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Title: Discrete Fréchet Distance Oracles
It is unlikely that the discrete Fréchet distance between two curves of length n can be computed in strictly subquadratic time. We thus consider the setting where one of the curves, P, is known in advance. In particular, we wish to construct data structures (distance oracles) of near-linear size that support efficient distance queries with respect to P in sublinear time. Since there is evidence that this is impossible for query curves of length Θ(n^α), for any α > 0, we focus on query curves of (small) constant length, for which we are able to devise distance oracles with the desired bounds. We extend our tools to handle subcurves of the given curve, and even arbitrary vertex-to-vertex subcurves of a given geometric tree. That is, we construct an oracle that can quickly compute the distance between a short polygonal path (the query) and a path in the preprocessed tree between two query-specified vertices. Moreover, we define a new family of geometric graphs, t-local graphs (which strictly contains the family of geometric spanners with constant stretch), for which a similar oracle exists: we can preprocess a graph G in the family, so that, given a query segment and a pair u,v of vertices in G, one can quickly compute the smallest discrete Fréchet distance between the segment and any (u,v)-path in G. The answer is exact, if t = 1, and approximate if t > 1.  more » « less
Award ID(s):
2008551
PAR ID:
10578970
Author(s) / Creator(s):
; ; ;
Editor(s):
Mulzer, Wolfgang; Phillips, Jeff M
Publisher / Repository:
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Date Published:
Volume:
293
ISSN:
1868-8969
ISBN:
978-3-95977-316-4
Page Range / eLocation ID:
10:1-10:14
Subject(s) / Keyword(s):
discrete Fréchet distance distance oracle heavy-path decomposition t-local graphs Theory of computation → Computational geometry
Format(s):
Medium: X Size: 14 pages; 817873 bytes Other: application/pdf
Size(s):
14 pages 817873 bytes
Location:
40th International Symposium on Computational Geometry (SoCG 2024), Athens, Greece
Right(s):
Creative Commons Attribution 4.0 International license; info:eu-repo/semantics/openAccess
Sponsoring Org:
National Science Foundation
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