Overview
- Editors:
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Richard Pollack
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János Pach
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Jacob E. Goodman
- Presents a comprehensive picture of the current state of the field of discrete and computational geometry
- Includes an expanded preface, with a set of photographs of groups and individuals who have played a major role in the history of the field in the past 20 years
- Contains 28 major articles, chosen for the importance of their results, the breadth of their scope, and to show the intimate connections between discrete and computational geometry and other areas of both computer science and mathematics
- Some articles solve long-outstanding problems in the field
- Editors are pre-eminent founders of the journal and the field itself
- Includes supplementary material: sn.pub/extras
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Table of contents (28 chapters)
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- Eyal Ackerman, Kevin Buchin, Christian Knauer, Rom Pinchasi, Günter Rote
Pages 1-14
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- Pankaj K. Agarwal, Rolf Klein, Christian Knauer, Stefan Langerman, Pat Morin, Micha Sharir et al.
Pages 1-21
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- Pankaj K. Agarwal, Sariel Har-Peled, Hai Yu
Pages 1-21
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- Imre Bárány, Alfredo Hubard, Jesús Jerónimo
Pages 1-9
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- Alexander Barvinok, Isabella Novik
Pages 1-24
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- Saugata Basu, Thierry Zell
Pages 1-23
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- Louis J. Billera, Samuel K. Hsiao, J. Scott Provan
Pages 1-15
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- Jean-Daniel Boissonnat, David Cohen-Steiner, Gert Vegter
Pages 1-20
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- Ciprian Borcea, Xavier Goaoc, Sylvain Petitjean
Pages 1-16
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- Otfried Cheong, Xavier Goaoc, Andreas Holmsen, Sylvain Petitjean
Pages 1-19
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- Mirela Damian, Robin Flatland, Joseph O’Rourke
Pages 1-26
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- Paolo Gronchi, Marco Longinetti
Pages 1-25
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- Leonid Khachiyan, Endre Boros, Konrad Borys, Vladimir Gurvich, Khaled Elbassioni
Pages 1-17
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- Jeong-Yup Lee, Boris Solomyak
Pages 1-20
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About this book
While we were busy putting together the present collection of articles celebrating the twentieth birthday of our journal, Discrete & Computational Geometry, and, in a way, of the ?eld that has become known under the same name, two more years have elapsed. There is no doubt that DCG has crossed the line between childhood and adulthood. By the mid-1980s it became evident that the solution of many algorithmic qu- tions in the then newly emerging ?eld of computational geometry required classical methodsandresultsfromdiscreteandcombinatorialgeometry. Forinstance,visibility and ray shooting problems arising in computer graphics often reduce to Helly-type questions for line transversals; the complexity (hardness) of a variety of geometric algorithms depends on McMullen’s upper bound theorem on convex polytopes or on the maximum number of “halving lines” determined by 2n points in the plane, that is, the number of different ways a set of points can be cut by a straight line into two parts of the same size; proximity questions stemming from several application areas turn out to be intimately related to Erdos’ ? s classical questions on the distribution of distances determined by n points in the plane or in space. On the other hand, the algorithmic point of view has fertilized several ?elds of c- vexity and of discrete geometry which had lain fallow for some years, and has opened new research directions.
About the authors
Jacob Goodman, Richard Pollack and János Pach are each distinguished professors and authors in their own right, and together they are the pre-eminent founders and editors-in-chief of the journal, Discrete & Computational Geometry. Over the 20 years since the founding of this premiere journal, it has become synonymous with the field of discrete and computational geometry itself.
