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Bottleneck Steiner Trees in the Plane
March 1992 (vol. 41 no. 3)
pp. 370-374

A Steiner tree with maximum-weight edge minimized is called a bottleneck Steiner tree (BST). The authors propose a Theta ( mod rho mod log mod rho mod ) time algorithm for constructing a BST on a point set rho , with points labeled as Steiner or demand; a lower bound, in the linear decision tree model, is also established. It is shown that if it is desired to minimize further the number of used Steiner points, then the problem becomes NP-complete. It is shown that when locations of Steiner points are not fixed the problem remains NP-complete; however, if the topology of the final tree is given, then the problem can be solved in Theta ( mod rho mod log mod rho mod ) time. The BST problem can be used, for example, in VLSI layout, communication network design, and (facility) location problems.

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Index Terms:
bottleneck Steiner trees; maximum-weight edge minimized; lower bound; linear decision tree model; NP-complete; VLSI layout; communication network design; location problems; computational complexity; optimisation; trees (mathematics).
Citation:
M. Sarrafzadeh, C.K. Wong, "Bottleneck Steiner Trees in the Plane," IEEE Transactions on Computers, vol. 41, no. 3, pp. 370-374, March 1992, doi:10.1109/12.127452
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