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An optimal algorithm for computing visible nearest foreign neighbors among colored line segments

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Algorithm Theory — SWAT'98 (SWAT 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1432))

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Abstract

Given a set S of n colored line segments in ℝ2 that may intersect only in endpoints. Let c(u) denote the color of a line segment u ∃ S chosen from χ ≤ n different colors. A line segment v ∃ S is a visible nearest foreign neighbor of u ∃ S if v is a nearest foreign neighbor of u in S, i.e. c(u) ≠ c(v) and no segment with a color different from c(u) is closer to u than v, and if there exist points u' ∃ u and v' ∃ v realizing the distance between u and v that are visible for each other, i.e. the open segment connecting u' and v' is not intersected by an open line segment in S. We present the first optimal θ(n log n) algorithm that computes for each line segment u ∃ S all its visible nearest foreign neighbors. The algorithm finds applications in polygon arrangement analysis, VLSI design rule checking and GIS.

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Author information

Authors and Affiliations

  1. Department ICG-4, Research Center Jülich, 52425, Jülich, Germany

    Thorsten Graf

  2. Institute of Mathematical Sciences, CIT Campus, 600 113, Chennai, India

    Kamakoti Veezhinathan

Authors
  1. Thorsten Graf
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  2. Kamakoti Veezhinathan
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Stefan Arnborg Lars Ivansson

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© 1998 Springer-Verlag Berlin Heidelberg

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Graf, T., Veezhinathan, K. (1998). An optimal algorithm for computing visible nearest foreign neighbors among colored line segments. In: Arnborg, S., Ivansson, L. (eds) Algorithm Theory — SWAT'98. SWAT 1998. Lecture Notes in Computer Science, vol 1432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054355

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  • DOI: https://doi.org/10.1007/BFb0054355

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64682-2

  • Online ISBN: 978-3-540-69106-8

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