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Advances in Discrete and Computational Geometry
 
Edited by: Bernard Chazelle :  Princeton University, Princeton, NJ
Jacob E. Goodman :  City College, City University of New York, New York, NY
Richard Pollack :  New York University-Courant Institute of Mathematical Sciences, New York, NY
Advances in Discrete and Computational Geometry
eBook ISBN:  978-0-8218-7814-9
Product Code:  CONM/223.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Add to cart
Advances in Discrete and Computational Geometry
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Advances in Discrete and Computational Geometry
Edited by: Bernard Chazelle :  Princeton University, Princeton, NJ
Jacob E. Goodman :  City College, City University of New York, New York, NY
Richard Pollack :  New York University-Courant Institute of Mathematical Sciences, New York, NY
eBook ISBN:  978-0-8218-7814-9
Product Code:  CONM/223.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Add to cart
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 223; 1999; 463 pp
    MSC: Primary 52; 68

    This volume is a collection of refereed expository and research articles in discrete and computational geometry written by leaders in the field. Articles are based on invited talks presented at the AMS-IMS-SIAM Summer Research Conference, “Discrete and Computational Geometry: Ten Years Later”, held in 1996 at Mt. Holyoke College (So. Hadley, MA). Topics addressed range from tilings, polyhedra, and arrangements to computational topology and visibility problems. Included are papers on the interaction between real algebraic geometry and discrete and computational geometry, as well as on linear programming and geometric discrepancy theory.
    Readership

    Graduate students and research mathematicians working in discrete and computational geometry; applied workers using geometric methods and results, such as computer graphics and design.
  • Table of Contents
     
     
    • Articles
    • Pankaj K. Agarwal and Jeff Erickson — Geometric range searching and its relatives [ MR 1661376 ]
    • Nina Amenta and Günter M. Ziegler — Deformed products and maximal shadows of polytopes [ MR 1661377 ]
    • Louis J. Billera, Clara S. Chan and Niandong Liu — Flag complexes, labelled rooted trees, and star shellings [ MR 1661378 ]
    • Bernard Chazelle — Discrepancy bounds for geometric set systems with square incidence matrices [ MR 1661379 ]
    • Tamal K. Dey, Herbert Edelsbrunner and Sumanta Guha — Computational topology [ MR 1661380 ]
    • Gábor Fejes Tóth — Recent progress on packing and covering [ MR 1661381 ]
    • Branko Grünbaum — Acoptic polyhedra [ MR 1661382 ]
    • Fred Holt and Victor Klee — A proof of the strict monotone $4$-step conjecture [ MR 1661383 ]
    • Ilia Itenberg and Marie-Françoise Roy — Interactions between real algebraic geometry and discrete and computational geometry [ MR 1661384 ]
    • Joseph O’Rourke — Open problems in the combinatorics of visibility and illumination [ MR 1661385 ]
    • János Pach and József Solymosi — Halving lines and perfect cross-matchings [ MR 1661386 ]
    • János Pach, Torsten Thiele and Géza Tóth — Three-dimensional grid drawings of graphs [ MR 1661387 ]
    • Michel Pocchiola and Gert Vegter — On polygonal covers [ MR 1661388 ]
    • Jürgen Richter-Gebert — The universality theorems for oriented matroids and polytopes [ MR 1661389 ]
    • Marjorie Senechal — Periodic and aperiodic tilings of $E^n$ [ MR 1661390 ]
    • Michael Ian Shamos — The early years of computational geometry—a personal memoir [ MR 1661391 ]
    • Micha Sharir — Arrangements of surfaces in higher dimensions [ MR 1661392 ]
    • Joel Spencer — Geometric discrepancy theory [ MR 1661393 ]
    • Helge Tverberg — Proof of Reay’s conjecture on certain positive-dimensional intersections [ MR 1661394 ]
    • Rephael Wenger — Progress in geometric transversal theory [ MR 1661395 ]
    • Günter M. Ziegler — Recent progress on polytopes [ MR 1661396 ]
    • Application Challenges to Computational Geometry
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Contemporary Mathematics
Volume: 223; 1999; 463 pp
MSC: Primary 52; 68

This volume is a collection of refereed expository and research articles in discrete and computational geometry written by leaders in the field. Articles are based on invited talks presented at the AMS-IMS-SIAM Summer Research Conference, “Discrete and Computational Geometry: Ten Years Later”, held in 1996 at Mt. Holyoke College (So. Hadley, MA). Topics addressed range from tilings, polyhedra, and arrangements to computational topology and visibility problems. Included are papers on the interaction between real algebraic geometry and discrete and computational geometry, as well as on linear programming and geometric discrepancy theory.
Readership

Graduate students and research mathematicians working in discrete and computational geometry; applied workers using geometric methods and results, such as computer graphics and design.
  • Articles
  • Pankaj K. Agarwal and Jeff Erickson — Geometric range searching and its relatives [ MR 1661376 ]
  • Nina Amenta and Günter M. Ziegler — Deformed products and maximal shadows of polytopes [ MR 1661377 ]
  • Louis J. Billera, Clara S. Chan and Niandong Liu — Flag complexes, labelled rooted trees, and star shellings [ MR 1661378 ]
  • Bernard Chazelle — Discrepancy bounds for geometric set systems with square incidence matrices [ MR 1661379 ]
  • Tamal K. Dey, Herbert Edelsbrunner and Sumanta Guha — Computational topology [ MR 1661380 ]
  • Gábor Fejes Tóth — Recent progress on packing and covering [ MR 1661381 ]
  • Branko Grünbaum — Acoptic polyhedra [ MR 1661382 ]
  • Fred Holt and Victor Klee — A proof of the strict monotone $4$-step conjecture [ MR 1661383 ]
  • Ilia Itenberg and Marie-Françoise Roy — Interactions between real algebraic geometry and discrete and computational geometry [ MR 1661384 ]
  • Joseph O’Rourke — Open problems in the combinatorics of visibility and illumination [ MR 1661385 ]
  • János Pach and József Solymosi — Halving lines and perfect cross-matchings [ MR 1661386 ]
  • János Pach, Torsten Thiele and Géza Tóth — Three-dimensional grid drawings of graphs [ MR 1661387 ]
  • Michel Pocchiola and Gert Vegter — On polygonal covers [ MR 1661388 ]
  • Jürgen Richter-Gebert — The universality theorems for oriented matroids and polytopes [ MR 1661389 ]
  • Marjorie Senechal — Periodic and aperiodic tilings of $E^n$ [ MR 1661390 ]
  • Michael Ian Shamos — The early years of computational geometry—a personal memoir [ MR 1661391 ]
  • Micha Sharir — Arrangements of surfaces in higher dimensions [ MR 1661392 ]
  • Joel Spencer — Geometric discrepancy theory [ MR 1661393 ]
  • Helge Tverberg — Proof of Reay’s conjecture on certain positive-dimensional intersections [ MR 1661394 ]
  • Rephael Wenger — Progress in geometric transversal theory [ MR 1661395 ]
  • Günter M. Ziegler — Recent progress on polytopes [ MR 1661396 ]
  • Application Challenges to Computational Geometry
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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