Jon Louis Bentley and Jerome H. Friedman. Fast algorithms for constructing minimal spanning trees in coordinate spaces. IEEE Transactions on Computers, C-27(2):97--105, February 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the current candidate match. Several single link clustering algorithms have been proposed, and a survey of these algorithms is provided in [141] We have chosen to use algorithms based on the minimal cost spanning tree (MCST) because of the natural relationship between MCST and nearest neighbours [9, 140], and because there are a number of good algorithms for constructing MCST s [11, 84, 93] The cluster information can be represented as a binary tree which can be computed from the MCST of the original codewords [62] Before we discuss the binary tree representation of the cluster information, we ....

....T = fV; E g of minimum length. Since we constructed G to be a complete graph, then we are guaranteed the existence of T . We also note that jE j = n Gamma 1) MCST s have been thoroughly studied, and there are a number of algorithms available for finding T for a given G (see for example [66, 9]) Among the most popular ones are those by J. Kruskal (1956) and R.C. Prim (1957) Prim s algorithm, for example, builds the MCST by starting with any vertex and always taking next the vertex closest to the vertices already taken. In other words, we find the edge of smallest weight among those ....

Jon Louis Bentley and Jerome H. Friedman. Fast algorithms for constructing minimal spanning trees in coordinate spaces. IEEE Transactions on Computers, C-27(2):97--105, February 1978. 275

....space with the interpoint distances satisfying the relationship given above. The computational effort required by the algorithm is reduced considerably by taking advantage of the geometrical properties of the space. The most efficient previously published algorithm is that of Bently and Friedman [1] (which uses a k d tree structure ) It has an effort of O(n log n) for normally distributed data sets. This has been given as the lower bound to the MST problem [2,11] The increased efficiency of the proposed algorothm for favorable data configurations is due to the use of systems of grids to ....

....connect the clusters. Data with numerous tight clusters will have intercluster distances that are not large in comparison to the total p volume of the space which means that such clusters can be linked together without having to consider all intercluster distances at once. Bentley and Friedman [ 1 ] state that their algorithm requires O(n log n) effort for favorable data. For unfavorable data (e.g. a pair of tight clusters) the effort can reach O(n 2) estimated based on a plot of their simulation result) In this latter case (as in the 8 MST method) the greatly increased computational ....

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J.L. Bentley and J. Friedman, Fast algorithms for constructing minimal spanning trees in coordinate spaces, Stanford Univ. Computer Sci. Report No. STAN-CS75 -482 (1975) 26pp.

....of our program with existing ones, including LEDA [Mehlhorn and N aher 1995] and Triangle [Shewchuk 1996] for d = 2, and Qhull [Barber et al. 1996] for d 2. After considering practical issues, several older algorithms were not selected for comparison. Among them, the best algorithm may be due to Bentley and Friedman [1978] (variant of Prim s using k d trees) Their experiments suggest that it runs in O(n log n) time and that it performs poorly on clustered inputs. It should be noted that algorithms having better expected running times do exist. Using the fact that geographic neighbor graphs can be computed in ....

....algorithm for computing (Euclidean) Delaunay triangulations for quasi uniform distributions in xed dimension. All these approaches used bucketing techniques, which tend to perform poorly on clustered distributions as argued by Shewchuk [1996] Also, Bentley [1992] chose the algorithm in [Bentley and Friedman 1978] (over the one based on [Bentley et al. 1980] when implementing the MST heuristic for TSP. We conclude that for computing GMSTs for points in d , d 3, the wellseparated pair decomposition is a practical and sophisticated tool and our resulting program outperforms available implementations ....

Bentley, J. L. and Friedman, J. H. 1978. Fast algorithms for constructing minimal spanning trees in coordinate spaces. IEEE Trans. Comput. C-27, 97-105.

....7 8717: Topics in Algorithms Semester Project Minimum Spanning Tree 1. Implement algorithms for minimum spanning trees (of a set of points in d dimensional space) based on the k d trees data structure [1], and then compare their performance to that of GeoMST2 [2] of which an implementation already exists) Also implement at least one bucketing based algorithms [3, 4] for computing minimum spanning trees of a set of points in d dimensional space; then compare their performance to that of GeoMST2 ....

J. L. Bentley and J. H. Friedman. Fast algorithms for constructing minimal spanning trees in coordinate spaces. IEEE Trans. Comput., C-27:97--105, 1978.

.... outputfile c( newkey x1( newkey x2( if ( i samplesize 1 ) outputfile , endl; else outputfile ) endl; outputfile endl; End graph table initialization output the data in a form Splus can plot outputfile endl plot(data.out[ 1],data.out[ 2] xlab= x ,ylab= y ,pch=16) endl; get minimal spanning tree mst = minimalspanningtree(sample, graphtable) output the mst in a form Splus can source PlaneEdgeSetIterator mstiterator = PlaneEdgeSetIterator(mst) for (i = 0; i ....

....for cubic spline smoothing. So future versions should include spline smoothing algorithms. The algorithm for finding the minimal spanning tree is not well suited for large datasets. If this proves to be a problem, alternative methods will be explored for obtaining the minimal spanning tree. See [1] for some of these alternative methods. 9 Glossary barycentric coordinates given a point x on a line, the barycentric coordinate is the ratio of the distance from x to the end of the line segment and the length of the line segment. minimal spanning tree the cheapest possible spanning tree ....

J.L. Bentley and J.H. Friedman. Fast algorithms for constructing minimal spanning trees in coordinate spaces. IEEE Transactions on Computers, C-27, No.2:97--105, 1978.

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Jon Louis Bentley and Jerome H. Friedman. Fast algorithms for constructing minimal spanning trees in coordinate spaces. IEEE Transactions on Computers, C-27(2):97--105, February 1978.

No context found.

Jon Louis Bentley and Jerome H. Friedman. Fast algorithms for constructing minimal spanning trees in coordinate spaces. IEEE Transactions on Computers, C-27(2):97--105, February 1978.

No context found.

Jon Louis Bentley and Jerome H. Friedman. Fast algorithms for constructing minimal spanning trees in coordinate spaces. IEEE Transactions on Computers, 1978.

No context found.

Bentley, J.L. and Friedman, J.H., \Fast algorithms for constructing minimal spanning trees in coordinate spaces", IEEE Transactions on Computers, C-27, 97-105, 1978.

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