A factoring approach for the Steiner tree problem in undirected networks

Abstract

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 O(vertical bar E vertical bar) algorithm is presented to find a minimum Steiner tree for series-parallel graphs where vertical bar E vertical bar is the number of edges. Based on this algorithm, we proposed an O(2(2c) . vertical bar E vertical bar) 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 vertical bar K vertical bar. (c) 2007 Elsevier Inc. All rights reserved.