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Steiner Minimal Trees in E 3: Theory, Algorithms, and Applications

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Handbook of Combinatorial Optimization

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Abstract

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.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA, 01003, USA

    J. MacGregor Smith

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  1. J. MacGregor Smith
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Editors and Affiliations

  1. University of Minnesota, Minneapolis, USA

    Ding-Zhu Du

  2. University of Florida, Gainesville, USA

    Panos M. Pardalos

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© 1998 Kluwer Academic Publishers

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MacGregor Smith, J. (1998). Steiner Minimal Trees in E 3: Theory, Algorithms, and Applications. In: Du, DZ., Pardalos, P.M. (eds) Handbook of Combinatorial Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0303-9_17

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  • DOI: https://doi.org/10.1007/978-1-4613-0303-9_17

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7987-4

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