A factoring approach for the Steiner tree problem in undirected networks

In communication networks, many applications, such as video on demand and video conferencing, must establish a communications tree that spans a subset K in a vertex set. The source node can then send identical data to all nodes in set K along this tree. This kind of communication is known as multicast communication. A network optimization problem, called the Steiner tree problem (STP), is presented to find a least cost multicasting tree. In this paper, an OðjEjÞ algorithm is presented to find a minimum Steiner tree for series–parallel graphs where jEj is the number of edges. Based on this algorithm, we proposed an Oð2 jEjÞ algorithm to solve the Steiner tree problem for general graphs where c is the number of applied factoring procedures. The c value is strongly related to the topology of a given graph. This is quite different from other algorithms with exponential time complexities in jKj. 2007 Elsevier Inc. All rights reserved.