Saturday, November 12, 2011

Difference between Steiner tree and Spanning tree in Networks

Based on the description below it is clear why Steiner trees are used for multicasting and why Spanning trees are used for configuring interfaces on bridges. Steiner trees ensure smallest common path by enforcing or adding Steiner points while spanning trees are just used to remove broadcast loops.

Some additional info from Wiki:
The Steiner tree problem is superficially similar to the minimum spanning tree problem: given a set V of points (vertices), interconnect them by a network (graph) of shortest length, where the length is the sum of the lengths of all edges. The difference between the Steiner tree problem and the minimum spanning tree problem is that, in the Steiner tree problem, extra intermediate vertices and edges may be added to the graph in order to reduce the length of the spanning tree. These new vertices introduced to decrease the total length of connection are known as Steiner points or Steiner vertices. It has been proved that the resulting connection is a tree, known as the Steiner tree. There may be several Steiner trees for a given set of initial vertices.

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