Computing the Fréchet Distance Between Uncertain Curves in One Dimension

Kevin Buchin, Maarten Löffler, Tim Ophelders, Aleksandr Popov, Jérôme Urhausen, Kevin Verbeek

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review


We consider the problem of computing the Fréchet distance between two curves for which the exact locations of the vertices are unknown. Each vertex may be placed in a given uncertainty region for that vertex, and the objective is to place vertices so as to minimise the Fréchet distance. This problem was recently shown to be NP-hard in 2D, and it is unclear how to compute an optimal vertex placement at all.

We give a polynomial-time algorithm for 1D curves with intervals as uncertainty regions. In contrast, we show that the problem is NP-hard in 1D in the case that vertices are placed to maximise the Fréchet distance.

We also study the weak Fréchet distance between uncertain curves. While finding the optimal placement of vertices seems more difficult than for the regular Fréchet distance—and indeed we can easily prove that the problem is NP-hard in 2D—the optimal placement of vertices in 1D can be computed in polynomial time. Finally, we investigate the discrete weak Fréchet distance, for which, somewhat surprisingly, the problem is NP-hard already in 1D.
Originele taal-2Engels
TitelAlgorithms and Data Structures
Subtitel17th International Symposium, WADS 2021, Virtual Event, August 9–11, 2021, Proceedings
RedacteurenAnna Lubiw, Mohammad Salavatipour
Plaats van productieCham, Switzerland
UitgeverijSpringer Nature
Aantal pagina's15
ISBN van elektronische versie978-3-030-83508-8
ISBN van geprinte versie978-3-030-83507-1
StatusGepubliceerd - 11 aug 2021
Evenement17th Algorithms and Data Structures Symposium - Online, Halifax, Canada
Duur: 9 aug 202111 aug 2021
Congresnummer: 17

Publicatie series

NaamLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12808 LNCS
ISSN van geprinte versie0302-9743
ISSN van elektronische versie1611-3349


Congres17th Algorithms and Data Structures Symposium
Verkorte titelWADS 2021
Internet adres


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