Approximate nearest neighbor for curves - simple, efficient, and deterministic

Arnold Filtser, Omrit Filtser, Matthew J. Katz

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


In the (1 + ε, r)-approximate near-neighbor problem for curves (ANNC) under some similarity measure δ, the goal is to construct a data structure for a given set C of curves that supports approximate near-neighbor queries: Given a query curve Q, if there exists a curve C ∈ C such that δ(Q, C) ≤ r, then return a curve C0 ∈ C with δ(Q, C0) ≤ (1 + ε)r. There exists an efficient reduction from the (1 + ε)-approximate nearest-neighbor problem to ANNC, where in the former problem the answer to a query is a curve C ∈ C with δ(Q, C) ≤ (1 + ε) · δ(Q, C), where C is the curve of C most similar to Q. Given a set C of n curves, each consisting of m points in d dimensions, we construct a data structure for ANNC that uses n · O(1ε )md storage space and has O(md) query time (for a query curve of length m), where the similarity measure between two curves is their discrete Fréchet or dynamic time warping distance. Our method is simple to implement, deterministic, and results in an exponential improvement in both query time and storage space compared to all previous bounds. Further, we also consider the asymmetric version of ANNC, where the length of the query curves is k m, and obtain essentially the same storage and query bounds as above, except that m is replaced by k. Finally, we apply our method to a version of approximate range counting for curves and achieve similar bounds.

Original languageEnglish
Title of host publication47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
EditorsArtur Czumaj, Anuj Dawar, Emanuela Merelli
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771382
StatePublished - 1 Jun 2020
Externally publishedYes
Event47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 - Virtual, Online, Germany
Duration: 8 Jul 202011 Jul 2020

Publication series

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


Conference47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
CityVirtual, Online

Bibliographical note

Funding Information:
Funding Arnold Filtser: Supported by the Simons Foundation. Omrit Filtser: Supported by the Eric and Wendy Schmidt Fund for Strategic Innovation, by the Council for Higher Education of Israel, and by Ben-Gurion University of the Negev. Matthew J. Katz: Supported by grant 1884/16 from the Israel Science Foundation.

Publisher Copyright:
© Arnold Filtser, Omrit Filtser, and Matthew J. Katz; licensed under Creative Commons License CC-BY 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020).


  • (asymmetric) approximate nearest neighbor
  • Approximation algorithms
  • Dynamic time warping
  • Fréchet distance
  • Polygonal curves
  • Range counting


Dive into the research topics of 'Approximate nearest neighbor for curves - simple, efficient, and deterministic'. Together they form a unique fingerprint.

Cite this