Sharir, Micha
Overview
Works:  145 works in 301 publications in 2 languages and 1,226 library holdings 

Genres:  Technical reports 
Roles:  Author, Editor, Honoree 
Publication Timeline
.
Most widely held works by
Micha Sharir
Combinatorial geometry and its algorithmic applications : the Alcalá lectures by
János Pach(
Book
)
11 editions published in 2009 in English and held by 261 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
11 editions published in 2009 in English and held by 261 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
DavenportSchinzel sequences and their geometric applications by
Micha Sharir(
Book
)
13 editions published between 1995 and 2010 in English and held by 256 WorldCat member libraries worldwide
13 editions published between 1995 and 2010 in English and held by 256 WorldCat member libraries worldwide
Planning, geometry, and complexity of robot motion(
Book
)
8 editions published between 1986 and 1987 in English and held by 206 WorldCat member libraries worldwide
8 editions published between 1986 and 1987 in English and held by 206 WorldCat member libraries worldwide
Algorithmic motion planning in robotics by
Micha Sharir(
Book
)
5 editions published between 1988 and 1991 in English and Undetermined and held by 20 WorldCat member libraries worldwide
5 editions published between 1988 and 1991 in English and Undetermined and held by 20 WorldCat member libraries worldwide
The complexity of many faces in arrangements of lines and of segments by
Herbert Edelsbrunner(
Book
)
6 editions published in 1988 in English and held by 19 WorldCat member libraries worldwide
6 editions published in 1988 in English and held by 19 WorldCat member libraries worldwide
The complexity of many cells in arrangements of planes and related problems by
Herbert Edelsbrunner(
Book
)
4 editions published in 1988 in English and held by 14 WorldCat member libraries worldwide
4 editions published in 1988 in English and held by 14 WorldCat member libraries worldwide
Randomized incremental construction of Delaunay and Voronoi diagrams by
Leonidas J Guibas(
Book
)
6 editions published between 1989 and 1990 in English and held by 14 WorldCat member libraries worldwide
The Voronoi diagram of n sites in the plane and its dual, the Delaunay tesselation, are among the most important constructs in twodimensional Computational Geometry. Their properties, as well as algorithms for their construction, are extensively covered in the standard textbooks of the field, such as (13) or (26), and in numerous papers, e.g. (19). The original papers on the subject are (29) and (30) by Voronoi (circa 1907), and (10) and (11) by Delaunay (circa 1932). Because of the practical importance of the Voronoi and Delaunay diagrams, some of the algorithms for constructing them have been carefully implemented and widely tested in practice. These diagrams are important tools in applications ranging from finite element codes, to pattern classification in statistics, to motion planning in robotics, etc. Analogs of these diagrams exist in higher dimensions as well. Though the higher dimensional diagrams are still very useful, a lot less is known about efficient algorithms for their construction because their topological structure is significantly harder to analyze.... (from the "Introduction" (there is no abstract))
6 editions published between 1989 and 1990 in English and held by 14 WorldCat member libraries worldwide
The Voronoi diagram of n sites in the plane and its dual, the Delaunay tesselation, are among the most important constructs in twodimensional Computational Geometry. Their properties, as well as algorithms for their construction, are extensively covered in the standard textbooks of the field, such as (13) or (26), and in numerous papers, e.g. (19). The original papers on the subject are (29) and (30) by Voronoi (circa 1907), and (10) and (11) by Delaunay (circa 1932). Because of the practical importance of the Voronoi and Delaunay diagrams, some of the algorithms for constructing them have been carefully implemented and widely tested in practice. These diagrams are important tools in applications ranging from finite element codes, to pattern classification in statistics, to motion planning in robotics, etc. Analogs of these diagrams exist in higher dimensions as well. Though the higher dimensional diagrams are still very useful, a lot less is known about efficient algorithms for their construction because their topological structure is significantly harder to analyze.... (from the "Introduction" (there is no abstract))
A design for optimizations of the bitvectoring class by
Jacob T Schwartz(
Book
)
1 edition published in 1979 in English and held by 14 WorldCat member libraries worldwide
1 edition published in 1979 in English and held by 14 WorldCat member libraries worldwide
On the zone theorem for hyperplane arrangements by
Herbert Edelsbrunner(
Book
)
4 editions published in 1991 in English and held by 12 WorldCat member libraries worldwide
Abstract: "The zone theorem for an arrangement of n hyperplanes in ddimensional real space says that the total number of faces bounding the cells intersected by another hyperplane is O(n[superscript d1]). This result is the basis of a timeoptimal incremental algorithm that constructs a hyperplane arrangement and has a host of other algorithmic and combinatorial applications. Unfortunately, the original proof of the zone theorem, for d[greater than or equal to]3, turned out to contain a serious and irreparable error. This paper presents a new proof of the theorem. Our proof is based on an inductive argument, which also applies in the case of pseudohyperplane arrangements. We also briefly discuss the fallacies of the old proof along with some ways of partially saving that approach."
4 editions published in 1991 in English and held by 12 WorldCat member libraries worldwide
Abstract: "The zone theorem for an arrangement of n hyperplanes in ddimensional real space says that the total number of faces bounding the cells intersected by another hyperplane is O(n[superscript d1]). This result is the basis of a timeoptimal incremental algorithm that constructs a hyperplane arrangement and has a host of other algorithmic and combinatorial applications. Unfortunately, the original proof of the zone theorem, for d[greater than or equal to]3, turned out to contain a serious and irreparable error. This paper presents a new proof of the theorem. Our proof is based on an inductive argument, which also applies in the case of pseudohyperplane arrangements. We also briefly discuss the fallacies of the old proof along with some ways of partially saving that approach."
Tail estimates for the space complexity of randomized incremental algorithms by
Kurt Mehlhorn(
Book
)
5 editions published in 1991 in English and German and held by 11 WorldCat member libraries worldwide
Abstract: "We give tail estimates for the space complexity of randomized incremental algorithms for line segment intersection in the plane. For n the number of segments, m is the number of intersections, and m [> or =] n ln n ln(³)n, there is a constant c such that the probability that the total space cost exceeds c times the expected space cost is e[superscript [Omega](m/(n ln n))]."
5 editions published in 1991 in English and German and held by 11 WorldCat member libraries worldwide
Abstract: "We give tail estimates for the space complexity of randomized incremental algorithms for line segment intersection in the plane. For n the number of segments, m is the number of intersections, and m [> or =] n ln n ln(³)n, there is a constant c such that the probability that the total space cost exceeds c times the expected space cost is e[superscript [Omega](m/(n ln n))]."
Tail estimates for the efficiency of randomized incremental algorithms for line segment intersection by
Kurt Mehlhorn(
Book
)
5 editions published in 1993 in English and German and held by 9 WorldCat member libraries worldwide
Abstract: "We give tail estimates for the efficiency of some randomized incremental algorithms for line segment intersection in the plane. In particular, we show that there is a constant C such that the probability that the running times of algorithms due to Mulmuley [Mul88] and Clarkson and Shor [CS89] exceed C times their expected time is bounded by e[superscript [omega](m/(n ln n))] where n is the number of segments, m is the number of intersections, and m [> or =] n ln n ln [superscript (3)]n."
5 editions published in 1993 in English and German and held by 9 WorldCat member libraries worldwide
Abstract: "We give tail estimates for the efficiency of some randomized incremental algorithms for line segment intersection in the plane. In particular, we show that there is a constant C such that the probability that the running times of algorithms due to Mulmuley [Mul88] and Clarkson and Shor [CS89] exceed C times their expected time is bounded by e[superscript [omega](m/(n ln n))] where n is the number of segments, m is the number of intersections, and m [> or =] n ln n ln [superscript (3)]n."
The upper envelope of piecewise linear functions : algorithms and applications by
Herbert Edelsbrunner(
Book
)
4 editions published in 1987 in English and held by 9 WorldCat member libraries worldwide
4 editions published in 1987 in English and held by 9 WorldCat member libraries worldwide
Efficient motion planning for an Lshaped object by
D Halperin(
Book
)
4 editions published in 1988 in English and held by 7 WorldCat member libraries worldwide
Abstract: "We present an algorithm that solves the following motionplanning problem. Given an Lshaped body L and a 2dimensional region with n point obstacles, decide whether there is a continuous motion connecting two given positions and orientations of L during which L avoids collision with the obstacles. The algorithm requires O(n²log²n) time and O(n²) storage. The algorithm is a variant of the celldecomposition technique of the configuration space ([SS, LS]) but it employs a new and efficient technique for obtaining a compact representation of the free space, which results in a saving of an order of magnitude. The approach used in our algorithm seems applicable to motionplanning of certain robotic arms whose spaces of free placements have a structure similar to that of the Lshaped body."
4 editions published in 1988 in English and held by 7 WorldCat member libraries worldwide
Abstract: "We present an algorithm that solves the following motionplanning problem. Given an Lshaped body L and a 2dimensional region with n point obstacles, decide whether there is a continuous motion connecting two given positions and orientations of L during which L avoids collision with the obstacles. The algorithm requires O(n²log²n) time and O(n²) storage. The algorithm is a variant of the celldecomposition technique of the configuration space ([SS, LS]) but it employs a new and efficient technique for obtaining a compact representation of the free space, which results in a saving of an order of magnitude. The approach used in our algorithm seems applicable to motionplanning of certain robotic arms whose spaces of free placements have a structure similar to that of the Lshaped body."
Separating two simple polygons by a sequence of translations by
R Pollack(
Book
)
3 editions published between 1986 and 1987 in English and held by 7 WorldCat member libraries worldwide
Abstract: "Let P and Q be two disjoint simple polygons having m and n sides respectively. We present an algorithm which determines whether Q can be moved by a sequence of translations to a position sufficiently far from P without colliding with P, and which produces such a motion if it exists. Our algorithm runs in time O(mn [alpha](mn) log m log n) where [alpha](k) is the extremely slowly growing inverse Ackermann's function. Since in the worst case [omega](mn) translations may be necessary to separate Q from P, our algorithm is close to optimal."
3 editions published between 1986 and 1987 in English and held by 7 WorldCat member libraries worldwide
Abstract: "Let P and Q be two disjoint simple polygons having m and n sides respectively. We present an algorithm which determines whether Q can be moved by a sequence of translations to a position sufficiently far from P without colliding with P, and which produces such a motion if it exists. Our algorithm runs in time O(mn [alpha](mn) log m log n) where [alpha](k) is the extremely slowly growing inverse Ackermann's function. Since in the worst case [omega](mn) translations may be necessary to separate Q from P, our algorithm is close to optimal."
Ray shooting, implicit point location, and related queries in arrangements of segments by
Leonidas J Guibas(
Book
)
4 editions published in 1989 in English and held by 6 WorldCat member libraries worldwide
4 editions published in 1989 in English and held by 6 WorldCat member libraries worldwide
A subexponential bound for linear programming by
Jiří Matoušek(
Book
)
3 editions published between 1992 and 1996 in 3 languages and held by 5 WorldCat member libraries worldwide
3 editions published between 1992 and 1996 in 3 languages and held by 5 WorldCat member libraries worldwide
Triangles in space, or, Building (and analyzing) castles in the air by
Boris Aronov(
Book
)
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
The upper envelope of Voronoi surfaces and its applications by
Daniel P Huttenlocher(
Book
)
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
We derive bounds on the number of vertices on the upper envelope of a collection of Voronoi surfaces, and provide efficient algorithms to calculate these vertices. We then discuss applications of the methods to the aforementioned problems."
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
We derive bounds on the number of vertices on the upper envelope of a collection of Voronoi surfaces, and provide efficient algorithms to calculate these vertices. We then discuss applications of the methods to the aforementioned problems."
Motion planning in the presence of moving obstacles by
J. H Reif(
Book
)
4 editions published in 1985 in English and held by 4 WorldCat member libraries worldwide
This paper investigates the computational complexity of planning the motion of a body B in 2D or 3D space, so as to avoid collision with moving obstacles of known, easily computed, trajectories. Dynamic movement problems are of fundamental importance to robotics, but their computational complexity has not previously been investigated. We provide evidence that the 3D dynamic movement problem is intractable even if B has only a constant number of degrees of freedom of movement. In particular, we prove the problem is PSPACEhard if B is given a velocity modulus bound on its movements and is NP hard even if B has no velocity modulus bound, where in both cases B has 6 degrees of freedom. To prove these results we use a unique method of simulation of a Turing machine which uses time to encode configurations (whereas previous lower bound proofs in robotics used the system position to encode configurations and so required unbounded number of degrees of freedom). We also investigate a natural class of dynamic problems which we call asteroid avoidance problems: B, the object we wish to move, is a convex polyhedron which is free to move by translation with bounded velocity modulus and the polyhedral obstacles have known translational trajectories but cannot rotate. This problem has many applications to robot, automobile, and aircraft collision avoidance
4 editions published in 1985 in English and held by 4 WorldCat member libraries worldwide
This paper investigates the computational complexity of planning the motion of a body B in 2D or 3D space, so as to avoid collision with moving obstacles of known, easily computed, trajectories. Dynamic movement problems are of fundamental importance to robotics, but their computational complexity has not previously been investigated. We provide evidence that the 3D dynamic movement problem is intractable even if B has only a constant number of degrees of freedom of movement. In particular, we prove the problem is PSPACEhard if B is given a velocity modulus bound on its movements and is NP hard even if B has no velocity modulus bound, where in both cases B has 6 degrees of freedom. To prove these results we use a unique method of simulation of a Turing machine which uses time to encode configurations (whereas previous lower bound proofs in robotics used the system position to encode configurations and so required unbounded number of degrees of freedom). We also investigate a natural class of dynamic problems which we call asteroid avoidance problems: B, the object we wish to move, is a convex polyhedron which is free to move by translation with bounded velocity modulus and the polyhedral obstacles have known translational trajectories but cannot rotate. This problem has many applications to robot, automobile, and aircraft collision avoidance
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Related Identities
 Pach, János Author Editor
 Agarwal, Pankaj K. Author
 Schwartz, Jacob T. Author Editor
 Hopcroft, John E. 1939 Author Editor
 Courant Institute of Mathematical Sciences Computer Science Department
 Guibas, Leonidas J. Author
 Edelsbrunner, Herbert Author
 University of Illinois at UrbanaChampaign Department of Computer Science
 Overmars, Mark H. (Markus Hendrik) 1958 Author
 Welzl, Emo
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Associated Subjects
Algorithms Combinatorial geometry Combinatorial geometryData processing Computational complexity Computer algorithms Computer graphics Computer programming Convex polytopes Data structures (Computer science) DavenportSchinzel sequences Envelopes (Geometry) Finite element methodData processing Geometry Geometry, Analytic Geometry, Plane GeometryData processing Incremental motion control Line geometryData processing Motion Pattern recognition systems Point mappings (Mathematics) Polygons Probabilistic number theory Robots RobotsMotion RobotsMotionPlanning Sampling (Statistics) SETL (Computer program language) Voronoi polygons