Steiner Minimal Trees in E3: Theory, Algorithms, and Applications

  • J. MacGregor Smith


Let’s say that you are going to design a new electronic circuit at the molecular/atomic level where you know beforehand the basic number of atomic elements of the circuit and you wish to arrange them so that they achieve an optimal configuration that is both compact, stable, and integrated electrically. How would you configure the atoms? If one assumes that the cost of putting together the molecular structure is proportional to distance i.e. the potential energy in the system, then you would want to minimize the overall interconnecting distance between the atoms. This is fundamentally the Steiner problem in E 3. Figure 1 demonstrates a geometric construction for the Steiner Minimal Tree of N=6 vertices in E 3.


Voronoi Diagram Steiner Tree Delaunay Triangulation Triple Helix Optimal Configuration 
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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • J. MacGregor Smith
    • 1
  1. 1.Department of Mechanical and Industrial EngineeringUniversity of MassachusettsAmherstUSA

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