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International Conference on Combinatorial Optimization and Applications

COCOA 2013: Combinatorial Optimization and Applications pp 13–24Cite as

Discretely Following a Curve

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8287))

Abstract

Finding the similarity between paths is an important problem that comes up in many areas such as 3D modeling, GIS applications, ordering, and reachability. Given a set of points S, a polygonal curve P, and an ε > 0, the discrete set-chain matching problem is to find another polygonal curve Q such that the nodes of Q are points in S and d f (P,Q) ≤ ε. Here, d F is the discrete Fréchet distance between the two polygonal curves. For the first time we study the set-chain matching problem based on the discrete Fréchet distance rather than the continuous Fréchet distance. We further extend the problem based on unique or non-unique nodes and on limiting the number of points used. We prove that three of the variations of the set-chain matching problem are NP-complete. For the version of the problem that we prove is polynomial, we give the optimal substructure and the recurrence for a dynamic programming solution.

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Author information

Authors and Affiliations

  1. Department of Computer Science, The University of Alberta, Edmonton, AB, Canada, T6G-2E8

    Tim Wylie

Authors
  1. Tim Wylie
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Editor information

Editors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zürich, Zürich, Switzerland

    Peter Widmayer

  2. State Key Lab for Manufacturing Systems Engineering, 710049, Xi’an, China

    Yinfeng Xu

  3. Department of Computer Science, Montana State University, 59717-3880, Bozeman, MT, USA

    Binhai Zhu

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© 2013 Springer International Publishing Switzerland

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Wylie, T. (2013). Discretely Following a Curve. In: Widmayer, P., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2013. Lecture Notes in Computer Science, vol 8287. Springer, Cham. https://doi.org/10.1007/978-3-319-03780-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-03780-6_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03779-0

  • Online ISBN: 978-3-319-03780-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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