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Page 6363 of Mathematical Reviews Vol. , Issue 97J [page]

1997 Mathematical Reviews  
(A-TGRZ-A; Graz); Prodinger, Helmut (A-TUWN-B; Vienna) On the optimality of an algorithm of Reingold and Supowit. (English summary) J. Autom. Lang. Comb. 1 (1996), no. 1, 5—11. Summary: “E. M.  ...  Applying an elementary strategy on an appropriate subinterval of the PLP yields the approximation algorithms. We give two such strategies.  ... 

Page 2473 of Mathematical Reviews Vol. , Issue 84f [page]

1984 Mathematical Reviews  
The worst case performance of an algorithm is defined as the greatest possible cost, as a function of n, of the matching produced by the algorithm on a set of n points.  ...  2473 90B Operations research and management science Supowit, Kenneth J.; Reingold, Edward M. 84f:90032a Divide and conquer heuristics for minimum weighted Euclidean matching. SIAM J.  ... 

Equidistribution in all Dimensions of Worst-case Point Sets for the Traveling Salesman Problem

Timothy Law Snyder, J. Michael Steele
1995 SIAM Journal on Discrete Mathematics  
Given a set S of n points in the unit square [0,1]d, an optimal traveling salesman tour of S is a tour of S that is of minimum length.  ...  An open problem is to determine the structure of S(n).  ...  We also note that Theorem 1 hs a close connection to some results and a conjecture of Supowit, Reingold, nd Plaisted [11].  ... 
doi:10.1137/s0895480194262710 fatcat:jli3yxktnzdhfbcy6vd5t5tioy

Aesthetic layout of generalized trees

Anthony Bloesch
1993 Software, Practice & Experience  
The algorithms described are suitable for such tasks as the layout of class hierarchies, directory trees and tableau-style proofs.  ...  Two algorithms are presented for the layout of generalized trees, and general issues, such as appropriate aesthetics, are discussed.  ...  Aesthetics 1-3 have been generalized from Wetherell and Shannon, 5 aesthetic 4 is from Reingold and Tilford 1 and 5-6 are based on aesthetics from Supowit and Reingold. 2 To facilitate the display of  ... 
doi:10.1002/spe.4380230802 fatcat:bmqxbqe7ljclvamdb4sw7bmpla

Page 4231 of Mathematical Reviews Vol. , Issue 81J [page]

1981 Mathematical Reviews  
Dobkin, Detection is easier than computation (extended abstract) (pp. 146-153); Leo J, Guibas and F, Frances Yao, On translating a set of rectangles (Pp. 154-160); Martin Tompa, An optimal solution to  ...  Reif and Paul G. Spirakis, Random matroids (pp. 385-397); Kenneth J. Supowit, David A. Plaisted and Edward M. Reingold, Heuristics for weighted perfect matching (pp. 398-419); Greg N.  ... 

Recurrence relations based on minimization and maximization

S Kapoor, E.M Reingold
1985 Journal of Mathematical Analysis and Applications  
Explicit and asymptotic solutions are presented to the recurrence M(1) =g( I), M(n+l)=g(n+l)+min lGri.(aM(t)+jM(n+  ...  A are as defined above. 1 KAPOOR AND REINGOLD ) was obtained, but not fully solved, by Supowit and Reingold in the worst case analysis of a heuristic for weighted Euclidean matching [ 63. . .  ...  Such recurrences arise commonly in the analysis of algorithms, especially algorithms based on dynamic programming or divide and conquer techniques [2] .  ... 
doi:10.1016/0022-247x(85)90170-2 fatcat:aoxqj4kcvrbtpfzrscbwa4hrum

The complexity of drawing trees nicely

Kenneth J. Supowit, Edward M. Reingold
1983 Acta Informatica  
The notion of what is aesthetically pleasing is embodied in several constraints on the placement of nodes, relative to other nodes.  ...  Among the results we give are: (1) There is no obvious "principle of optimality" that can be applied, since globally narrow, aesthetic placements of trees may require wider than necessary subtrees. (2)  ...  Suboptimality of the Reingold-Tilford algorithm The Reingold-Tilford (RT) algorithm for producing eumorphous placements works on a tree T essentially as follows: 1.  ... 
doi:10.1007/bf00289576 fatcat:zcnu5iyn6vcnpemikijnoxjbh4

A survey of heuristics for the weighted matching problem

David Avis
1983 Networks  
Applications to practical problems and some mathematical complements are also included. [ 271 D. W. Walkup, On the expected value of a random assignment problem. SZAM J.  ...  This survey paper reviews results on heuristics for two weighted matching problems: matchings where the vertices are points in the plane and weights are Euclidean distances, and the assignment problem.  ...  Finally, in Reingold and Supowit [ 191, some average-case results are given for the heuristics described in their earlier papers.  ... 
doi:10.1002/net.3230130404 fatcat:ltmjfisuwzcd5ptfnm76qvxzky

Page 1168 of Mathematical Reviews Vol. , Issue 84c [page]

1984 Mathematical Reviews  
D’ Antona (Pavia) Supowit, Kenneth J.; Reingold, Edward M. 84c:68033 The complexity of drawing trees nicely. Acta Inform. 18 (1982/83), no. 4, 377-392.  ...  We derive a new linear lower bound, and we describe an algorithm leading to a quasilinear upper bound.” Mansfield, Anthony Determining the thickness of graphs is NP-hard. Math. Proc.  ... 

Worst case bounds for the Euclidean matching problem

David Avis
1981 Computers and Mathematics with Applications  
In the case of 2 dimensions, bounds are obtained directly. For higher dimensions, an appeal is made to known bounds for the sphere packing problem that have appeared in the mathematical literature.  ...  It is shown how the classical mathematical theory of sphere packing can be used to obtain bounds for a greedy heuristic for the bounded euclidean matching problem.  ...  An example similar to the first example of Section 2 was also discovered independently by him.  ... 
doi:10.1016/0898-1221(81)90084-5 fatcat:biozpvgbmvhrrjy7pxmzfy356e

CySpanningTree: Minimal Spanning Tree computation in Cytoscape

Faizaan Shaik, Srikanth Bezawada, Neena Goveas
2015 F1000Research  
This article demonstrates the procedure for extraction of a spanning tree from complex data sets like gene expression data and world network.  ...  CySpanningTree provides two historical ways for calculating a spanning tree: Prim's and Kruskal's algorithms.  ...  open source community for helping with Cytoscape API to extract the subnetwork in an intuitive way.  ... 
doi:10.12688/f1000research.6797.1 fatcat:b5fvela6jbcczad2bo3einqkhy

A Randomized O(log2 k)-Competitive Algorithm for Metric Bipartite Matching

Nikhil Bansal, Niv Buchbinder, Anupam Gupta, Joseph Naor
2012 Algorithmica  
This analysis of the greedy algorithm allows us to lower bound the optimal cost of an instance.  ...  In an α-HST, edge weights increase by a factor of α as one goes from the leaves to the root. Specifically, the algorithm of [19] requires α = O(log k).  ...  A possible starting point can be the "hyper-greedy" heuristic of Supowit, Plaisted, and Reingold [23] that achieves an O(log k)-approximation to the offline metric matching problem, or the (offline)  ... 
doi:10.1007/s00453-012-9676-9 fatcat:27ilmekjxjfkxohmebdfdnelgu

Algorithms for drawing graphs: an annotated bibliography

Giuseppe Di Battista, Peter Eades, Roberto Tamassia, Ioannis G Tollis
1994 Computational geometry  
Research on this topic is spread over the broad spectrum of Computer Science.  ...  In this paper we present a bibliographic survey on algorithms whose goal is to produce aesthetically pleasing drawings of graphs.  ...  Acknowledgements The authors wish to thank the many graph drawers who have pointed out errors and omissions in the first three versions, and those who have helped with updates to create this fourth version  ... 
doi:10.1016/0925-7721(94)00014-x fatcat:rwudrni2evgkle42lecplbjhle

Technical Foundations [chapter]

Michael Jünger, Petra Mutzel
2004 Mathematics and Visualization  
We gratefully acknowledge the many contributions of the authors of the subsequent chapters. In particular, were very helpful for corrections and improvements.  ...  [43] have presented an algorithm which solves the one-edge insertion problem optimally over the set of all embeddings of G in linear time, thus overcoming this problem.  ...  It has been shown by Supowit and Reingold [65] that achieving minimum grid width is N P-hard, and, even worse, that, unless P = N P, there is no polynomial time algorithm for achieving a width that is  ... 
doi:10.1007/978-3-642-18638-7_2 fatcat:mb3iwcem7zfl7mxkop54qr24vm

The Travelling Salesman Problem and Minimum Matching in the Unit Square

Kenneth J. Supowit, Edward M. Reingold, David A. Plaisted
1983 SIAM journal on computing (Print)  
The cost of the minimum 4+ O(4), where matching of n points in the unit square is shown to be, in the worst case, a opt 0.537 mat <0.707 Furthermore, for each of these two problems there is an almost linear  ...  time heuristic opt algorithm whose worst case cost is, neglecting lower order terms, as low as possible.  ...  To derive an upper bound on the cost of the tour produced, we will bound the sum of the horizontal and vertical components, and then use the triangle inequality.  ... 
doi:10.1137/0212009 fatcat:sikverobmzdovd5xw6aewshbee
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