For large n , Sankoffs algorithm must be used with iterative improvement. Werner, The role of topology and geometry in optimal network design. The Euclidean metric approach also assumes that sequences can be com- pared position by position. Lundy, Applications of the annealing algorithm to combinatorial problems in statics. Further, each species is labeled with m states corresponding to m different characters. Smith, Studies in computational geometry motivated by mesh generation. Hwang, A new bound for the Steiner ratio.
Weng, Steiner minimal trees on zig-zag lines. The Melzak Algorithm 35 2. Minimum spanning networks have been well-studied when all connections are required to be between the given points. It can be concluded that the authors wrote a comprehensive book on the Steiner Tree Problem. Hewgill, Exact computation of Steiner minimal trees in the plane.
This is different from the I-Steiner problem in which the S-point need be connected to only a subset of the N-points. Very useful is the discussion on computational experience for exact and heuristic algorithms. Bern, Faster exact algorithms for Steiner trees in planar networks. J Algo- rithms 8 1987 122-130. Foulds, Unlikelihood that minimal phylogenies for a realistic biological study can be constructed in reasonable computation time.
This last subject represents a Steiner tree problem in biology. Richter, New heuristic algorithms for solving the Steiner tree problem in graphs. Jaffe, Routing to multiple destinations in computer networks. Wing, Supoptimal algorithm for a wire routing problem. Computational complexity of inferring phylogenies from dissimi- larity matrices.
It should be noted that the. Weighted Steiner Tree Problem 203 6. Saks, Dynamic search in graphs. This is equivalent to the directed rectilinear Steiner problem where all edges are di- rected away from the origin progenitor ; the algorithms from the previous section can be applied here. The major source of exponentiality is due to the large number of topologies. The vertices not in N with degree 2 3 in the tree are called Steiner vertices.
Sorenson, Resolving the query inference problem using Steiner trees. Hendy, TurboTree: A fast algorithm for minimal trees. Proceedings of the Third International Conference on Genetic Algo- rithms 1989 231-236. Provan, The role of Steiner hulls in the solution to Steiner tree problems. Academic Press, New York 1985 119-161. Clark, Communication networks, soap films, and vectors.
Liebman, An O n2 heuristic algorithm for the directed Steiner minimal tree problem. Hwang, An O n log n algorithm for rectilinear minimal spanning trees. A second group of algorithms use suboptimal variants of exact algorithms. Weng, Steiner minimal trees for regular polygons. Mitchell, Rectilinear Steiner trees in rectangle trees. Hendrickson, Clustering in numerical cladistics: A minimum-length di- rected tree problem. Proceedings of the 14th Annual Conference of the Opera- tional Research Society of New Zealand 1978 , Vol.
Hwang, On Steiner minimal trees with rectilinear distance. A Graph Approximation Algorithm 71 4. Plesnik, On heuristics for the Steiner problem in graphs. Howard, Theoretical model to optimal drainage. There are several obvious reductions that can be made e.