Approximate Range Counting Revisited

Author Saladi Rahul

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Saladi Rahul

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Saladi Rahul. Approximate Range Counting Revisited. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


We study range-searching for colored objects, where one has to count (approximately) the number of colors present in a query range. The problems studied mostly involve orthogonal range-searching in two and three dimensions, and the dual setting of rectangle stabbing by points. We present optimal and near-optimal solutions for these problems. Most of the results are obtained via reductions to the approximate uncolored version, and improved data-structures for them. An additional contribution of this work is the introduction of nested shallow cuttings.
  • orthogonal range searching
  • rectangle stabbing
  • colors
  • approximate count
  • geometric data structures


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