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Constrained Minimum Enclosing Circle with Center on a Query Line Segment

  • Sasanka Roy
  • Arindam Karmakar
  • Sandip Das
  • Subhas C. Nandy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)

Abstract

In this paper, we will study the problem of locating the center of smallest enclosing circle of a set P of n points, where the center is constrained to lie on a query line segment. The preprocessing time and space complexities of our proposed algorithm are O(n logn) and O(n) respectively; the query time complexity is O(log2 n). We will use this method for solving the following problem proposed by Bose and Wang [3] – given r simple polygons with a total of m vertices along with the point set P, compute the smallest enclosing circle of P whose center lies in one of the r polygons. This can be solved in O( nlogn+mlog2 n) time using our method in a much simpler way than [3]; the time complexity of the problem is also being improved.

Keywords

Intersection Point Leaf Node Space Complexity Voronoi Diagram Convex Polygon 
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 2006

Authors and Affiliations

  • Sasanka Roy
    • 1
  • Arindam Karmakar
    • 1
  • Sandip Das
    • 2
  • Subhas C. Nandy
    • 1
  1. 1.Indian Statistical InstituteCalcuttaIndia
  2. 2.Institut de Mathématiques de BourgogneDijonFrance

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