Construction Algorithms and Approximation Bounds for the Streaming Cache Placement Problem in Multicast Networks

We study a problem in the area of multicast networks, called the Streaming Cache Placement Problem (SCPP). In the SCPP one wants to determine the minimum number of multicast routers needed to deliver content to a specified number of destinations, subject to predetermined link capacities. The SCPP is known to be NP-hard [1] and also MAX SNP hard [2]. We improve the approximation results for this problem, using a reduction from Set Cover. In particular, given k destinations, we show that the SCPP cannot have a O(log log k− δ)approximation algorithm, for a very small δ, unless NP can be solved in sub-exponential time. We also propose construction algorithms for the SCPP, based on two general techniques: adding destinations to a partial solution, and reducing the number of infeasible nodes in an initial solution. We report the results of computational experiments based on these two algorithms and its variations.