Efficient nearest-neighbor query and clustering of planar curves

Boris Aronov, Omrit Filtser, Michael Horton, Matthew J. Katz, Khadijeh Sheikhan

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

1 Scopus citations

Abstract

We study two fundamental problems dealing with curves in the plane, namely, the nearest-neighbor problem and the center problem. Let C be a set of n polygonal curves, each of size m. In the nearest-neighbor problem, the goal is to construct a compact data structure over C, such that, given a query curve Q, one can efficiently find the curve in C closest to Q. In the center problem, the goal is to find a curve Q, such that the maximum distance between Q and the curves in C is minimized. We use the well-known discrete Fréchet distance function, both under L and under L2, to measure the distance between two curves. For the nearest-neighbor problem, despite discouraging previous results, we identify two important cases for which it is possible to obtain practical bounds, even when m and n are large. In these cases, either Q is a line segment or C consists of line segments, and the bounds on the size of the data structure and query time are nearly linear in the size of the input and query curve, respectively. The returned answer is either exact under L, or approximated to within a factor of 1 + ε under L2. We also consider the variants in which the location of the input curves is only fixed up to translation, and obtain similar bounds, under L. As for the center problem, we study the case where the center is a line segment, i.e., we seek the line segment that represents the given set as well as possible. We present near-linear time exact algorithms under L, even when the location of the input curves is only fixed up to translation. Under L2, we present a roughly O(n2m3) -time exact algorithm.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings
EditorsZachary Friggstad, Mohammad R. Salavatipour, Jörg-Rüdiger Sack
PublisherSpringer Verlag
Pages28-42
Number of pages15
ISBN (Print)9783030247652
DOIs
StatePublished - 1 Jan 2019
Event16th International Symposium on Algorithms and Data Structures, WADS 2019 - Edmonton, Canada
Duration: 5 Aug 20197 Aug 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11646 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th International Symposium on Algorithms and Data Structures, WADS 2019
Country/TerritoryCanada
CityEdmonton
Period5/08/197/08/19

Keywords

  • (Approximation) algorithms
  • Clustering
  • Data structures
  • Fréchet distance
  • Nearest-neighbor queries
  • Polygonal curves

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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