Issue No. 03 - March (1992 vol. 41)

ISSN: 0018-9340

pp: 370-374

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.127452

ABSTRACT

<p>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.</p>

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

C. Wong and M. Sarrafzadeh, "Bottleneck Steiner Trees in the Plane," in

*IEEE Transactions on Computers*, vol. 41, no. , pp. 370-374, 1992.

doi:10.1109/12.127452

CITATIONS