Advertisement

Rotation distance, triangulations of planar surfaces and hyperbolic geometry

  • Jin-Yi Cai
  • Michael D. Hirsch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 834)

Abstract

This paper extends the results of Sleator, Tarjan and Thurston to rotation distance problems of triangulations of planar surfaces. We give upper and lower bounds for this problem. The upper bound is obtained by looking at the triangulations in the universal covering space, and the lower bound is obtained by extending and applying the technique of volume estimate in hyperbolic geometry.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. S, M. Coxeter, Introduction to Geometry, 1969, Wiley, New York.Google Scholar
  2. 2.
    W. S. Massey, Singular Homology Theory, 1980, Springer-Verlag, New York.Google Scholar
  3. 3.
    D. D. Sleator and R. E. Tarjan, Self-adjusting binary trees, J. ACM, 32, 1985, 652–686.CrossRefGoogle Scholar
  4. 4.
    D. D. Sleator, R. E. Tarjan and W. P. Thurston, Rotation distance, triangulations, and hyperbolic geometry, Proc. ACM STOC, 1986, 122–135.Google Scholar
  5. 5.
    D. D. Sleator, R. E. Tarjan and W. P. Thurston, Rotation distance, triangulations, and hyperbolic geometry, J. AMS, vol 1, Num 3, 1988, 647–681.Google Scholar
  6. 6.
    R. E. Tarjan, Data structures and network algorithms, SIAM, PA, 1983.Google Scholar
  7. 7.
    R. E. Tarjan, Private communications.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Jin-Yi Cai
    • 1
  • Michael D. Hirsch
    • 2
  1. 1.Dept. of Computer ScienceState Univ. of New York at BuffaloBuffalo
  2. 2.Department of Math and CSEmory UniversityAtlanta

Personalised recommendations