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Sunday, July 26, 2020 | History

6 edition of Intersection and decomposition algorithms for planar arrangements found in the catalog.

Intersection and decomposition algorithms for planar arrangements

by Pankaj K. Agarwal

  • 43 Want to read
  • 18 Currently reading

Published by Cambridge University Press in Cambridge, New York .
Written in English

    Subjects:
  • Combinatorial geometry.,
  • Geometry -- Data processing.,
  • Algorithms.

  • Edition Notes

    Includes bibliographical references (p. 259-271) and indexes.

    StatementPankaj K. Agarwal.
    Classifications
    LC ClassificationsQA167 .A33 1991
    The Physical Object
    Paginationxvii, 277 p. :
    Number of Pages277
    ID Numbers
    Open LibraryOL1614554M
    ISBN 100521404460
    LC Control Number91155565

      This book has grown out of the material of both undergraduate and graduate courses in mathematics and computer science given by János Pach at the Courant Institute of Mathematical Sciences, New York University. Divided into two parts-- Arrangements of Convex Sets and Arrangements of Points and Lines--it presents and explains some of the most Reviews: 1. That is, there are algorithms that, when they work, work considerably faster than than the dual decomposition algorithm. And, more so than most, it has a lot of tunable parameters and design choices which make it a somewhat finicky algorithm to apply in practice because one has to play around quite a bit in order to get the performance.

    The desired rounded arrangement is the planar straight-line embedding of this graph, where each vertex is located at the center of its corresponding hot pixel. The algorithm starts with computing the set H of hot pixels by finding all the vertices of the arrangement A(S). This gives us the nodes of the graph G. It remains to find the arcs, which. We also present numerous applications of these results, including (i) data structures for several generalized 3-dimensional range-searching problems; (ii) dynamic data structures for planar nearest- and farthest-neighbor searching under various fairly general distance functions; (iii) an improved (near-quadratic) algorithm for minimum-weight.

    Trapezoidal maps and planar point location (CGAA, Chapter 6). Voronoi diagrams of points in the plane: structure, complexity, and Fortune's algorithm (CGAA, Chapter 7). Point-Line duality, arrangements of lines in the plane, the zone theorem and incremental construction of the arrangement (CGAA, Chapter 8). (Nearly all references are to books in English, with occassional references to journal articles.) Some of the sections have very detailed lists while other sections are not as thoroughly covered. My goal is to encourage mathematicians at all levels to explore the exciting world of geometry and show more of its wonders to their students.


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Intersection and decomposition algorithms for planar arrangements by Pankaj K. Agarwal Download PDF EPUB FB2

Intersection and Decomposition Algorithms for Planar Arrangements di Agarwal, Pankaj K. su - ISBN - ISBN - Cambridge University Press - - Price Range: 2,€ - 15,€. This book, first published inpresents a study of various problems related to arrangements of lines, segments, or curves in the plane.

The first problem is a proof of almost tight bounds on the length of (n,s)-Davenport–Schinzel sequences, a technique for obtaining optimal bounds for.

Intersection and Decomposition Algorithms for Planar Arrangements. By Pankaj K. Agarwal. Cambridge University Press, Cambridge, xvii+ pp. $ cloth. ISBN This book encapsulates perfectly the primary concerns and methods in the field of Computational Geometry at the start of the 's. It illustrates, as well as any piece of work, the deep and beautiful.

Books. Agarwal is the author or co-author of: Intersection and Decomposition Algorithms for Planar Arrangements (Cambridge University Press,ISBN ).The topics of this book are algorithms for, and the combinatorial geometry of, arrangements of lines and arrangements of more general types of curves in the Euclidean plane and the real projective : Fellow, Association for Computing.

He received his PhD in computer science from the Courant Institute of Mathematical Sciences, New York University, in He is the author of Intersection and Decomposition Algorithms for Planar Arrangements, and a coauthor of Davenport--Schinzel Sequences and Their Geometric Applications.

Publications: Books. See also: Papers by Subject | Papers by Year | Surveys Robotics: The Algorithmic Perspective with L. Kavraki and M. Mason, eds., A.

Peters. This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems. Intersection and decomposition algorithms for planar. Intersection and Decomposition Algorithms for Planar Arrangements, Cambridge Univ.

Press, Cambridge (). Let S be a set of convex polygons in the plane with a total of n vertices, where a polygon consists of the boundary as well as the interior. Efficient. () A Faster Algorithm for Minimum-cost Bipartite Perfect Matching in Planar Graphs.

ACM Transactions on Algorithms() Exact and approximation algorithms for weighted matroid intersection. Intersection and Decomposition Algorithms for Planar Arrangements. Cambridge University Press, Google Scholar Space-efficient ray-shooting and intersection searching: Algorithms, dynamization, and applications.

More on cutting arrangements and spanning trees with low crossing number. Technical Report BFreie Universität. Given two disjoint convex polygons in standard representations, one can compute outer common tangents in logarithmic time without first obtaining a separating line. If the polygons are not disjoint, there is an additional factor of the logarithm of the intersection.

Recommend & Share. Recommend to Library. Email to a friend. According to our current on-line database, Pankaj Agarwal has 10 students and 28 descendants.

We welcome any additional information. If you have additional information or corrections regarding this mathematician, please use the update submit students of this mathematician, please use the new data form, noting this mathematician's MGP ID of for the advisor ID.

We remark that a solution to the above problems allows us to answer all necessary queries for arrangement computations with planar algebraic curves [7, 8, 21, 25, 31].Namely, for a set of planar. Agarwal, Intersection and Decomposition Algorithms for Planar Arrangements In addition, though not monographs, there are many edited collections that are relevant to the topic, including the annual proceedings of ACM SoCG, CCCG, and JCDCG, and possibly also including more specialized conferences such as WAFR, Graph Drawing, and the Meshing.

We present an algorithm that constructively produces a solution to the k-dominating set problem for planar graphs in time O(c. To obtain this result, we show that the treewidth of a planar graph with domination number (G) is O((G)), and that such a tree decomposition can be found in O((G)n) time.

the general intersection problem was achieved in Chazelle [6], where an algorithm with a running time of 0(n log 2n /log log n + k) was described. Unlike most intersection algorithms, this one had the particularity of not following a sweep-line approach. Instead, it used a hierarchical subdivision of.

Exact, e cient, and complete algorithms for planar arrangements have been published by Wein [77] and Berberich et al. [11] for conic segments, and by Wolpert [78,73] for special quartic curves as part of a surface intersection algorithm. A generalization of Jacobi curves (used for locating tangential in-tersections) is described by Wolpert [79].

tree–decomposition and branchdecomposition is of great importance for the running time of the algorithm. Secondly, branchwidth is polynomial for planar graphs. The treewidth problem is open. Clique–width, NLC–width and Efficient Algorithms Egon. Among the other algorithms studied are: a naïve approach, a “walk along a line” strategy, and a trapezoidal decomposition-based search structure.

The current implementation addresses general arrangements of planar curves, including arrangements of nonlinear segments (e.g., conic arcs) and allows for degenerate input (for example, more than.Course Overview: Introduction to algorithms and data structures for computational problems in discrete geometry (for points, lines, and polygons) primarily in 2 and 3 dimensions.

Topics include triangulations and planar subdivisions, geometric search and intersection, convex hulls, Voronoi diagrams, Delaunay triangulations, line arrangements.Our linear-time algorithm improves upon the decomposition algorithm used in the state-of-the-art algo-rithmforminimumst–cut(Italiano,Nussbaum,Sankowski, andWulff-Nilsen,STOC),removingoneofthebottle- decomposition of a planar graph .