Alternating Paths along Orthogonal Segments

  • Csaba D. Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2748)


It was shown recently that the segment endpoint visibility graph Vis(S) of any set S of n disjoint line segments in the plane admits an alternating path of length Θ(log n), and this bound is best possible apart from a constant factor. This paper focuses on the variant of the problem where S is a set of n disjoint axis-parallel line segments. We show that the length of a longest alternating path in the worst case is \(\Theta(\sqrt{n})\). We also present an O(n 2.5) time algorithm to find an alternating path of length \(\Omega(\sqrt{n})\). Finally, we consider sets of axis-parallel segments where the extensions of no two segments meet in the free space \(\mathbb{E}^2 \setminus \cup S\), and show that in that case all the segments can be included in a common alternating path.


Line Segment Lower Left Corner Vertical Segment Horizontal Segment Visibility Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Csaba D. Tóth
    • 1
  1. 1.Department of Computer ScienceUniversity of California at Santa BarbaraUSA

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