Approximation and Heuristic Algorithms for End-System Based Application-Layer Multicast for Voice Conferences

This paper studies the problem of constructing application-layer multicast trees for end-system based voice conferences in which voice mixing and replication are performed at end systems. This problem is formulated as a degree-constrained node-weighted Steiner tree problem with a degree-dependent cost associated with each node, which is a generalization of the degree-constrained node-weighted Steiner tree problem with a fixed cost associated with each node. This paper devises a novel technique to deal with degree-dependent nodal costs and develops a bicriteria approximation algorithm, with the degree of each node and the cost of the tree as two objectives, for this more general Steiner tree problem. The bound on the degree of each node and the bound on the cost of the tree constructed by the bicriteria approximation algorithm are derived. Two heuristic algorithms which construct multicast trees that obey the degree constraint on each node are obtained by modifying the bicriteria approximation algorithm. The performances of the two heuristic algorithms are studied via simulations.