Streaming cache placement problems: complexity and algorithms

Virtual private networks are often used to distribute live content, such as video or audio streams, to a potentially large number of destinations. Streaming caches (also called splitters) are deployed in these multicast systems to allow content distribution without overloading the network. In this paper, we consider two related combinatorial optimization problems that arise in multicast networks. In the tree cache placement problem, the objective is to find a routing tree in which the number of cache nodes needed for (feasible) multicasting is minimized. In a generalization of this problem, called the flow cache placement problem, we seek any feasible flow from the source to the destinations that minimizes the number of cache nodes. We prove that these problems are NP-hard using a transformation from Satisfiability. This transformation allows us to give a proof of hardness of approximation by showing that it is gap-preserving. We also consider approximation algorithms, as well as special cases where these problems can be solved in polynomial time.