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Computing the Maximum Detour and Spanning Ratio of Planar Paths, Trees, and Cycles

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STACS 2002 (STACS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2285))

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Abstract

The maximum detour and spanning ratio of an embedded graph G are values that measure how well G approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe O(n log n) time algorithms for computing the maximum detour and spanning ratio of a planar polygonal path. These algorithms solve open problems posed in at least two previous works [5],[10]. We also generalize these algorithms to obtain O(nlog2 n) time algorithms for computing the maximum detour and spanning ratio of planar trees and cycles.

This research was partly funded by CRM, FCAR, MITACS, and NSERC. This research was done while the third author was affiliated with SOCS, McGill University.

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References

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Author information

Authors and Affiliations

  1. School of Computer Science, McGill University, 3480 University St., Suite 318, H3A 2A7, Montréal, Québec, CANADA

    Stefan Langerman & Pat Morin

  2. Chemical Computing Group, Inc., 1010 Sherbrooke Street West, Suite 910, H3A 2R7, Montréal, Québec, CANADA

    Michael Soss

Authors
  1. Stefan Langerman
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  2. Pat Morin
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  3. Michael Soss
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Free University of Berlin, Takustraße 9, 14195, Berlin, Germany

    Helmut Alt

  2. CNRS - I3S - INRIA Sophia Antipolis, 2004 Route des Lucioles, 06902, Sophia Antipolis, France

    Afonso Ferreira

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© 2002 Springer-Verlag Berlin Heidelberg

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Langerman, S., Morin, P., Soss, M. (2002). Computing the Maximum Detour and Spanning Ratio of Planar Paths, Trees, and Cycles. In: Alt, H., Ferreira, A. (eds) STACS 2002. STACS 2002. Lecture Notes in Computer Science, vol 2285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45841-7_20

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  • DOI: https://doi.org/10.1007/3-540-45841-7_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43283-8

  • Online ISBN: 978-3-540-45841-8

  • eBook Packages: Springer Book Archive

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