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Geometric searching and link distance

  • Gautam Das
  • Giri Narasimhan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 519)

Abstract

Given n orthogonal line segments on the plane, their intersection graph is defined such that each vertex corresponds to a segment, and each edge corresponds to a pair of intersecting segments. Although this graph can have Θ(n2) edges, we show that breadth first search can be accomplished in O(nlogn) time and O(n) space. As an application, we show that the minimum link rectilinear path between two points s and t amidst rectilinear polygonal obstacles can be computed in O(nlogn) time and O(n) space, which is optimal. We mention other related results in the paper.

Keywords

Line Segment Intersection Graph Vertical Segment Simple Polygon Horizontal Segment 
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 1991

Authors and Affiliations

  • Gautam Das
    • 1
  • Giri Narasimhan
    • 1
  1. 1.Mathematical Sciences DepartmentMemphis State UniversityMemphis

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