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

  • Frederick C. HarrisJr.
Chapter

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°.

Keywords

Simulated Annealing Parallel Computation Parallel Algorithm Point Problem Steiner Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Frederick C. HarrisJr.
    • 1
  1. 1.Department of Computer ScienceUniversity of NevadaRenoUSA

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