@inproceedings{dcc8b4e1027d4d10bdbc535947012cde,
title = "Folding free-space diagrams: Computing the Fr{\'e}chet distance between 1-dimensional curves",
abstract = "By folding the free-space diagram for efficient preprocessing, we show that the Fr{\'e}chet distance between 1D curves can be computed in O(nk log n) time, assuming one curve has ply k.",
keywords = "Fr{\'e}chet distance, K-packed curves, Ply",
author = "Kevin Buchin and Jinhee Chun and Maarten L{\"o}ffler and Aleksandar Markovic and Wouter Meulemans and Yoshio Okamoto and Taichi Shiitada",
note = "Funding Information: Each case takes O(1) time, thus this runs in O(|A| + |E|) = O(k) time (Lemma 2). Including the query in S, this results in a total time of O(log n + k). Correctness follows from the invariant that we collected all reachable intervals before A[x], that intervals before E[j] cannot reach up to A[x] or later intervals, and that intervals before A[x] do not limit how high E[j] can reach (via Lemma 5). J Acknowledgments. This research was initiated at the Dutch-Japanese Bilateral Workshop on Kinetic Geometric Networks, supported under the Japan-Netherlands Research Cooperative Program by NWO (grant 040.05.033) and JSPS. Funding Information: ∗ K.B. is supported by NWO (612.001.207); W.M. by NLeSC (027.015.G02) and NWO (639.023.208); and Y.O. by Kayamori Foundation of Informational Science Advancement, JST CREST (JPMJCR1402), and JSPS KAKENHI (JP24106005, JP15K00009).; 33rd International Symposium on Computational Geometry, SoCG 2017 ; Conference date: 04-07-2017 Through 07-07-2017",
year = "2017",
month = jun,
day = "1",
doi = "10.4230/LIPIcs.SoCG.2017.64",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
pages = "641--645",
editor = "Katz, {Matthew J.} and Boris Aronov",
booktitle = "33rd International Symposium on Computational Geometry, SoCG 2017",
}