Computational geometry: an introduction
Computational geometry: an introduction
On some distance problems in fixed orientations
SIAM Journal on Computing
Minimum cuts for circular-arc graphs
SIAM Journal on Computing
An O(n log n) Algorithm for Rectilinear Minimal Spanning Trees
Journal of the ACM (JACM)
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
IEEE Transactions on Computers
An approximation algorithm for a bottleneck k-Steiner tree problem in the Euclidean plane
Information Processing Letters
The Euclidean Bottleneck Steiner Tree and Steiner Tree with Minimum Number of Steiner Points
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Performance-driven register insertion in placement
Proceedings of the 2004 international symposium on Physical design
On Exact Solutions to the Euclidean Bottleneck Steiner Tree Problem
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Exact Algorithms for the Bottleneck Steiner Tree Problem
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On exact solutions to the Euclidean bottleneck Steiner tree problem
Information Processing Letters
On the euclidean bottleneck full Steiner tree problem
Proceedings of the twenty-seventh annual symposium on Computational geometry
The bottleneck 2-connected k-Steiner network problem for k≤2
Discrete Applied Mathematics
Optimal and approximate bottleneck Steiner trees
Operations Research Letters
Monochromatic geometric k-factors for bicolored point sets with auxiliary points
Information Processing Letters
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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.