Optimally computing the shortest weakly visible subedge of a simple polygon preliminary version

  • Danny Z. Chen
Conference paper

DOI: 10.1007/3-540-57568-5_263

Part of the Lecture Notes in Computer Science book series (LNCS, volume 762)
Cite this paper as:
Chen D.Z. (1993) Optimally computing the shortest weakly visible subedge of a simple polygon preliminary version. In: Ng K.W., Raghavan P., Balasubramanian N.V., Chin F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg

Abstract

Given an n-vertex simple polygon P, the problem of computing the shortest weakly visible subedge of P is that of finding a shortest line segment s on the boundary of P such that P is weakly visible from s (if s exists). In this paper, we present new geometric observations that are useful for solving this problem. Based on these geometric observations, we obtain optimal sequential and parallel algorithms for solving this problem. Our sequential algorithm runs in O(n) time, and our parallel algorithm runs in O(log n) time using O(n/log n) processors in the CREW PRAM computational model. Using the previously best known sequential algorithms to solve this problem would take O(n2) time. We also give geometric observations that lead to extremely simple and optimal algorithms for solving, both sequentially and in parallel, the case of this problem where the polygons are rectilinear.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Danny Z. Chen
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of Notre DameNotre DameUSA

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