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This study introduces efficient data structures for reporting intersecting object pairs within query ranges. These structures optimize spatial queries for axis-aligned rectangles and boxes in various dimensions.

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Area of Science:

  • Computational Geometry
  • Data Structures
  • Spatial Databases

Background:

  • Efficiently querying intersecting geometric objects within specified ranges is a fundamental problem in computational geometry.
  • Existing methods often struggle with scalability and performance when dealing with large datasets or high-dimensional spaces.

Purpose of the Study:

  • To develop novel data structures for preprocessing sets of geometric objects.
  • To enable efficient reporting of intersecting object pairs within axis-aligned query ranges.
  • To analyze the performance of these structures in 2D and 3D spatial dimensions.

Main Methods:

  • Development of specialized data structures for geometric object preprocessing.
  • Analysis of query time complexity based on the number of reported pairs (k).
  • Adaptation of methods for axis-aligned rectangles, objects with small union complexity, and 3D boxes.

Main Results:

  • Achieved data structure size of O(n log n) and query time of O(log n + k) for 2D objects.
  • Presented a 3D data structure with O(n log n) size and O(n^(2/3) log n + k) query time for axis-aligned boxes.
  • Demonstrated improved query time of O(log n + k) for fat objects and queries in 3D.

Conclusions:

  • The proposed data structures offer significant improvements in query efficiency for spatial intersection problems.
  • The methods are effective for various object types and dimensions, enhancing performance in computational geometry applications.
  • This work contributes to the advancement of spatial data management and query processing techniques.