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Topic: Steiner tree


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  Steiner Points and Trees   (Site not responding. Last check: 2007-10-20)
A steiner point cannot be an endpoint, else we could simply delete it and its associated edge, reducing the length of the spanning tree.
In a minimal steiner tree, the steiner points of degree 3 all have angles of 120°.
Next, split the steiner point in two and pull the two points apart, towards the left and right sides of the square, until the angles are 120°.
www.mathreference.com /gph,stein.html   (544 words)

  
 Steiner Tree
Many different phylogenic tree construction algorithms have been developed, which vary in the data they attempt to model and what the desired optimization criterion is. Because they all give different answers, identifying the correct algorithm for a given application is somewhat a matter of faith.
Steiner was apparently one of several mathematicians who worked the general problem for n points, and he was mistakenly credited with the problem.
The hardness of Steiner tree for Euclidean and rectilinear metrics was established in [GGJ77, GJ77].
www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE181.HTM   (1383 words)

  
 OpenWaldorf-Tree climbing
Tree climbing can be a wonderful experience for a child, providing it is done in a safe and supervised manner.
While tree climbing can boost children's self-esteem and appreciation of their relationship to nature, free tree climbing can also be injurious and even fatal.
Under proper conditions, tree climbing is a fun, safe way for children to explore their own potential and the natural wonder of trees.
www.openwaldorf.com /treeclimbing.html   (1317 words)

  
 OpenWaldorf - Rudolf Steiner
Rudolf Steiner, the founder and "guru" of Waldorf education was a clairvoyant occult scientist and mystic.
Steiner is rarely mentioned as a significant contributor to the body of scientific knowledge, and is by no means essential to modern science.
Steiner is quick to point out when modern science supports one of his theories, but he often disagrees with modern science as either incorrect, misguided, or marginally relevant.
www.openwaldorf.com /steiner.html   (2298 words)

  
 Comparisons with Network Multicast Trees
In Figure 2.6(a), the cost of the trees is measured as the total distance of sending one packet to the multicast session.
The curves for the overlay spanning tree and for the approximate Steiner tree are quite close to each other, with the overlay tree outperforming slightly the approximate Steiner tree.
While the shortest path tree and the Steiner tree are able to aggregate the paths from regional routers to the backbone by using the MST links, the tree always selects the star links.
www.arl.wustl.edu /~sherlia/thesis/chap2/node7.html   (1200 words)

  
 Local Steiner Improvement
These differ from Steiner trees in that they are sets of edges between points while Steiner trees are collections of grid edges spanning the points.
The Steiner tree of figure 1c contains these three edges too, but they are drawn differently, and if the overlaps between edges are not included twice when determining the length of the tree, the shortest possible Steiner spanning tree over the points is formed.
For example, the tree in figure 1c can be constructed by drawing the edge with a horizontal line through a, connecting this to the point b with the edge , and then filling in the edge .
www.cs.engr.uky.edu /~lewis/research/Papers/Steiner-Local/local.html   (4174 words)

  
 MINIMUM STEINER TREE
A Steiner tree, i.e., a subtree of G that includes all the vertices in S.
A prize-collecting variation in which a penalty is associated with each vertex and the goal is to minimize the cost of the tree and the vertices in S not in the tree is approximable within
Finally, if before computing the Steiner tree the graph can be modified by reducing the weight of the edges within a given budget the problem of looking for the best reduction strategy is A
www.nada.kth.se /~viggo/wwwcompendium/node78.html   (334 words)

  
 Steiner tree summary   (Site not responding. Last check: 2007-10-20)
One method to find the minimal spanning tree is the "brute force method".
When you are finished, all the nodes will have the same label (i.e., they are all connected) and there will be no circuits.
Figuring out how where to put these Steiner points is a non-trivial matter (NP-complete, actually).
www.colorstudy.com /static/ianb/old/steiner/summary.html   (264 words)

  
 Steiner Tree Problem's Heauristic Algorithm with Minimum Spanning Tree Problem
Here, the input is a set of points in space that are the terminals, and the objective is to compute a tree of minimum length (in the appropriate metric) that connects all the terminals.
Insert a Steiner point between the first three fixed points, connect it to each, and locally optimize to obtain the Steiner tree for those three points.
Here is the minimum spanning tree applet in case you would like to campare Steiner tree problem with MST problem.
www.personal.kent.edu /~rmuhamma/Compgeometry/MyCG/CG-Applets/SteinerTree/msteinercli.htm   (508 words)

  
 Steiner Trees: Open Problems   (Site not responding. Last check: 2007-10-20)
Hwang's theorem allows us to construct an optimal rectilinear Steiner tree of a full set in linear time.
I know of no other metric or type of graph in which computing the optimal Steiner tree of a full set is polynomial-time solvable but computing a general Steiner tree is NP-hard.
These are Steiner-like trees on points in the (first quadrant of the) plane, in which every segment in the tree is directed left to right or bottom to top.
ganley.org /steiner/open.html   (497 words)

  
 Steiner tree
Definition: A minimum-weight tree connecting a designated set of vertices, called terminals, in an undirected, weighted graph or points in a space.
The tree may include non-terminals, which are called Steiner vertices or Steiner points.
Note: This differs from the minimum spanning tree in that the set of Steiner vertices must be identified.
www.nist.gov /dads/HTML/steinertree.html   (132 words)

  
 [No title]   (Site not responding. Last check: 2007-10-20)
Hannan shows that Manhattan SMT can be reduced to the Steiner tree problem in finite grid graph: there always exists an optimum solution where all line segments lie on the grid induced by the coordinates of the terminals.
In RMST (minimal rectilinear Steiner problems), the cost of a tree is the Manhattan distance between its endpoints, and the cost of a tree is the sum of its edge cost.
Constructing of Rectilinear Steiner tree is closely related with the delay of the electrical components.
www.eecs.umich.edu /~seokwoo/doc/elmore.doc   (1628 words)

  
 Steiner - Wikipedia, the free encyclopedia
Steiner is a German surname that is derived from the word Stein, meaning stone.
Hillel Steiner, Professor of Political Philosophy and a Fellow of the British Academy
Rudolf Steiner (1861–1925), Austrian philosopher, educator, and mystic, founder of anthroposophy (spiritual science)
en.wikipedia.org /wiki/Steiner   (165 words)

  
 Approximation the Steiner Tree in the Placement Process   (Site not responding. Last check: 2007-10-20)
By simulating the movement of a node in a tree, an iso-distance error graph (IDEG) with its equivalent non-Steiner tree is developed.
To reduce connection errors in the IDEG and pursue computational efficiency, a row-based tree family in which the tree length is primarily dependent on the terminal coordinates of each row, is constructed.
Then, based on the analysis of the error distribution on the IDEG, the row-based trees and the spanning tree are compared in terms of their approximation to the Steiner tree.
www.calce.umd.edu /articles/abstracts/1989/steiner.htm   (137 words)

  
 The Silver Tree Steiner School
From the first time I drove under the canopy of trees, that lead up the narrow winding road to the cottage like buildings which make up the Silver Tree School, nestled in the forest, I knew this was the place I wanted my young daughter to begin her journey of discovery and learning.
The Silver Tree Steiner School is a refreshing and new experience when compared to mainstream educational schools.
The teachers are incredibly dedicated and appear to develop a special bond with their pupils over time which to us, as parents, we consider to be important for our children's learning development.
www.silvertree.wa.edu.au /testimonials.htm   (730 words)

  
 C-tree : Buffered Steiner Trees for Difficult Instances
It constructs a Steiner tree for each sink cluster and then a top-level timing driven Steiner tree is built such that each cluster is considered as a sink in the top-level.
The timing driven Steiner tree is constructed by the Prim-Dijkstra tradeoff method [2].
the location of the steiner node with the node id i; x and y can be any integer which shows the x- and y- coordinates of the physical location.
dropzone.tamu.edu /~cnsze/GSRC/ctree.html   (1040 words)

  
 About "The Steiner Tree Page"   (Site not responding. Last check: 2007-10-20)
The most basic version is in a graph: given a weighted graph in which a subset of vertices are identified as terminals, find a minimum-weight connected subgraph that includes all the terminals.
The problem can also be applied in the geometric realm; the two most common variants are the Euclidean Steiner tree and rectilinear Steiner tree problems.
The Math Forum is a research and educational enterprise of the Drexel School of Education.
mathforum.org /library/view/16611.html   (96 words)

  
 Heuristic Algorithm for Steiner Trees   (Site not responding. Last check: 2007-10-20)
Heuristic Algorithm for Steiner Trees (H) INPUT: An undirected graph G = (V, E) and a set of Steiner Points
Length(P) Length of a spanning tree for G
Length(P) Length of the minimal spanning tree for G
www.eas.asu.edu /~cse534/steiner.html   (292 words)

  
 Euclidean Steiner tree   (Site not responding. Last check: 2007-10-20)
Definition: A tree of minimum Euclidean distance connecting a set of points, called terminals, in the plane.
This tree may include points other than the terminals, which are called Steiner points.
Joseph L. Ganley, "Euclidean Steiner tree", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
www.nist.gov /dads/HTML/euclidSteinerTree.html   (98 words)

  
 The Steiner Tree Page   (Site not responding. Last check: 2007-10-20)
So, I've created a Steiner tree mailing list, through which the Steiner tree community can easily communicate with one another.
Open Problems: some open problems related to Steiner trees.
This package, entitled GeoSteiner 3.0, computes optimal Euclidean and rectilinear Steiner trees (as well as minimum spanning trees in hypergraphs).
ganley.org /steiner   (208 words)

  
 1.5.10 Steiner Tree   (Site not responding. Last check: 2007-10-20)
Excerpt from The Algorithm Design Manual: Steiner tree often arises in network design and wiring layout problems.
Suppose we are given a set of sites that must be connected by wires as cheaply as possible.
The Steiner tree problem is distinguished from the minimum spanning tree problem in that we are permitted to construct or select intermediate connection points to reduce the cost of the tree.
www.cs.sunysb.edu /~algorith/files/steiner-tree.shtml   (166 words)

  
 Amazon.com: Steiner Trees in Industry (Combinatorial Optimization): Books: Xiuzhen Cheng,Ding-Zhu Du   (Site not responding. Last check: 2007-10-20)
This book is a collection of 16 state-of-the-art articles contributed by the most influential experts in the field of Steiner tree applications.
The articles are designed to explore the impact on industries of the long-term theoretical development of Steiner tree problems.
The authors address various Steiner tree problems originating from and applied to industry fields, such as the design of electronic circuits, telecommunication networks, computer networks, and computer biology.
www.amazon.com /Steiner-Trees-Industry-Combinatorial-Optimization/dp/1402000995   (887 words)

  
 An Efficient Hierarchical Timing-Driven Steiner Tree Algorithm for Global Routing   (Site not responding. Last check: 2007-10-20)
In this paper, we propose a hierarchical timing-driven Steiner tree algorithm for global routing which considers the minimization of timing delay during the tree construction as the goal.
The algorithm uses heuristic approach to decompose the problem of minimum delay Steiner tree into hierarchy and to construct the sub-trees respectively based on dynamic programming technique.
Taking the net topology into consideration, we build the final routing tree by reconnecting the sub-trees at each level recursively and then improve the connection with the objective of minimizing the delay from source to sink pins on the critical path.
csdl.computer.org /comp/proceedings/vlsid/2002/1441/00/14410473abs.htm   (200 words)

  
 1.4.3 Minimum Spanning Tree   (Site not responding. Last check: 2007-10-20)
Telephone companies are particularly interested in minimum spanning trees, because the minimum spanning tree of a set of sites defines the wiring scheme that connects the sites using as little wire as possible.
Deleting the long edges from a minimum spanning tree leaves connected components that define natural clusters in the data set, as shown in the output figure above.
They can be used to give approximate solutions to hard problems such as Steiner tree and traveling salesman.
www.cs.sunysb.edu /~algorith/files/minimum-spanning-tree.shtml   (305 words)

  
 [No title]
This problem is known in the literature as the Steiner tree problem.
We find all possible trees that span the the S nodes.
where Talg is the cost tree of the algorithm, and Topt is the cost of the optimal solution.
www.cs.ucr.edu /~michalis/COURSES/99-141/steiner.html   (613 words)

  
 Steiner tree - Wikipedia, the free encyclopedia
In addition, the vertices in V cannot have direct connections amongst themselves.
The Steiner tree problem has applications in circuit layout or network design.
F.K. Hwang, D.S. Richards, P. Winter, The Steiner Tree Problem.
en.wikipedia.org /wiki/Steiner_tree   (413 words)

  
 Steiner Tree Extraction   (Site not responding. Last check: 2007-10-20)
This project explores parallel algorithms for computing the final stage of Fred Harris's algorithm for Steiner Tree Extraction.
The overall project was led by Roy Pargas.
Spoon, Steven A. "A Parallel Branch-and-Bound Algorithm for Finding Steiner Minimal Trees".
www.lexspoon.org /steiner   (47 words)

  
 Martin Zachariasen
I have been working on heuristics and exact methods for two classical NP-hard problems: The Travelling Salesman Problem and the Steiner Tree Problem, in particular their geometric (plane) versions.
Full list of publications sorted by date or publication type.
Brazil, M. and Zachariasen, M. Steiner Trees for Fixed Orientation Metrics.
www.diku.dk /users/martinz   (336 words)

  
 GeoSteiner Homepage   (Site not responding. Last check: 2007-10-20)
Warme, D.M. Spanning Trees in Hypergraphs with Applications to Steiner Trees.
Winter, P. and Zachariasen, M. Euclidean Steiner Minimum Trees: An Improved Exact Algorithm.
Warme, D. M., Winter, P. and Zachariasen, M. Exact Algorithms for Plane Steiner Tree Problems: A Computational Study.
www.diku.dk /geosteiner   (194 words)

  
 GSRC Calibrating Achievable Design Bookshelf: Rectilinear Steiner Minimum Tree Slot   (Site not responding. Last check: 2007-10-20)
Given a set P of n points, find a set S of Steiner points such that the Minimum Spanning Tree (MST) over P + S has minimum cost.
The BI1S, BOI, and batched greedy heuristics come on the average within 0.5-0.7% of the optimum RSMT.
Highly scalable rectilinear and octilinear Steiner Tree code based on batched triple contraction
vlsicad.ucsd.edu /GSRC/bookshelf/Slots/RSMT   (154 words)

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