Generalized connection caching

Cohen et al. [5] recently initiated the theoretical study of connection caching in the world-wide web. They extensively studied uniform connection caching, where the establishment cost is uniform for all connections [5, 6]. They showed that ordinary paging algorithms can be used to derive algorithms for uniform connection caching and analyzed various algorithms such as Belady's rule, LRU and Marking strategies. In particular, in [5] Cohen et al. showed that LRU yields a (2k - 1)-competitive algorithm, where k is the size of the largest cache in the network. In [6], they investigated Marking algorithms with different types of communication among nodes and presented deterministic k-competitive algorithms.

In this paper we study generalized connection caching, also introduced in [5], where connections can incur varying establishment costs. This model is reasonable because the cost of establishing a connection may depend, for instance, on the distance of the nodes to be connected. We present optimal online algorithms for this generalized problem. Algorithms for ordinary weighted caching can be used to derive algorithms for generalized connection caching. We present tight or nearly tight analyses on the performance achieved by the currently known weighted caching algorithms when applied in generalized connection caching. The popular Balance algorithm yields a 2k-competitive algorithm. We prove that its competitive ratio is not smaller than (2k - 1). We then present implementations of the deterministic algorithm Landlord and the randomized algorithm Harmonic and show that they are k-competitive. This the best competitive ratio that can achieved by deterministic algorithms resp. by randomized algorithms against adaptive online adversaries. Additionally we consider two extensions of generalized connection caching where (1) connections have time-out values, or (2) the establishment cost of connections is asymmetric. We study the performance of Landlord and show that in the case of (1) it remains k-competitive. In the case of (2) we derive nearly tight upper and lower bounds.