Layout of facilities with some fixed points
Computers and Operations Research
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Introduction to algorithms
Bottleneck Steiner Trees in the Plane
IEEE Transactions on Computers
Geometric interconnection and placement algorithms
Geometric interconnection and placement algorithms
Global routing based on Steiner min-max trees
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Utilization of vacant terminals for improved over-the-cell channel routing
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
The power-pSteiner tree problem
Nordic Journal of Computing
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
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Given a set of terminals in the plane, a bottleneck Steiner tree is a tree interconnecting the terminals, in which the length of the longest edge is minimized. The bottleneck Steiner tree problem, or special cases thereof, has applications in facility location and electronic physical design automation. In this paper, we first consider algorithms for computing optimal bottleneck Steiner trees. For a given topology, we give a direct, geometric algorithm that computes an optimal rectilinear bottleneck Steiner tree in O(n^2) time, which improves on the time complexity of previous algorithms. We also give a linear-time algorithm that, given the output from the previous algorithm, computes a rectilinear Steiner tree with minimum bottleneck length and that, among all trees with minimum bottleneck length, has minimum total length. These topology-specific algorithms provide solutions to many facility location applications, and in combination with a topology enumeration algorithm, can be used to solve the more general problems that arise in other applications. We also describe some difficulties in generalizing these results to the Euclidean problem, and give a simple approximation algorithm for the Euclidean problem. We then consider computation of approximate bottleneck Steiner trees. Specifically, we derive the exact value of the bottleneck Steiner ratio in any distance metric. The bottleneck Steiner ratio is the maximum ratio of the length of the longest edge in a minimum spanning tree to the length of the longest edge in an optimal bottleneck Steiner tree. Thus, the bottleneck Steiner ratio indicates the quality of a minimum spanning tree as an approximation of an optimal bottleneck Steiner tree.