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DOI: 10.4230/LIPIcs.SWAT.2022.11
URN: urn:nbn:de:0030-drops-161710
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16171/
Aronov, Boris ; Katz, Matthew J.
Dynamic Approximate Multiplicatively-Weighted Nearest Neighbors
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Abstract
We describe a dynamic data structure for approximate nearest neighbor (ANN) queries with respect to multiplicatively weighted distances with additive offsets. Queries take polylogarithmic time, while the cost of updates is amortized polylogarithmic. The data structure requires near-linear space and construction time.The approach works not only for the Euclidean norm, but for other norms in ℝ^d, for any fixed d.
We employ our ANN data structure to construct a faster dynamic structure for approximate SINR queries, ensuring polylogarithmic query and polylogarithmic amortized update for the case of non-uniform power transmitters, thus closing a gap in previous state of the art.
To obtain the latter result, we needed a data structure for dynamic approximate halfplane range counting in the plane. Since we could not find such a data structure in the literature, we also show how to dynamize one of the known static data structures.
BibTeX - Entry
@InProceedings{aronov_et_al:LIPIcs.SWAT.2022.11,
author = {Aronov, Boris and Katz, Matthew J.},
title = {{Dynamic Approximate Multiplicatively-Weighted Nearest Neighbors}},
booktitle = {18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
pages = {11:1--11:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-236-5},
ISSN = {1868-8969},
year = {2022},
volume = {227},
editor = {Czumaj, Artur and Xin, Qin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16171},
URN = {urn:nbn:de:0030-drops-161710},
doi = {10.4230/LIPIcs.SWAT.2022.11},
annote = {Keywords: Nearest neighbors, Approximate nearest neighbors, Weighted nearest neighbors, Nearest neighbor queries, SINR queries, Dynamic data structures}
}
| Keywords: | Nearest neighbors, Approximate nearest neighbors, Weighted nearest neighbors, Nearest neighbor queries, SINR queries, Dynamic data structures | |
| Seminar: | 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 22.06.2022 |
