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The geometry of graphs and some of its algorithmic applications

Nathan Linial, Eran London, Yuri Rabinovich
1995 Combinatorica  
In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graph-theoretic and algorithmic problems.  ...  Given a graph G we map its vertices to a normed space in an attempt to (i) Keep down the dimension of the host space and (ii) Guarantee a small distortion, i.e., make sure that *Supported in part by grants  ...  Acknowledgments The authors wish to thank Mike Saks, Micha A. Perles and Gil Kalai for stimulating discussions. Thanks are also due to Alex Samorodnitsky.  ... 
doi:10.1007/bf01200757 fatcat:lhkhob7abvhc7bhcfzyci7uqoy

The geometry of graphs and some of its algorithmic applications

N. Linial, E. London, Y. Rabinovich
Proceedings 35th Annual Symposium on Foundations of Computer Science  
In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graph-theoretic and algorithmic problems.  ...  Given a graph G we map its vertices to a normed space in an attempt to (i) Keep down the dimension of the host space and (ii) Guarantee a small distortion, i.e., make sure that *Supported in part by grants  ...  Acknowledgments The authors wish to thank Mike Saks, Micha A. Perles and Gil Kalai for stimulating discussions. Thanks are also due to Alex Samorodnitsky.  ... 
doi:10.1109/sfcs.1994.365733 dblp:conf/focs/LinialLR94 fatcat:iunifgtvojelnotboe7bezoplu

Classical computational geometry in GeomNet

Gill Barequet, Stina S. Bridgeman, Christian A. Duncan, Michael T. Goodrich, Roberto Tamassia
1997 Proceedings of the thirteenth annual symposium on Computational geometry - SCG '97  
We also provide seved examples of actual geometric algorithms that our system already supports. Application domains for GeomNet include collaborative research and dist ante education.  ...  In this paper we present GeomNet, a system for performing dktributed geometric computing over the Internet.  ...  References Having covered some of the features of GeomNet, let us now discuss some example applications. Fundamental Algorithms.  ... 
doi:10.1145/262839.263035 dblp:conf/compgeom/BarequetBDGT97 fatcat:ax6ffc37ojeilnmsfqgehmqhya

A National Effort for Motivating Indian Students and Teachers towards Algorithmic Research [article]

Subir Kumar Ghosh, Sudebkumar Prasant Pal
2016 arXiv   pre-print
The lectures were meant to provide exposure to the field of graph and geometric algorithms and to motivate the participants towards research.  ...  During 2008-2015, twenty-two introductory workshops on graph and geometric algorithms were organized for teachers and students (undergraduate, post-graduate and doctoral) of engineering colleges and universities  ...  These lectures can be classified broadly into four categories: (i) Algorithmic Paradigms, (ii) Graphs and Algorithms, (iii) Geometry and Algorithms, and (iv) Geometry and Applications.  ... 
arXiv:1507.06056v3 fatcat:6u6faxlkajf5fmdx3monmibge4

GeomNet: geometric computing over the Internet

G. Barequet, C.A. Duncan, M.T. Goodrich, S.S. Bridgeman, R. Tamassia
1999 IEEE Internet Computing  
ACKNOWLEDGMENTS We thank Yair Amir, Jim Baker, Ashim Garg, and Subodh Kumar for several useful discussions regarding geometric software and distributed computing.  ...  His research interests include analysis, design, and implementation of algorithms; computational geometry; graph algorithms; data structures; graph drawing; and information visualization.  ...  Figure 4 . 4 Some graph-drawing examples: (a) the flights database, (b) the Bend-Stretch algorithm, (c) the Giotto algorithm, (d) the Sugiyama algorithm.  ... 
doi:10.1109/4236.761650 fatcat:vuwx4sap7nfnnhsge6xuie3rru

Non-Euclidean Spring Embedders

S.G. Kobourov, K. Wampler
2005 IEEE Transactions on Visualization and Computer Graphics  
We present a method by which force-directed algorithms for graph layouts can be generalized to calculate the layout of a graph in an arbitrary Riemannian geometry.  ...  In particular, we formally describe the calculations needed to extend such algorithms to hyperbolic and spherical geometries.  ...  Acknowledgments We would like to thank the anonymous referees for pointing out two publications, relevant to our work [2, 6] .  ... 
doi:10.1109/tvcg.2005.103 pmid:16270867 fatcat:nhshmnhfrngdfbcuh4ezg6b3xi

Methodology and Techniques [chapter]

Dirk Knaust
2012 Developments in Sedimentology  
We present a method by which force-directed algorithms for graph layouts can be generalized to calculate the layout of a graph in an arbitrary Riemannian geometry.  ...  In particular, we formally describe the calculations needed to extend such algorithms to hyperbolic and spherical geometries.  ...  Acknowledgments We would like to thank the anonymous referees for pointing out two publications, relevant to our work [2, 6] .  ... 
doi:10.1016/b978-0-444-53813-0.00009-5 fatcat:ojtyvy2asnhm7mhuhhmf65li7q

Page 1111 of Mathematical Reviews Vol. 51, Issue 4 [page]

1976 Mathematical Reviews  
It is shown how sequential graphs can be used for modelling and the solution of some dynamic pro- gramming problems.  ...  Ford’s algorithm, the Bellmann-Kalaba COMBINATORICS 51 #47911-7915 algorithm for finding the shortest paths in a graph, the branch and bound method and Little’s algorithm for the determination of the minimal  ... 

Preface: Special issue on distances in optimization and graphs dedicated to the memory of Michel Deza

Antonio Mucherino, Carlile Lavor
2019 Optimization Letters  
Other scientific interests of Michel mainly include geometry, optimization and graph theory.  ...  Sikirić of one of the contributions (the one entitled "Generalized Cut and Metric Polytopes of Graphs and Simplicial Complexes"), as he had started to work on the topic with his co-author.  ...  Together with other colleagues, we co-authored together a paper where we have introduced some auxiliary graphs in the context of distance geometry, which can be exploited for the study of its solution  ... 
doi:10.1007/s11590-019-01466-1 fatcat:vh3m6bon3jcwbnes6cjlxyru7y

Computational Geometry (Dagstuhl Seminar 19181)

Siu-Wing Cheng, Anne Driemel, Jeff Erickson, Michael Wagner
2019 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 19181 "Computational Geometry".  ...  The seminar was held from April 28 to May 3, 2019 and 40 participants from various countries attended it. New advances and directions in computational geometry were presented and discussed.  ...  Applications have been found not only in making progress on long-standing combinatorial geometry problems, but also in the design and analysis of efficient algorithms for fundamental geometric problems  ... 
doi:10.4230/dagrep.9.4.107 dblp:journals/dagstuhl-reports/ChengD019 fatcat:w2kqoyd5mngt7bn32gc25w4jie

Design Enabler to Recognize Duplicate Geometries in CAD Assemblies

Aravind Shanthakumar, Joshua D. Summers
2013 Computer-Aided Design and Applications  
This paper presents the algorithm, a justification, and example test cases and scenarios that demonstrate its utility.  ...  might be integrated in some manner to reduce mass in the assembly.  ...  between geometries based on the application and experience for the duplicate geometry analysis.  ... 
doi:10.3722/cadaps.2013.889-904 fatcat:osxcj7mbsvgtxkqoc2bzfbi7la

Spatial Query Localization Method In Limited Reference Point Environment

Victor Krebss
2013 Zenodo  
Due to the known coordinates of individual nodes (anchors), it is possible to determine the location of all (or part) of the remaining nodes of the graph.  ...  search routines and geometry functions.  ...  We expect that research interest in such queries will grow as the number of embedded or mobile devices and related services continue to increase.  ... 
doi:10.5281/zenodo.1074278 fatcat:cunbivwsu5ffvggicsso2uyt5u

An efficient algorithm for finding a two-pair, and its applications

Srinivasa R. Arikati, C. Pandu Rangan
1991 Discrete Applied Mathematics  
A pair (u, o) of nonadjacent vertices in G form a two-pair if every chordless path between u and v is of length two. We shall digress briefly to remark on the applications of our problem.  ...  One of the fundamental notions in computational geometry is the concept of visibility.  ...  Acknowledgement We thank the referees for their helpful comments.  ... 
doi:10.1016/0166-218x(91)90033-s fatcat:dknozmqdeveffdoe5z5buk7dni

Guest editor's foreword

David Kirkpatrick
2012 Computational geometry  
Acknowledgements I acknowledge with thanks the diligence, commitment and energy of the authors and the referees without which this special issue would not have been possible.  ...  It provides several new algorithms for computing the length of shortest non-contractible and shortest non-separating cycles in graphs embedded on surfaces of genus g.  ...  All submissions were carefully refereed and revised in accordance with the high standards of Computational Geometry: Theory and Applications.  ... 
doi:10.1016/j.comgeo.2011.12.004 fatcat:o2d5lfmohreabjm2jgegutptwq

Editorial: 3rd International Castle Meeting on Coding Theory and Applications

Joaquim Borges, Mercè Villanueva, Victor Zinoviev
2012 Designs, Codes and Cryptography  
Auger, Cohen, and Mesnager consider the covering problem in a simple, finite, connected graph by the minimum number of spheres with fixed radius and connected it to some other problems in combinatorics  ...  Relationships between Graph Theory and Coding Theory is also the subject of some papers.  ... 
doi:10.1007/s10623-012-9775-2 fatcat:pa276hqqgja4fjsq44biyataja
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