A 4-geometry maze router and its application on multiterminal nets
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Geometric data structures approximations for network optimisation problems
MAMECTIS'09 Proceedings of the 11th WSEAS international conference on Mathematical methods, computational techniques and intelligent systems
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The Euclidean Steiner tree problem is to find the tree with minimalEuclidean length spanning a set of fixed points in the plane, allowing theaddition of auxiliary points to the set (Steiner points). The problem isNP-hard, so polynomial-time heuristics are desired. We present two suchheuristics, both of which utilize an efficient method for computing alocally optimal tree with a given topology. The first systematically insertsSteiner points between edges of the minimal spanning tree meeting at anglesless than 120 degrees, performing a local optimization at the end. Thesecond begins by finding the Steiner tree for three of the fixed points.Then, at each iteration, it introduces a new fixed point to the tree,connecting it to each possible edge by inserting a Steiner point, andminimizes over all connections, performing a local optimization for each. Wepresent a variety of test cases that demonstrate the strengths andweaknesses of both algorithms.