Author
J. F. Weng
Bio: J. F. Weng is an academic researcher. The author has contributed to research in topics: Steiner point & Steiner tree problem. The author has an hindex of 1, co-authored 1 publications receiving 51 citations.
Topics: Steiner point, Steiner tree problem
Papers
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TL;DR: It is shown that the set ofn equally spaced points yields the longest Steiner minimal tree among all sets ofn cocircular points on a given circle.
Abstract: Fifty years ago Jarnik and Kossler showed that a Steiner minimal tree for the vertices of a regularn-gon contains Steiner points for 3 ≤n≤5 and contains no Steiner point forn=6 andn?13. We complete the story by showing that the case for 7≤n≤12 is the same asn?13. We also show that the set ofn equally spaced points yields the longest Steiner minimal tree among all sets ofn cocircular points on a given circle.
53 citations
Cited by
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TL;DR: A survey up to 1989 on the Steiner tree problems which include the four important cases of euclidean, rectilinear, graphic, phylogenetic and some of their generalizations.
Abstract: We give a survey up to 1989 on the Steiner tree problems which include the four important cases of euclidean, rectilinear, graphic, phylogenetic and some of their generalizations. We also provide a rather comprehensive and up-to-date bibliography which covers more than three hundred items.
573 citations
TL;DR: It is shown that in two-dimensions, Steiner minimum trees may be found exactly in exponential time O(CN) on a real RAM on a “real RAM” model of computation allowing infinite precision arithmetic.
Abstract: This paper has two purposes. The first is to present a new way to find a Steiner minimum tree (SMT) connectingN sites ind-space,d >- 2. We present (in Appendix 1) a computer code for this purpose. This is the only procedure known to the author for finding Steiner minimal trees ind-space ford > 2, and also the first one which fits naturally into the framework of “backtracking” and “branch-and-bound.” Finding SMTs of up toN = 12 general sites ind-space (for anyd) now appears feasible.
152 citations
TL;DR: The history of the Euclidean Steiner tree problem goes back to Gergonne in the early nineteenth century as discussed by the authors, who presented a detailed account of the mathematical contributions of some of the earliest papers on the problem.
Abstract: The history of the Euclidean Steiner tree problem, which is the problem of constructing a shortest possible network interconnecting a set of given points in the Euclidean plane, goes back to Gergonne in the early nineteenth century. We present a detailed account of the mathematical contributions of some of the earliest papers on the Euclidean Steiner tree problem. Furthermore, we link these initial contributions with results from the recent literature on the problem.
82 citations
AT&T1
TL;DR: This paper develops the calculus of hexagonal coordinates and shows how it can be applied to the Steiner tree problem.
33 citations
AT&T1
TL;DR: An up-to-date survey on the Euclidean Steiner problem which deals with the construction of a shortest network interconnecting a given set of points in the Euclidesan plane is given.
Abstract: We give an up-to-date survey on the Euclidean Steiner problem which deals with the construction of a shortest network interconnecting a given set of points in the Euclidean plane.
14 citations