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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

1995
*
SIAM Journal on Discrete Mathematics
*

Given a set S

doi:10.1137/s0895480194262710
fatcat:jli3yxktnzdhfbcy6vd5t5tioy
*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]. ...##
###
Aesthetic layout of generalized trees

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*...

##
###
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

1985
*
Journal of Mathematical Analysis and Applications
*

Explicit

doi:10.1016/0022-247x(85)90170-2
fatcat:aoxqj4kcvrbtpfzrscbwa4hrum
*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] . ...##
###
The complexity of drawing trees nicely

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. ...

##
###
A survey of heuristics for the weighted matching problem

1983
*
Networks
*

Applications to practical problems

doi:10.1002/net.3230130404
fatcat:ltmjfisuwzcd5ptfnm76qvxzky
*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. ...##
###
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

1981
*
Computers and Mathematics with Applications
*

In

doi:10.1016/0898-1221(81)90084-5
fatcat:biozpvgbmvhrrjy7pxmzfy356e
*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. ...##
###
CySpanningTree: Minimal Spanning Tree computation in Cytoscape

2015
*
F1000Research
*

This article demonstrates

doi:10.12688/f1000research.6797.1
fatcat:b5fvela6jbcczad2bo3einqkhy
*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. ...##
###
A Randomized O(log2 k)-Competitive Algorithm for Metric Bipartite Matching

2012
*
Algorithmica
*

This analysis

doi:10.1007/s00453-012-9676-9
fatcat:27ilmekjxjfkxohmebdfdnelgu
*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) ...##
###
Algorithms for drawing graphs: an annotated bibliography

1994
*
Computational geometry
*

Research

doi:10.1016/0925-7721(94)00014-x
fatcat:rwudrni2evgkle42lecplbjhle
*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 ...##
###
Technical Foundations
[chapter]

2004
*
Mathematics and Visualization
*

We gratefully acknowledge

doi:10.1007/978-3-642-18638-7_2
fatcat:mb3iwcem7zfl7mxkop54qr24vm
*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 ...##
###
The Travelling Salesman Problem and Minimum Matching in the Unit Square

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. ...

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