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

In: Handbook of Combinatorial Optimization

Author

Listed:
  • Frederick C. Harris Jr.

    (University of Nevada, Department of Computer Science)

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°.

Suggested Citation

  • Frederick C. Harris Jr., 1998. "Steiner Minimal Trees: An Introduction, Parallel Computation, and Future Work," Springer Books, in: Ding-Zhu Du & Panos M. Pardalos (ed.), Handbook of Combinatorial Optimization, pages 851-903, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0303-9_13
    DOI: 10.1007/978-1-4613-0303-9_13
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