Optimal dynamic vertical ray shooting in rectilinear planar subdivisions

Yoav Giora, Haim Kaplan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider the dynamic vertical ray shooting problem against horizontal disjoint segments, that is, the task of maintaining a dynamic set S of n nonintersecting horizontal line segments in the plane under a query that reports the first segment in S intersecting a vertical ray from a query point. We develop a linear-size structure that supports queries, insertions, and deletion in O(log n) worst-case time. Our structure works in the comparison model on a random access machine.

Original languageEnglish
Article number28
JournalACM Transactions on Algorithms
Issue number3
StatePublished - 1 Jul 2009


  • Planar point location
  • Ray shooting


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