eBook ISBN:  9780821881323 
Product Code:  CONM/453.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821881323 
Product Code:  CONM/453.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 453; 2008; 556 ppMSC: Primary 01; 05; 14; 51; 52; 55; 68
This volume contains nineteen survey papers describing the state of current research in discrete and computational geometry as well as a set of open problems presented at the 2006 AMSIMSSIAM Summer Research Conference "Discrete and Computational Geometry—Twenty Years Later", held in Snowbird, Utah, in June 2006. Topics surveyed include metric graph theory, lattice polytopes, the combinatorial complexity of unions of geometric objects, line and pseudoline arrangements, algorithmic semialgebraic geometry, persistent homology, unfolding polyhedra, pseudotriangulations, nonlinear computational geometry, \(k\)sets, and the computational complexity of convex bodies.
Discrete and computational geometry originated as a discipline in the mid1980s when mathematicians in the wellestablished field of discrete geometry and computer scientists in the (then) nascent field of computational geometry began working together on problems of common interest. The combined field has experienced a huge growth in the past twenty years, which the present volume attests to.
ReadershipGraduate students and research mathematicians interested in discrete and computational geometry.

Table of Contents

Articles

Branko Grünbaum — Musings on discrete geometry and “20 years of discrete & computational geometry” [ MR 2405675 ]

Pankaj K. Agarwal, János Pach and Micha Sharir — State of the union (of geometric objects) [ MR 2405676 ]

HansJürgen Bandelt and Victor Chepoi — Metric graph theory and geometry: a survey [ MR 2405677 ]

Imre Bárány — Extremal problems for convex lattice polytopes: a survey [ MR 2405678 ]

Nicolas Bartholdi, Jérémy Blanc and Sébastien Loisel — On simple arrangements of lines and pseudolines in $\Bbb P^2$ and $\Bbb R^2$ with the maximum number of triangles [ MR 2405679 ]

Alexander Barvinok and Ellen Veomett — The computational complexity of convex bodies [ MR 2405680 ]

Saugata Basu — Algorithmic semialgebraic geometry and topology—recent progress and open problems [ MR 2405681 ]

Robert Connelly — Expansive motions [ MR 2405682 ]

Erik D. Demaine, Blaise Gassend, Joseph O’Rourke and Godfried T. Toussaint — All polygons flip finitely$\ldots $ right? [ MR 2405683 ]

Herbert Edelsbrunner and John Harer — Persistent homology—a survey [ MR 2405684 ]

Andreas F. Holmsen — Recent progress on line transversals to families of translated ovals [ MR 2405685 ]

Gabriel Nivasch — An improved, simple construction of many halving edges [ MR 2405686 ]

Joseph O’Rourke — Unfolding orthogonal polyhedra [ MR 2405687 ]

Radoš Radoičić and Géza Tóth — The discharging method in combinatorial geometry and the PachSharir conjecture [ MR 2405688 ]

Günter Rote, Francisco Santos and Ileana Streinu — Pseudotriangulations—a survey [ MR 2405689 ]

Frank Sottile and Thorsten Theobald — Line problems in nonlinear computational geometry [ MR 2405690 ]

Pavel Valtr — On empty hexagons [ MR 2405691 ]

Uli Wagner — $k$sets and $k$facets [ MR 2405692 ]

Xianglin Wei and Ren Ding — An ErdősSzekeres type problem for interior points [ MR 2405693 ]

Chuanming Zong — The kissing number, blocking number and covering number of a convex body [ MR 2405694 ]

Edited by János Pach — Open problems [ MR 2405695 ]


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This volume contains nineteen survey papers describing the state of current research in discrete and computational geometry as well as a set of open problems presented at the 2006 AMSIMSSIAM Summer Research Conference "Discrete and Computational Geometry—Twenty Years Later", held in Snowbird, Utah, in June 2006. Topics surveyed include metric graph theory, lattice polytopes, the combinatorial complexity of unions of geometric objects, line and pseudoline arrangements, algorithmic semialgebraic geometry, persistent homology, unfolding polyhedra, pseudotriangulations, nonlinear computational geometry, \(k\)sets, and the computational complexity of convex bodies.
Discrete and computational geometry originated as a discipline in the mid1980s when mathematicians in the wellestablished field of discrete geometry and computer scientists in the (then) nascent field of computational geometry began working together on problems of common interest. The combined field has experienced a huge growth in the past twenty years, which the present volume attests to.
Graduate students and research mathematicians interested in discrete and computational geometry.

Articles

Branko Grünbaum — Musings on discrete geometry and “20 years of discrete & computational geometry” [ MR 2405675 ]

Pankaj K. Agarwal, János Pach and Micha Sharir — State of the union (of geometric objects) [ MR 2405676 ]

HansJürgen Bandelt and Victor Chepoi — Metric graph theory and geometry: a survey [ MR 2405677 ]

Imre Bárány — Extremal problems for convex lattice polytopes: a survey [ MR 2405678 ]

Nicolas Bartholdi, Jérémy Blanc and Sébastien Loisel — On simple arrangements of lines and pseudolines in $\Bbb P^2$ and $\Bbb R^2$ with the maximum number of triangles [ MR 2405679 ]

Alexander Barvinok and Ellen Veomett — The computational complexity of convex bodies [ MR 2405680 ]

Saugata Basu — Algorithmic semialgebraic geometry and topology—recent progress and open problems [ MR 2405681 ]

Robert Connelly — Expansive motions [ MR 2405682 ]

Erik D. Demaine, Blaise Gassend, Joseph O’Rourke and Godfried T. Toussaint — All polygons flip finitely$\ldots $ right? [ MR 2405683 ]

Herbert Edelsbrunner and John Harer — Persistent homology—a survey [ MR 2405684 ]

Andreas F. Holmsen — Recent progress on line transversals to families of translated ovals [ MR 2405685 ]

Gabriel Nivasch — An improved, simple construction of many halving edges [ MR 2405686 ]

Joseph O’Rourke — Unfolding orthogonal polyhedra [ MR 2405687 ]

Radoš Radoičić and Géza Tóth — The discharging method in combinatorial geometry and the PachSharir conjecture [ MR 2405688 ]

Günter Rote, Francisco Santos and Ileana Streinu — Pseudotriangulations—a survey [ MR 2405689 ]

Frank Sottile and Thorsten Theobald — Line problems in nonlinear computational geometry [ MR 2405690 ]

Pavel Valtr — On empty hexagons [ MR 2405691 ]

Uli Wagner — $k$sets and $k$facets [ MR 2405692 ]

Xianglin Wei and Ren Ding — An ErdősSzekeres type problem for interior points [ MR 2405693 ]

Chuanming Zong — The kissing number, blocking number and covering number of a convex body [ MR 2405694 ]

Edited by János Pach — Open problems [ MR 2405695 ]