Computing the Diameter of 17-Pancake Graph Using a PC Cluster

  • Shogo Asai
  • Yuusuke Kounoike
  • Yuji Shinano
  • Keiichi Kaneko
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4128)


An n-pancake graph is a graph whose vertices are the permutations of n symbols and each pair of vertices are connected with an edge if and only if the corresponding permutations can be transitive by a prefix reversal. Since the n-pancake graph has n! vertices, it is known to be a hard problem to compute its diameter by using an algorithm with the polynomial order of the number of vertices. Fundamental approaches of the diameter computation have been proposed. However, the computation of the diameter of 15-pancake graph has been the limit in practice. In order to compute the diameters of the larger pancake graphs, it is indispensable to establish a sustainable parallel system with enough scalability. Therefore, in this study, we have proposed an improved algorithm to compute the diameter and have developed a sustainable parallel system with the Condor/MW framework, and computed the diameters of 16- and 17-pancake graphs by using PC clusters.


Distance Computation Child Problem Operation Sequence Previous Implementation Parallel Computing System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dweighter, H.: Amer. Math. Monthly 82, 1010 (1975)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Akl, S.G., Qiu, K.: Fundamental algorithms for the star and pancake interconnection networks with applications to computational geometry. Networks 23, 215–225 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bass, D.W., Sudborough, I.H.: Pancake problems with restricted prefix reversals and some corresponding cayley networks. Journal of Parallel and Distributed Computing 63(3), 327–336 (2003)zbMATHCrossRefGoogle Scholar
  4. 4.
    Berthomé, P., Ferreira, A., Perennes, S.: Optimal information dissemination in star and pancake networks. IEEE Transactions on Parallel and Distributed Systems 7(12), 1292–1300 (1996)CrossRefGoogle Scholar
  5. 5.
    Kumar, V., Grama, A., Gupta, A., Karypis, G.: Introduction to Parallel Computing: Design and Analysis of Algorithms. Benjaming/Cummings (1994)Google Scholar
  6. 6.
    Quinn, M.J.: Parallel Computing: Theory and Practice, 2nd edn. McGraw-Hill, New York (1994)Google Scholar
  7. 7.
    Kounoike, Y., Kaneko, K., Shinano, Y.: Computing the diameters of 14- and 15-pancake graphs. In: Proceedings of the International Symposium on Parallel Architectures, Algorithms and Networks, pp. 490–495 (2005)Google Scholar
  8. 8.
    Heydari, M.H., Sudborough, I.H.: On the diameter of the pancake network. J. Algorithms 25(1), 67–94 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    AT&T: On-Line Encyclopedia of Integer Sequences
  10. 10.
    MW project: MW Homepage,
  11. 11.
    Condor Team: Condor Project Homepage,

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Shogo Asai
    • 1
  • Yuusuke Kounoike
    • 1
  • Yuji Shinano
    • 1
  • Keiichi Kaneko
    • 1
  1. 1.Tokyo University of Agriculture and TechnologyTokyoJapan

Personalised recommendations