We initiate the study of a natural and practically relevant new variant of online caching with bypassing where the to-be-cached items can have dependencies. We assume that the universe is a tree T and items are tree nodes; we require that if a node v is cached then the whole subtree T(v) rooted at v is cached as well. This theoretical problem finds an immediate application in the context of forwarding table optimization in IP routing and software-defined networks. We present an elegant online deterministic algorithm TC for this problem, and rigorously prove that its competitive ratio is O(height(T)·kONL/(kONL−kOPT+1)), where kONL and kOPT denote the cache sizes of an online and the optimal offline algorithm, respectively. The result is optimal up to a factor of O(height(T)).

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