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Insight into the computation of Steiner minimal trees in Euclidean space of general dimension

Marcia Fampa(fampa***at***cos.ufrj.br)

Abstract: We present well known properties related to the topology of Steiner minimal trees and to the geometric position of Steiner points, and investigate their application in the main exact algorithms that have been proposed for the Euclidean Steiner problem. We discuss the difficulty in the application of properties that were very successfully applied to solve the problem in the plane, when the dimension of the space increases, and point out that the application of some geometric conditions for Steiner points is hindered when the well known implicit enumeration scheme proposed by Smith in 1992 is considered. Finally, we mention mathematical-optimization methods as a direction to explore in the search for good formulations of inequalities that would allow the application of these restrictive geometric conditions.

Keywords: Steiner minimal tree; Euclidean Steiner problem; MINLP

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Global Optimization


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Entry Submitted: 12/06/2018
Entry Accepted: 12/06/2018
Entry Last Modified: 12/06/2018

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