Optimal dynamic vertical ray shooting in rectilinear planar subdivisions

  • Authors:
  • Yoav Giora;Haim Kaplan

  • Affiliations:
  • Tel-Aviv University, Tel-Aviv, Israel;Tel-Aviv University, Tel-Aviv, Israel

  • Venue:
  • ACM Transactions on Algorithms (TALG)
  • Year:
  • 2009

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Abstract

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.