Mathematica: a system for doing mathematics by computer
Mathematica: a system for doing mathematics by computer
Scientific computing: an introduction with parallel computing
Scientific computing: an introduction with parallel computing
Performance-driven Steiner tree algorithm for global routing
DAC '93 Proceedings of the 30th international Design Automation Conference
High-performance routing trees with identified critical sinks
DAC '93 Proceedings of the 30th international Design Automation Conference
Performance-driven interconnect design based on distributed RC delay model
DAC '93 Proceedings of the 30th international Design Automation Conference
Studies in computational geometry motivated by mesh generation
Studies in computational geometry motivated by mesh generation
Geometric interconnection and placement algorithms
Geometric interconnection and placement algorithms
Optimal and approximate bottleneck Steiner trees
Operations Research Letters
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This paper introduces the power-p Steiner tree problem, which is to find a geometric Steiner tree that minimizes the sum of the edge lengths each raised to the p power. A number of results are presented on computing optimal and approximate power-p Steiner trees. Specifically, a linear-time numerical algorithm is presented for computing optimal Euclidean power-2 Steiner trees with respect to a given topology, and the algorithm is proved to be numerically stable. It is conjectured, and strong evidence given, that the power-p Steiner tree problem is not finitely solvable for p ≥ 5. Finally, bounds are given on the power-p Steiner ratio, which measures the quality of a minimum spanning tree as an approximation of an optimal power-p Steiner tree.