Abstract
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 four points in the Euclidean plane. However, it has been proved that the length of the Steiner minimal tree on four points cannot be computed using radicals if the four 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 are sufficient to identify Steiner minimal trees on four points in space? This problem is investigated and some sufficient conditions are proved in this paper. These sufficient conditions can help us to solve the general Steiner tree problem on n(> 4) points in Euclidean space.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
