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Steiner Minimal Trees: An Introduction, Parallel Computation, and Future Work

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Handbook of Combinatorial Optimization

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Abstract

Minimizing a network’s length is one of the oldest optimization problems in mathematics and, consequently, it has been worked on by many of the leading mathematicians in history. In the mid-seventeenth century a simple problem was posed: Find the point P that minimizes the sum of the distances from P to each of three given points in the plane. Solutions to this problem were derived independently by Fermat, Torricelli, and Cavaliers. They all deduced that either P is inside the triangle formed by the given points and that the angles at P formed by the lines joining P to the three points are all 120°, or P is one of the three vertices and the angle at P formed by the lines joining P to the other two points is greater than or equal to 120°.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Nevada, Reno, NV, 89557, USA

    Frederick C. Harris Jr.

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  1. Frederick C. Harris Jr.
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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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Harris, F.C. (1998). Steiner Minimal Trees: An Introduction, Parallel Computation, and Future Work. In: Du, DZ., Pardalos, P.M. (eds) Handbook of Combinatorial Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0303-9_13

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  • DOI: https://doi.org/10.1007/978-1-4613-0303-9_13

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7987-4

  • Online ISBN: 978-1-4613-0303-9

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