Minimum Cycle Bases and Surface Reconstruction

(Abstract)
  • Kurt Mehlhorn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)

Abstract

I report on recent work on minimum cycle basis in graphs and their application to surface reconstruction. The talk is based on joint work with C. Gotsmann, R. Hariharan, K. Kaligosi, T. Kavitha, D. Michail, K. Paluch, and E. Pyrga. I refer the reader to [KMMP04, KM05, HKM, GKM + , MM05, Kav05] for details.

References

  1. [GKM+]
    Gotsman, C., Kaligosi, K., Mehlhorn, K., Michail, D., Pyrga, E.: Cycle basis and surface reconstruction (in preparation)Google Scholar
  2. [HKM]
    Hariharan, R., Kavitha, T., Mehlhorn, K.: A faster deterministic algorithm for minimum cycle basis in directed graphs, www.mpi-sb.mpg.de/~mehlhorn/ftp/ImprovedDirCycleBasis.ps
  3. [Kav05]
    Kavitha, T.: An \(\tilde{O}(m^2n)\) Randomized Algorithm to compute a Minimum Cycle Basis of a Directed Graph. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 273–284. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. [KM05]
    Kavitha, T., Mehlhorn, K.: A polynomial time algorithm for minimum cycle basis in directed graphs. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 654–665. Springer, Heidelberg (2005), www.mpi-sb.mpg.de/~mehlhorn/ftp/DirCycleBasis.ps CrossRefGoogle Scholar
  5. [KMMP04]
    Kavitha, T., Mehlhorn, K., Michail, D., Paluch, K.: A faster algorithm for minimum cycle bases of graphs. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 846–857. Springer, Heidelberg (2004), www.mpi-sb.mpg.zde/~mehlhorn/ftp/MinimumCycleBasis.ps CrossRefGoogle Scholar
  6. [MM05]
    Mehlhorn, K., Michail, D.: Implementing minimum cycle basis algorithms. In: Nikoletseas, S.E. (ed.) WEA 2005. LNCS, vol. 3503, pp. 32–43. Springer, Heidelberg (2005), www.mpi-sb.mpg.de/~mehlhorn/ftp/CycleBasisImpl.pdf CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kurt Mehlhorn
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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