Computing the kernel of a point set in a polygon

Extended abstract
  • Yan Ke
  • Joseph O'Rourke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 382)


ElGindy posed the following problem: given a simple polygon P of n vertices and a set S of k points inside P, find the collection of points of P that can see all points of S. This collection of points is called the kernel of S in P. In this paper, we study this problem and show that the kernel of S can be computed in O(n log log n+k log n+k log k) time and O(n+k) space. We also present an O(n log n+k log k) time and O(n+k) space algorithm to determine if there exists a line segment in P that can see all points of S, and if so, to find the shortest one. Several other related problems are also addressed.


Convex Hull Convex Polygon Simple Polygon Geodesic Path Prefer Side 
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 1989

Authors and Affiliations

  • Yan Ke
    • 1
  • Joseph O'Rourke
    • 2
  1. 1.Department of Computer ScienceThe Johns Hopkins UniversityBaltimore
  2. 2.Department of Computer ScienceSmith CollegeNorthampton

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