Labeled Nearest Neighbor Search and Metric Spanners via Locality Sensitive Orderings

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Chan, Har-Peled, and Jones [SICOMP 2020] developed locality-sensitive orderings (LSO) for Euclidean space. A (τ, ρ)-LSO is a collection Σ of orderings such that for every x, y ∈ Rd there is an ordering σ ∈ Σ, where all the points between x and y w.r.t. σ are in the ρ-neighborhood of either x or y. In essence, LSO allow one to reduce problems to the 1-dimensional line. Later, Filtser and Le [STOC 2022] developed LSO's for doubling metrics, general metric spaces, and minor free graphs. For Euclidean and doubling spaces, the number of orderings in the LSO is exponential in the dimension, which made them mainly useful for the low dimensional regime. In this paper, we develop new LSO's for Euclidean, ℓp, and doubling spaces that allow us to trade larger stretch for a much smaller number of orderings. We then use our new LSO's (as well as the previous ones) to construct path reporting low hop spanners, fault tolerant spanners, reliable spanners, and light spanners for different metric spaces. While many nearest neighbor search (NNS) data structures were constructed for metric spaces with implicit distance representations (where the distance between two metric points can be computed using their names, e.g. Euclidean space), for other spaces almost nothing is known. In this paper we initiate the study of the labeled NNS problem, where one is allowed to artificially assign labels (short names) to metric points. We use LSO's to construct efficient labeled NNS data structures in this model.

Original languageEnglish
Title of host publication39th International Symposium on Computational Geometry, SoCG 2023
EditorsErin W. Chambers, Joachim Gudmundsson
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772730
StatePublished - 1 Jun 2023
Event39th International Symposium on Computational Geometry, SoCG 2023 - Dallas, United States
Duration: 12 Jun 202315 Jun 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference39th International Symposium on Computational Geometry, SoCG 2023
Country/TerritoryUnited States

Bibliographical note

Publisher Copyright:
© Arnold Filtser; licensed under Creative Commons License CC-BY 4.0.


  • Locality sensitive ordering
  • doubling dimension
  • fault tolerant spanner
  • high dimensional Euclidean space
  • light spanner
  • nearest neighbor search
  • path reporting low hop spanner
  • planar and minor free graphs
  • reliable spanner


Dive into the research topics of 'Labeled Nearest Neighbor Search and Metric Spanners via Locality Sensitive Orderings'. Together they form a unique fingerprint.

Cite this