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Spanning Ratio and Maximum Detour of Rectilinear Paths in the L 1 Plane

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Algorithms and Computation (ISAAC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6507))

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Abstract

The spanning ratio and maximum detour of a graph G embedded in a metric space measure how well G approximates the minimum complete graph containing G and metric space, respectively. In this paper we show that computing the spanning ratio of a rectilinear path P in L 1 space has a lower bound of Ω(n logn) in the algebraic computation tree model and describe a deterministic O(n log2 n) time algorithm. On the other hand, we give a deterministic O(n log2 n) time algorithm for computing the maximum detour of a rectilinear path P in L 1 space and obtain an O(n) time algorithm when P is a monotone rectilinear path.

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Author information

Authors and Affiliations

  1. Institut für Informatik I, Universität Bonn, Bonn, Germany

    Ansgar Grüne, Rolf Klein & Elmar Langetepe

  2. Institute of Information Science, Academia Sinica, Nankang, Taipei, Taiwan

    Tien-Ching Lin, Teng-Kai Yu & D. T. Lee

  3. Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan

    Teng-Kai Yu & D. T. Lee

  4. Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan

    Sheung-Hung Poon

Authors
  1. Ansgar Grüne
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  2. Tien-Ching Lin
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  3. Teng-Kai Yu
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  4. Rolf Klein
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  5. Elmar Langetepe
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  6. D. T. Lee
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  7. Sheung-Hung Poon
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Editor information

Editors and Affiliations

  1. Department of Computer Science, KAIST, Gwahangno 335, Yuseong-gu, 305-701, Daejeon, Korea

    Otfried Cheong  & Kyung-Yong Chwa  & 

  2. School of Computer Science and Engineering, Seoul National University, 151-742, Seoul, Korea

    Kunsoo Park

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Grüne, A. et al. (2010). Spanning Ratio and Maximum Detour of Rectilinear Paths in the L 1 Plane. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17514-5_11

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  • DOI: https://doi.org/10.1007/978-3-642-17514-5_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17513-8

  • Online ISBN: 978-3-642-17514-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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