Online Tree Caching

TL;DR

This paper introduces a new online caching problem with tree-structured dependencies, providing an optimal deterministic algorithm and analyzing its competitive ratio in the context of network routing.

Contribution

The paper formulates the tree caching problem, proposes an online deterministic algorithm, and proves its competitive ratio is near-optimal up to a factor related to tree height.

Findings

The algorithm has a competitive ratio of O(height(T) * k_ALG/(k_ALG - k_OPT + 1)).

The competitive ratio is proven to be optimal up to a factor of O(height(T)).

Application to IP routing and software-defined networks is demonstrated.

Abstract

We initiate the study of a natural and practically relevant new variant of online caching 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) * k_ALG/(k_ALG-k_OPT+1)), where k_ALG and k_OPT 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)).