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Relative Convex Hulls in Semi-dynamic Subdivisions

  • Mashhood Ishaque
  • Csaba D. Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5193)

Abstract

We present data structures for maintaining the relative convex hull of a set of points (sites) in the presence of pairwise non-crossing line segments (barriers) that subdivide a bounding box into simply connected faces. Our data structures have O((n + m)logn) size for n sites and m barriers. They support O(m) barrier insertions and O(n) site deletions in O((m + n) polylog (mn)) total time, and can answer analogues of standard convex hull queries in O(polylog(mn)) time.

Our data structures support a generalization of the sweep line technique, in which the sweep wavefront may have arbitrary polygonal shape, possibly bending around obstacles. We reduce the total time of m online updates of a polygonal sweep wavefront from \(O(m\sqrt{n}\,{\rm polylog} n)\) to O((m + n) polylog (mn)).

Keywords

Convex Hull Simple Polygon Geodesic Path Common Tangent Sweep Line 
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 2008

Authors and Affiliations

  • Mashhood Ishaque
    • 1
  • Csaba D. Tóth
    • 2
  1. 1.Dept. of Comp. Sci.Tufts UniversityMedford
  2. 2.Dept. of MathematicsUniversity of Calgary

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