Optimal dynamic solutions for fixed windowing problems

Given a point set in plane and a fixed planar region (window) a window query consists of enumerating the points in a translate of the region. A recently presented result shows that a static data structure of optimal size enables window queries for convex regions in optimal time. We show that if the windows are (maybe non-convex) polygons another data structure of optimal size supports not only window queries in optimal time but also allows updating of the point set in optimal time.

[1]  Robert E. Tarjan,et al.  Updating a Balanced Search Tree in O(1) Rotations , 1983, Inf. Process. Lett..

[2]  Jan van Leeuwen,et al.  Dynamization of Decomposable Searching Problems , 1980, Inf. Process. Lett..

[3]  Edward M. McCreight,et al.  Priority Search Trees , 1985, SIAM J. Comput..

[4]  Bernard Chazelle,et al.  Optimal Solutions for a Class of Point Retrieval Problems , 1985, ICALP.

[5]  Mark H. Overmars,et al.  The Design of Dynamic Data Structures , 1987, Lecture Notes in Computer Science.

[6]  Jon Louis Bentley,et al.  Decomposable Searching Problems , 1979, Inf. Process. Lett..

[7]  Jon Louis Bentley,et al.  Decomposable Searching Problems I: Static-to-Dynamic Transformation , 1980, J. Algorithms.