Optimal dynamic vertical ray shooting in rectilinear planar subdivisions

Authors:
Yoav Giyora;Haim Kaplan
Affiliations:
Tel-Aviv University, Israel;Tel-Aviv University, Israel
Venue:
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2007

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Abstract

In this paper we consider the dynamic vertical ray shooting problem, that is the task of maintaining a dynamic set S of n non intersecting horizontal line segments in the plane subject to 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 deletions in O(log n) worst-case time. Our structure works in the comparison model and uses a RAM.