Dynamic Approximate Multiplicatively-Weighted Nearest Neighbors

Authors Boris Aronov , Matthew J. Katz

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Boris Aronov
  • Department of Computer Science and Engineering, Tandon School of Engineering, New York University, Brooklyn, NY, USA
Matthew J. Katz
  • Department of Computer Science, Ben Gurion University of the Negev, Beer Sheva, Israel


We wish to thank Pankaj K. Agarwal for his help and encouragement, and David Mount for a clarification regarding the approximating polytope in [Rahul Arya et al., 2020].

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Boris Aronov and Matthew J. Katz. Dynamic Approximate Multiplicatively-Weighted Nearest Neighbors. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Design and analysis of algorithms
  • Nearest neighbors
  • Approximate nearest neighbors
  • Weighted nearest neighbors
  • Nearest neighbor queries
  • SINR queries
  • Dynamic data structures


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