Neural and delay based heuristics for the Steiner problem in networks

Abstract

High speed networks such as the B-ISDN must be adequately equipped to handle multipoint communication in a fast and economical manner. Multicast applications include desktop video conferencing, distance learning, distributed database applications, etc. In networks employing the asynchronous transfer mode (ATM) technology, routing a multicast is achieved by constructing a tree that spans the source and all the destinations. For the purpose of routing, the network is modeled as a weighted, undirected graph. The graph-theoretic solution is to find a minimum Steiner tree for the graph given a set of destinations. This formulation suffices for building multicast trees with a single optimization constraint as would be the xcase for best effort transport. For real-time traffic, however, it is necessary to ensure that the delay between the sender and each of the receivers is bounded. In this case the network is modeled as an undirected graph, where the edges have both a cost and a delay associated with them. The graph-theoretic solution is then to find a constrained minimum Steiner tree such that the delay between the source and each of the destinations does not violate the specified bound. Both of these problems are NP-complete. In this paper we review prior work on the multipoint routing problem and discuss the formulation of the unconstrained and constrained Steiner problems. We use the random neural network (RNN) to significantly improve the quality of trees found by the two existing best heuristics for finding Steiner trees - the minimum spanning tree heuristic and the average distance heuristic. We also develop a new heuristic for finding delay constrained Steiner trees. Experimental results are presented which show that the new heuristics improve significantly over existing ones.