Abstract
We present a new dynamic technique for locating a point in a convex planar subdivision whose n vertices lie on a fixed set of N horizontal lines. The supported update operations are insertion/deletion of vertices and edges, and (horizontal) translation of vertices. Our method achieves query time O(log n + log N), space O(N + n log N), and insertion/deletion time O(log n log N). Hence, for N=O (n), the query time is O(log n), which is optimal. The proposed technique, based on the trapezoid method, provides an efficient solution to many significant applications where the most frequent operation is the point location query, while updates are more rarely executed.
This work was carried out at the University of Illinois and was supported in part by National Science Foundation Grant ECS-84-10902 and by the Joint Services Electronics Program under Contract N00014-84-C-0149.
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Preparata, F.P., Tamassia, R. (1989). Dynamic planar point location with optimal query time. In: Monien, B., Cori, R. (eds) STACS 89. STACS 1989. Lecture Notes in Computer Science, vol 349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028975
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DOI: https://doi.org/10.1007/BFb0028975
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