Farthest-Point Queries with Geometric and Combinatorial Constraints

  • Ovidiu Daescu
  • Ningfang Mi
  • Chan-Su Shin
  • Alexander Wolff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3742)


In this paper we discuss farthest-point problems in which a set or sequence S of n points in the plane is given in advance and can be preprocessed to answer various queries efficiently. First, we give a data structure that can be used to compute the point farthest from a query line segment in O(log2 n) time. Our data structure needs O(n log n) space and preprocessing time. To the best of our knowledge no solution to this problem has been suggested yet. Second, we show how to use this data structure to obtain an output-sensitive query-based algorithm for polygonal path simplification. Both results are based on a series of data structures for fundamental farthest-point queries that can be reduced to each other.


Convex Hull Voronoi Diagram Computational Geometry Convex Polygon Query Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ovidiu Daescu
    • 1
  • Ningfang Mi
    • 2
  • Chan-Su Shin
    • 3
  • Alexander Wolff
    • 4
  1. 1.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA
  2. 2.Department of Computer ScienceCollege of William and MaryWilliamsburgUSA
  3. 3.School of Electronics and Information EngineeringHankuk University of Foreign StudiesKorea
  4. 4.Department of Computer ScienceKarlsruhe UniversityKarlsruheGermany

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