Euclidean Steiner Minimal Trees on 4 Points-from the Plane to Space

摘要：

A Steiner minimal tree is a network with minimuM length spanning a given set of points in space. There are several criteria for identifying the Steiner minimal tree on 4 points in the Euclidean plane, however, it has been proved that the length of the Steiner minimal tree on 4 points cannot be computed by radicals if the 4 points lie in Euclidean space. This unsolvability implies that it is unlikely that similar necessary and sufficient conditions exist in the spatial case. Hence, a problem arises: Is it possible to generalize the known planar criteria to space in the sense that they would be sufficient to identify Steiner minimal trees on 4 points in space? In this paper we study this problem and some sufficient conditions are found. These sufficient conditions can help us to solve the general Steiner tree problem on n(>4) points in Euclidean space.

关键词： network optimisation Steiner tree Euclidean space

作者: Jia F. Weng I. Mareels D. A. Thomas

作者单位: Victoria Research Lab (VRL), National ICT Australia (NICTA), VIC 3010 Australia Melbourne School of Engineering, The University of Melbourne, VIC 3010 Australia Department of Mechanical Engineering, The University of Melbourne, VIC 3010 Australia

会议类型: 国际会议

会议名称: The First World Congress on Global Optimization in Engineering & Science(第一届工程与科学全局优化国际会议 WCGO2009)

会议地点: 长沙

会议语种:英文

页码: 147-153

在线出版日期: 2009-06-01（万方平台首次上网日期，不代表论文的发表时间）