Pach, János
Overview
Works:  60 works in 203 publications in 2 languages and 4,041 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor, Thesis advisor 
Classifications:  QA167, 516.13 
Publication Timeline
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Most widely held works by
János Pach
Combinatorial geometry by
János Pach(
Book
)
15 editions published between 1991 and 1995 in English and Undetermined and held by 531 WorldCat member libraries worldwide
15 editions published between 1991 and 1995 in English and Undetermined and held by 531 WorldCat member libraries worldwide
Research problems in discrete geometry by
Peter Brass(
Book
)
20 editions published between 2005 and 2007 in English and held by 292 WorldCat member libraries worldwide
Research Problems in Discrete Geometry is the result of a 25yearold project initiated by the late Leo Moser. It is a collection of more than 500 attractive open problems in the field. The largely selfcontained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research. (Midwest)
20 editions published between 2005 and 2007 in English and held by 292 WorldCat member libraries worldwide
Research Problems in Discrete Geometry is the result of a 25yearold project initiated by the late Leo Moser. It is a collection of more than 500 attractive open problems in the field. The largely selfcontained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research. (Midwest)
Combinatorial geometry and its algorithmic applications : the Alcalá lectures by
János Pach(
Book
)
9 editions published in 2009 in English and held by 251 WorldCat member libraries worldwide
"Based on a lecture series given by the authors at a satellite meeting of the 2006 International Congress of Mathematicians and on many articles written by them and their collaborators, this volume provides a comprehensive uptodate survey of several core areas of combinatorial geometry. It describes the beginnings of the subject, going back to the nineteenth century (if not to Euclid), and explains why counting incidences and estimating the combinatorial complexity of various arrangements of geometric objects became the theoretical backbone of computational geometry in the 1980s and 1990s. The combinatorial techniques outlined in this book have found applications in many areas of computer science from graph drawing through hidden surface removal and motion planning to frequency allocation in cellular networks. "Combinatorial Geometry and Its Algorithmic Applications" is intended as a source book for professional mathematicians and computer scientists as well as for graduate students interested in combinatorics and geometry. Most chapters start with an attractive, simply formulated, but often difficult and only partially answered mathematical question, and describes the most efficient techniques developed for its solution. The text includes many challenging open problems, figures, and an extensive bibliography."Jacket
9 editions published in 2009 in English and held by 251 WorldCat member libraries worldwide
"Based on a lecture series given by the authors at a satellite meeting of the 2006 International Congress of Mathematicians and on many articles written by them and their collaborators, this volume provides a comprehensive uptodate survey of several core areas of combinatorial geometry. It describes the beginnings of the subject, going back to the nineteenth century (if not to Euclid), and explains why counting incidences and estimating the combinatorial complexity of various arrangements of geometric objects became the theoretical backbone of computational geometry in the 1980s and 1990s. The combinatorial techniques outlined in this book have found applications in many areas of computer science from graph drawing through hidden surface removal and motion planning to frequency allocation in cellular networks. "Combinatorial Geometry and Its Algorithmic Applications" is intended as a source book for professional mathematicians and computer scientists as well as for graduate students interested in combinatorics and geometry. Most chapters start with an attractive, simply formulated, but often difficult and only partially answered mathematical question, and describes the most efficient techniques developed for its solution. The text includes many challenging open problems, figures, and an extensive bibliography."Jacket
Towards a theory of geometric graphs(
Book
)
9 editions published in 2004 in English and held by 231 WorldCat member libraries worldwide
This volume contains a collection of papers on graph theory, with the common theme that all the graph theoretical problems addressed are approached from a geometrical, rather than an abstract point of view. This is no accident; the editor selected these papers not as a comprehensive literature revie
9 editions published in 2004 in English and held by 231 WorldCat member libraries worldwide
This volume contains a collection of papers on graph theory, with the common theme that all the graph theoretical problems addressed are approached from a geometrical, rather than an abstract point of view. This is no accident; the editor selected these papers not as a comprehensive literature revie
Graph drawing : 12th international symposium, GD 2004, New York, NY, USA, September 29October 2, 2004 : revised selected
papers by
János Pach(
Book
)
17 editions published between 2004 and 2005 in English and held by 227 WorldCat member libraries worldwide
17 editions published between 2004 and 2005 in English and held by 227 WorldCat member libraries worldwide
Combinatorial and computational geometry by
Jacob E Goodman(
Book
)
12 editions published between 2005 and 2011 in English and held by 225 WorldCat member libraries worldwide
There are points of contact with many applied areas such as mathematical programming, visibility problems, kinetic data structures, and biochemistry, as well as with algebraic topology, geometric probability, real algebraic geometry, and combinatorics."Jacket
12 editions published between 2005 and 2011 in English and held by 225 WorldCat member libraries worldwide
There are points of contact with many applied areas such as mathematical programming, visibility problems, kinetic data structures, and biochemistry, as well as with algebraic topology, geometric probability, real algebraic geometry, and combinatorics."Jacket
New trends in discrete and computational geometry by
János Pach(
Book
)
15 editions published between 1992 and 2013 in English and held by 218 WorldCat member libraries worldwide
Discrete and computational geometry are two fields which in recent years have benefitted from the interaction between mathematics and computer science. The results are applicable in areas such as motion planning, robotics, scene analysis, and computer aided design. The book consists of twelve chapters summarizing the most recent results and methods in discrete and computational geometry. All authors are wellknown experts in these fields. They give concise and selfcontained surveys of the most efficient combinatorical, probabilistic and topological methods that can be used to design effective geometric algorithms for the applications mentioned above. Most of the methods and results discussed in the book have not appeared in any previously published monograph. In particular, this book contains the first systematic treatment of epsilonnets, geometric tranversal theory, partitions of Euclidean spaces and a general method for the analysis of randomized geometric algorithms. Apart from mathematicians working in discrete and computational geometry this book will also be of great use to computer scientists and engineers, who would like to learn about the most recent results
15 editions published between 1992 and 2013 in English and held by 218 WorldCat member libraries worldwide
Discrete and computational geometry are two fields which in recent years have benefitted from the interaction between mathematics and computer science. The results are applicable in areas such as motion planning, robotics, scene analysis, and computer aided design. The book consists of twelve chapters summarizing the most recent results and methods in discrete and computational geometry. All authors are wellknown experts in these fields. They give concise and selfcontained surveys of the most efficient combinatorical, probabilistic and topological methods that can be used to design effective geometric algorithms for the applications mentioned above. Most of the methods and results discussed in the book have not appeared in any previously published monograph. In particular, this book contains the first systematic treatment of epsilonnets, geometric tranversal theory, partitions of Euclidean spaces and a general method for the analysis of randomized geometric algorithms. Apart from mathematicians working in discrete and computational geometry this book will also be of great use to computer scientists and engineers, who would like to learn about the most recent results
Surveys on discrete and computational geometry : twenty years later : AMSIMSSIAM Joint Summer Research Conference, June
1822, 2006, Snowbird, Utah by AMSIMSSIAM Joint Summer Research Conference Discrete and Computational Geometry  Twenty Years Later(
Book
)
12 editions published in 2008 in English and held by 186 WorldCat member libraries worldwide
12 editions published in 2008 in English and held by 186 WorldCat member libraries worldwide
Thirty Essays on Geometric Graph Theory by
János Pach(
Book
)
11 editions published between 2012 and 2013 in English and held by 40 WorldCat member libraries worldwide
In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of ""abstract"" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions. This contributed volume contains thirty original survey and research papers on imp
11 editions published between 2012 and 2013 in English and held by 40 WorldCat member libraries worldwide
In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of ""abstract"" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions. This contributed volume contains thirty original survey and research papers on imp
Twentieth anniversary volume : discrete & computational geometry by
Richard Pollack(
Book
)
11 editions published between 2008 and 2009 in English and Undetermined and held by 34 WorldCat member libraries worldwide
Contains the 28 major articles that appeared in the 2008 Twentieth Anniversary Issue of the journal "Discrete & Computational Geometry". This title also includes articles that show the intimate connections that have arisen between discrete and computational geometry and other areas of both computer science and mathematics
11 editions published between 2008 and 2009 in English and Undetermined and held by 34 WorldCat member libraries worldwide
Contains the 28 major articles that appeared in the 2008 Twentieth Anniversary Issue of the journal "Discrete & Computational Geometry". This title also includes articles that show the intimate connections that have arisen between discrete and computational geometry and other areas of both computer science and mathematics
Geometry  intuitive, discrete, and convex : a tribute to Laszlo Fejes Toth(
Book
)
3 editions published between 2013 and 2014 in English and held by 25 WorldCat member libraries worldwide
The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, László Fejes Tóth, on the 99th anniversary of his birth. Each article reviews recent progress in an important field in intuitive, discrete, and convex geometry. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by László Fejes Tóth
3 editions published between 2013 and 2014 in English and held by 25 WorldCat member libraries worldwide
The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, László Fejes Tóth, on the 99th anniversary of his birth. Each article reviews recent progress in an important field in intuitive, discrete, and convex geometry. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by László Fejes Tóth
On vertical visibility in arrangements of segments and the queue size in the BentleyOttman line sweeping algorithm by
János Pach(
Book
)
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
We show that there are at most O(n log[superscript 2]n) such pairs, and only O(n log n) in the case of full rays, where the latter bound can be attained in the worst case. We apply these results to obtain similar upper and lower bounds on the maximum size of the queue in the original implementation of the BentleyOttman algorithm for reporting all intersections between the segments in S, i.e. the implementation where future events are not deleted from the queue. We also show that, without the extra conditions on the segments in S and on the pairs of segments to be counted, the number of nonintersecting vertically visible pairs of segments is [formula], and can be [formula] in the worst case."
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
We show that there are at most O(n log[superscript 2]n) such pairs, and only O(n log n) in the case of full rays, where the latter bound can be attained in the worst case. We apply these results to obtain similar upper and lower bounds on the maximum size of the queue in the original implementation of the BentleyOttman algorithm for reporting all intersections between the segments in S, i.e. the implementation where future events are not deleted from the queue. We also show that, without the extra conditions on the segments in S and on the pairs of segments to be counted, the number of nonintersecting vertically visible pairs of segments is [formula], and can be [formula] in the worst case."
An upper bound on the number of planar ksets by
János Pach(
Book
)
3 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
Abstract: "Given a set S of n points, a subset X of size k is called a kset if there is a hyperplane II that separates X from S  X. We prove that [formula] is an upper bound for the number of ksets in the plane, thus improving the previous bound of Erdös, Lovász, Simmons and Strauss by a factor of [formula]."
3 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
Abstract: "Given a set S of n points, a subset X of size k is called a kset if there is a hyperplane II that separates X from S  X. We prove that [formula] is an upper bound for the number of ksets in the plane, thus improving the previous bound of Erdös, Lovász, Simmons and Strauss by a factor of [formula]."
Universal elements and the complexity of certain classes of infinite graph by
Péter Komjáth(
Book
)
2 editions published between 1989 and 1990 in English and held by 4 WorldCat member libraries worldwide
This is defined to be the minimum cardinal such that there exist [kappa] elements in [symbol] with the property that any other element of [symbol] can be embedded into at least one of them as an induced subgraph. [symbol] has a universal element if and only if cp([symbol]) = 1. Among other theorems we prove that (i) the complexity of the class of all countable graphs without n[greater than or equal to]2 independent edges is finite; (ii) for any cardinal [kappa], [formula], it is consistent that the complexity of the class of all locally finite countable graphs is equal to [kappa]. In section 6 we consider some analogous questions for hypergraphs."
2 editions published between 1989 and 1990 in English and held by 4 WorldCat member libraries worldwide
This is defined to be the minimum cardinal such that there exist [kappa] elements in [symbol] with the property that any other element of [symbol] can be embedded into at least one of them as an induced subgraph. [symbol] has a universal element if and only if cp([symbol]) = 1. Among other theorems we prove that (i) the complexity of the class of all countable graphs without n[greater than or equal to]2 independent edges is finite; (ii) for any cardinal [kappa], [formula], it is consistent that the complexity of the class of all locally finite countable graphs is equal to [kappa]. In section 6 we consider some analogous questions for hypergraphs."
Repeated angles in the plane and related problems by
János Pach(
Book
)
3 editions published in 1990 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We show that a set of n points in the plane determine O(n²logn) triples that define the same angle [alpha], and that for many angles [alpha] (including [formula]) this bound is tight in the worst case. We also show that, for a broad family of properties P, the number of triangles spanned by the given points and having property P is O(n[superscript 7/3]). Typical such properties are: having a specified area, a specified perimeter, being isosceles, etc."
3 editions published in 1990 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We show that a set of n points in the plane determine O(n²logn) triples that define the same angle [alpha], and that for many angles [alpha] (including [formula]) this bound is tight in the worst case. We also show that, for a broad family of properties P, the number of triangles spanned by the given points and having property P is O(n[superscript 7/3]). Typical such properties are: having a specified area, a specified perimeter, being isosceles, etc."
Recent developments in combinatorial geometry by
W. O. J Moser(
Book
)
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
Twentieth Anniversary Volume Discrete et Computational Geometry by
Richard Pollack(
)
1 edition published in 2009 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2009 in English and held by 3 WorldCat member libraries worldwide
Risan kikagaku ni okeru mikaiketsu mondaishū by
Peter Brass(
Book
)
3 editions published in 2009 in Japanese and held by 3 WorldCat member libraries worldwide
3 editions published in 2009 in Japanese and held by 3 WorldCat member libraries worldwide
Cell decomposition of polytopes by bending by
Jacob E Goodman(
Book
)
2 editions published in 1988 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 3 WorldCat member libraries worldwide
Graph Drawing (vol. # 3383) by
János Pach(
Book
)
6 editions published in 2005 in English and held by 2 WorldCat member libraries worldwide
6 editions published in 2005 in English and held by 2 WorldCat member libraries worldwide
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Related Identities
 Goodman, Jacob E. Author Editor
 Moser, W. O. J. Author
 Brass, Peter Author
 Pollack, Richard Author Editor
 Agarwal, Pankaj K.
 Sharir, Micha Editor
 Welzl, Emo Editor
 Bárány, Imre Editor
 Fejes Tóth, L.
 Fejes Tóth, G. Editor
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Associated Subjects
Algorithms ChemistryMathematics Combinatorial analysis Combinatorial geometry Computational complexity Computer graphics Computer science Computer scienceMathematics Computer software Convex geometry Data structures (Computer science) Discrete geometry Discrete groups Economics Engineering Geometry Geometry, Algebraic Geometry, Plane GeometryData processing Graph theory Mathematics Queuing theory Set theory Topology