In multicasting routing, the main objective is to send data from one or more source to multiple destinations, while at the same time minimizing the usage of resources. Examples of resources which can be minimized include bandwidth, time and connection costs. In this paper we survey applications of combinatorial optimization to multicast routing. We discuss the most important problems considered in this area, as well as their models. Algorithms for each of the main problems are also presented.

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 #)- approximation algorithm, for a very small #, 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.

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ABSTRACT. Multicasting is a technique for data routing in networks that allows multiple destinations to be addressed simultaneously. The implementation of multicasting requires, however, the solution of difficult combinatorial optimization problems. In this chapter, we discuss combinatorial issues occurring in the implementation of multicast routing, including multicast tree construction, minimization of the total message delay, center-based routing, and multicast message packing. Optimization methods for these problems are discussed and the corresponding literature reviewed. Mathematical programming as well as graph models for these problems are discussed. 1.