@inproceedings{e7098444650f4abaa28b1417b9d8fa1f,

title = "A branch-and-bound algorithm for computing node weighted steiner minimum trees",

abstract = "Given n regular points in the Euclidean plane, the node-weighted Steiner minimum tree (NWSMT) is a straight line network interconnecting these n regular points and some Steiner points with a minimum cost, where the cost of the network is the sum of the edge lengths plus the total cost of the Steiner points. In 1995, [11] proved that a tight upper bound on the maximum degree of Steiner points in a NWSMT is 4. In 1996, [14] used this result to propose a modified Melzak procedure for computing a NWSMT. However, that procedure requires exponential time to compute a minimum cost network under a given topology. In this paper, we prove that there exists a NWSMT in which the maximum degree of regular points is no more than 5 and that this upper bound is tight. For a given topology interconnecting n regular points, we show that the Xue-Ye algorithm [15] for minimizing a sum of Euclidean norms can be used to compute an (1 + ε)-approximation of the minimum cost network in n1.5(log n + log 1/ε time for any positive ε. These results enable an algorithm that computes a NWSMT by enumerating all the possible Steiner topologies. We prove a bounding theorem that can be used in a branch-and-bound algorithm and present preliminary computational experience.",

keywords = "Branch-and-bound, Maximum node degrees, Minimum cost network under a given topology, Node weighted Steiner minimum trees",

author = "Guoliang Xue",

year = "1997",

doi = "10.1007/bfb0045105",

language = "English (US)",

isbn = "354063357X",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "383--392",

editor = "Tao Jiang and D.T. Lee",

booktitle = "Computing and Combinatorics - 3rd Annual International Conference COCOON 1997, Proceedings",

note = "3rd Annual International Computing and Combinatorics Conference, COCOON 1997 ; Conference date: 20-08-1997 Through 22-08-1997",

}