Optimal algorithms for hierarchical web caches

Hierarchical topologies have been applied in many existing systems that provide public IPTV or massive content delivery services. The efficient operation of these services requires massive bandwidth resources. Data caching has emerged as an effective way in reducing bandwidth consumption and accelerating content access. In hierarchical caching systems requests for content are routed upwards until they reach a cache that stores a copy of the requested file. When the requested file is found, it is sent on the reverse path to the client. In this work, we focus on the problem of caching redundant copies of content in intermediate caches on the reverse path in order to minimize the bandwidth consumption within a given time horizon. The above problem is known to be NP-hard. However, we show that replacing the cache capacity constraints by a cost term paid each time we store a file in a cache, results to the tractable problem of minimizing the overall bandwidth and caching expenses. We use its optimal solution to establish a novel algorithm for the efficient solution of the original problem. We furthermore study the case that segments of encoded versions of the files instead of only complete files are allowed to be stored at the caches. We show that this problem is of polynomial complexity. Numerical experiments for typical popularity distributions reveal the performance distance between the proposed algorithms and heuristic algorithms that are commonly applied nowadays.