Online Compression Caching

Motivated by the possibility of storing a file in a compressed format, we formulate the following class of compression caching problems. We are given a cache with a specified capacity, a certain number of compression/uncompression algorithms, and a set of files, each of which can be cached as it is or by applying one of the compression algorithms. Each compressed format of a file is specified by three parameters: encode cost, decode cost, and size. The miss penalty of a file is the cost of accessing the file if the file or any compressed format of the file is not present in the cache. The goal of a compression caching algorithm is to minimize the total cost of executing a given sequence of requests for files. We say an online algorithm is resource competitive if the algorithm is constant competitive with a constant factor resource advantage. A well-known result in the framework of competitive analysis states that the least-recently used (LRU) algorithm is resource competitive for the traditional paging problem. Since compression caching generalizes the traditional paging problem, it is natural to ask whether a resource competitive online algorithm exists or not for compression caching. In this work, we address three problems in the class of compression caching. The first problem assumes that the encode cost and decode cost associated with any format of a file are equal. For this problem we present a resource competitive online algorithm. To explore the existence of resource competitive online algorithms for compression caching with arbitrary encode costs and decode costs, we address two other natural problems in the aforementioned class, and for each of these problems, we show that there exists a non-constant lower bound on the competitive ratio of any online algorithm, even if the algorithm is given an arbitrary factor capacity blowup. Thus, we establish that there is no resource competitive algorithm for compression caching in its full generality.