A Heuristic for Steiner Tree Construction
نویسنده
چکیده
The problem of constructing an optimal Steiner tree is NP-complete. Mapping the problem to standard Cartesian coordinates, the cost of an optimal Steiner tree is defined as the minimal rectilinear distance of all the edges. The heuristic proposed in this paper then finds a close approximation in fast (polynomial) time. The basis of exploits the idea of triangular distance, that is, using distance inequality to find the shortest path between three points. This is then further propagated across the coordinate plane. Thus, this solution makes an in order sweep based on the x-coordinates. The proposed solution has a varying running time, depending upon the distribution of the points. The worst case performance is given to be O(n).
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