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Better Approximation of Diagonal-Flip Transformation and Rotation Transformation

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Abstract

Approximation algorithms are developed for the diagonal- flip transformation of convex polygon triangulations and equivalently rotation transformation of binary trees. For two arbitrary triangulations in which each vertex is an end of at most d diagonals, Algorithm A has the approximation ratio \(2 - \frac{2}{{4(d - 1)(d + 6) + 1}}.\)For triangulations containing no internal triangles, Algorithm B has the approximation ratio 1.97. Two self-interesting lower bounds on the diagonal-flip distance are also established in the analyses of these two algorithms.

Supported in part by the NSERC Operating Grant OGP0046506, ITRC and a CGAT grant.

Part of the work was done at Waterloo and supported by a CGAT grant.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Waterloo, Canada, N2L 3G1

    Ming Li

  2. BioInformatics Center, NUS, Singapore

    Louxin Zhang

  3. Kent Ridge Digital Labs, Singapore, 119613

    Louxin Zhang

Authors
  1. Ming Li
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  2. Louxin Zhang
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Editor information

Editors and Affiliations

  1. Institute of Information Science, Academia Sinica, 11529, Nankang, Taipei, Taiwan

    Wen-Lian Hsu

  2. Department of Computer Science, Yale University, 51 Prospect Street, New Haven, CT, 06520, USA

    Ming-Yang Kao

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© 1998 Springer-Verlag Berlin Heidelberg

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Li, M., Zhang, L. (1998). Better Approximation of Diagonal-Flip Transformation and Rotation Transformation. In: Hsu, WL., Kao, MY. (eds) Computing and Combinatorics. COCOON 1998. Lecture Notes in Computer Science, vol 1449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68535-9_12

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  • DOI: https://doi.org/10.1007/3-540-68535-9_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64824-6

  • Online ISBN: 978-3-540-68535-7

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