A study of the LMT-skeleton

  • Siu-Wing Cheng
  • Naoki Katoh
  • Manabu Sugai
Session 7a: Invited Presentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1178)


We present improvements in finding the LMT-skeleton, which is a subgraph of all minimum weight triangulations, independently proposed by Belleville et al, and Dickerson and Montague. Our improvements consist of: (1) A criteria is proposed to identify edges in all minimum weight triangulations, which is a relaxation of the definition of local minimality used in Dickerson and Montague's method to find the LMT-skeleton; (2) A worst-case efficient algorithm is presented for performing one pass of Dickerson and Montague's method (with our new criteria); (3) Improvements in the implementation that may lead to substantial space reduction for uniformly distributed point sets.


Priority Queue Space Usage Simple Polygon Lower Envelope Active Edge 
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  1. 1.
    A. Aggarwal, M.M. Klawe, S. Moran, P.W. Shor, and R. Wilber: Geometric applications of a matrix-searching algorithm, Algorithmica, 2 (1987), pp. 195–208.CrossRefGoogle Scholar
  2. 2.
    O. Aichholzer, F. Aurenhammer, S.W. Cheng, N. Katoh, G. Rote, M, Taschwer, and Y.F. Xu, Triangulations intersect nicely, manuscript, 1996.Google Scholar
  3. 3.
    P. Belleville, M. Keil, M. McAllister, and J. Snoeyink, On computing edges that are in all minimum-weight triangulations, Video Presentation, Symp. Computational Geometry, 1996.Google Scholar
  4. 4.
    P. Bose, L. Devroye, and W. Evans, Diamonds are not a minimum weight triangulation's best friend, Proceedings of Canadian Conference on Computational Geometry, 1996. See also technical report 96-01, Dept. of Computer Science, Univ. of British Columbia, January 1996.Google Scholar
  5. 5.
    S.W. Cheng and Y.F. Xu, Approaching the largest β-skeleton within a minimum weight triangulation, Proc. Symp. Computational Geometry, 1996, pp. 196–203.Google Scholar
  6. 6.
    M.T. Dickerson and M.H. Montague, A (usually?) connected subgraph of minimum weight triangulation, Proc. Symp. Computational Geometry, 1996, pp. 204–213.Google Scholar
  7. 7.
    M. Golin, Limit theorems for minimum-weight triangulations, other Euclidean functionals, and probabilistic recurrence relations, Proc. Symp. Discrete Algorithms, 1996, pp. 252–260.Google Scholar
  8. 8.
    L. Heath and S.V. Pemmaraju, New results for the minimum weight triangulation problem, Algorithmica, 12 (1994), pp. 533–552.CrossRefGoogle Scholar
  9. 9.
    J.M. Keil, Computing a subgraph of the minimum weight triangulation, Computational Geometry: Theory and Applications, 4 (1994), pp. 13–26.Google Scholar
  10. 10.
    C. Levcopoulos and D. Krznaric, Quasi-greedy triangulations approximating the minimum weight triangulation, Proc. Symp. Discrete Algorithms, 1996, pp. 392–401.Google Scholar
  11. 11.
    C. Levcopoulos and D. Krznaric, A fast heuristic for approximating the minimum weight triangulation, Proc. Scandinavian Workshop on Algorithmic Theory, 1996.Google Scholar
  12. 12.
    B. Yang, Y. Xu, and Z. You, A chain decomposition algorithm for the proof of a property on minimum weight triangulation, in Proc. International Symposium on Algorithms and Computation, 1994, pp. 423–427.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Siu-Wing Cheng
    • 1
  • Naoki Katoh
    • 2
  • Manabu Sugai
    • 2
  1. 1.Department of Computer ScienceHKUSTClear Water BayHong Kong
  2. 2.Kobe University of CommerceKobeJapan

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