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.
@InProceedings{rahul:LIPIcs.SoCG.2017.55, author = {Rahul, Saladi}, title = {{Approximate Range Counting Revisited}}, booktitle = {33rd International Symposium on Computational Geometry (SoCG 2017)}, pages = {55:1--55:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-038-5}, ISSN = {1868-8969}, year = {2017}, volume = {77}, editor = {Aronov, Boris and Katz, Matthew J.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.55}, URN = {urn:nbn:de:0030-drops-72354}, doi = {10.4230/LIPIcs.SoCG.2017.55}, annote = {Keywords: orthogonal range searching, rectangle stabbing, colors, approximate count, geometric data structures} }
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