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

Frederick C. Harris ()
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Frederick C. Harris: University of Nevada, Department of Computer Science

A chapter in Handbook of Combinatorial Optimization, 1998, pp 851-903 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4613-0303-9_13

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