the classic problem with uniform weights and sizes. We use the same LP based techniques as Bansal et al. but provide improved and slightly simplified methods for rounding fractional solutions online