Skip to main content
Springer Nature Link
Log in

Bounds on the Geometric Mean of Arc Lengths for Bounded-Degree Planar Graphs

  • Conference paper
Frontiers in Algorithmics (FAW 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5598))

Included in the following conference series:

  • 1014 Accesses

Abstract

Data access time becomes the main bottleneck in applications dealing with large-scale graphs. Cache-oblivious layouts, constructed to minimize the geometric mean of arc lengths of graphs, have been adapted to reduce data access time during random walks on graphs. In this paper, we present a constant factor approximation algorithm for the Minimum Geometric Mean Layout (MGML) problem for bounded-degree planar graphs. We also derive an upper bound for any layout of the MGML problem. To the best of our knowledge, these are the first results for the MGML problem with bounded-degree planar graphs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Yoon, S.E., Lindstrom, P., Pascucci, V., Manocha, D.: Cache-Oblivious Mesh Layouts. ACM Transactions on Graphics (SIGGRAPH) 24(3), 886–893 (2005)

    Article  Google Scholar 

  2. Eubank, S., Kumar, V.S.A., Marathe, M.V., Srinivasan, A., Wang, N.: Structural and algorithmic aspects of massive social networks. In: SODA 2004: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, Philadelphia, PA, USA, Society for Industrial and Applied Mathematics, pp. 718–727 (2004)

    Google Scholar 

  3. Hennessy, J.L., Patterson, D.A., Goldberg, D.: Computer Architecture, A Quantitative Approach. Morgan Kaufmann, San Francisco (2007)

    MATH  Google Scholar 

  4. Yoon, S.E., Lindstrom, P.: Mesh layouts for block-based caches. IEEE Transactions on Visualization and Computer Graphics (Proceedings Visualization) 12(5), 1213–1220 (2006)

    Article  Google Scholar 

  5. Garey, M.R., Johnson, D.S., Stockmeyer, L.: Some simplified np-complete problems. In: STOC 1974: Proceedings of the sixth annual ACM symposium on Theory of computing, pp. 47–63. ACM, New York (1974)

    Chapter  Google Scholar 

  6. Papadimitriou, C.H.: The NP-completeness of the bandwidth minimization problem 16(3), 263–270 (1976)

    Google Scholar 

  7. Gavril, F.: Some np-complete problems on graphs. In: 11th Conference on Information Science and Systems, pp. 91–95 (1977)

    Google Scholar 

  8. Hansen, M.: Approximation algorithms for geometric embeddings in the plane with applications to parallel processing problems. In: 30th Annual Symposium on Foundations of Computer Science, October-November 1, 1989, pp. 604–609 (1989)

    Google Scholar 

  9. Feige, U., Lee, J.R.: An improved approximation ratio for the minimum linear arrangement problem. Inf. Process. Lett. 101(1), 26–29 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Goldberg, M.K., Klipker, I.A.: An algorithm for minimal numeration of tree vertices. Sakharth. SSR Mecn. Akad. Moambe 81(3), 553–556 (1976) (in Russian)

    MathSciNet  MATH  Google Scholar 

  11. Muradyan, D.O., Piliposyan, T.E.: Minimal numberings of a rectangular lattice. Akad. Nauk. Armyan. SRR 1(70), 21–27 (1980) (in Russian)

    MathSciNet  MATH  Google Scholar 

  12. Garey, M.R., Graham, R.L., Johnson, D.S., Knuth, D.E.: Complexity results for bandwidth minimization 34(3), 477–495 (1978)

    Google Scholar 

  13. Díaz, J., Penrose, M.D., Petit, J., Serna, M.: Approximating layout problems on random geometric graphs. Journal of Algorithms 39 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. Díaz, J., Petit, J., Serna, M.: A survey of graph layout problems. ACM Comput. Surv. 34(3), 313–356 (2002)

    Article  Google Scholar 

  15. Sagan, H.: Space-Filling Curves. Springer, Heidelberg (1994)

    Book  MATH  Google Scholar 

  16. Velho, L., de Miranda Gomes, J.: Digital halftoning with space filling curves. In: ACM SIGGRAPH, pp. 81–90 (1991)

    Google Scholar 

  17. Lindstrom, P., Pascucci, V.: Visualization of large terrains made easy. IEEE Visualization, 363–370 (2001)

    Google Scholar 

  18. Pascucci, V., Frank, R.J.: Global static indexing for real-time exploration of very large regular grids. In: Supercomputing (2001)

    Google Scholar 

  19. Gotsman, C., Lindenbaum, M.: On the metric properties of discrete space-filling curves. IEEE Transactions on Image Processing 5(5), 794–797 (1996)

    Article  Google Scholar 

  20. Wierum, J.M.: Logarithmic path-length in space-filling curves. In: 14th Canadian Conference on Computational Geometry, pp. 22–26 (2002)

    Google Scholar 

  21. Aggarwal, A., Vitter, J.S.: The input/output complexity of sorting and related problems. Communications of ACM 31, 1116–1127 (1988)

    Article  MathSciNet  Google Scholar 

  22. Yoon, S.E., Manocha, D.: Cache-efficient layouts of bounding volume hierarchies. Computer Graphics Forum (Eurographics) 25(3), 507–516 (2006)

    Article  Google Scholar 

  23. van Emde Boas, P.: Preserving order in a forest in less than logarithmic time and linear space. Inf. Process. Lett. 6, 80–82 (1977)

    Article  MATH  Google Scholar 

  24. Diks, K., Djidjev, H., Sýkora, O., Vrto, I.: Edge separators of planar and outerplanar graphs with applications. J. Algorithms 14(2), 258–279 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  25. Lipton, R.J., Tarjan, R.E.: A separator theorem for planar graphs. SIAM Journal on Applied Mathematics 36(2), 177–189 (1979)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Computer Science, Korea Advanced Institute of Science and Technology (KAIST), Republic of Korea

    Mohammad Khairul Hasan, Sung-Eui Yoon & Kyung-Yong Chwa

Authors
  1. Mohammad Khairul Hasan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sung-Eui Yoon
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kyung-Yong Chwa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science,, City University of Hong Kong, No. 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, China

    Xiaotie Deng

  2. Computer Science Department, Cornell University, 5144 Upson Hall, NY 14853, Ithaca, USA

    John E. Hopcroft

  3. Provincial Key Laboratory of High-Performance Computing, Jiangxi Normal University, 330027, Nanchang, China

    Jinyun Xue

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hasan, M.K., Yoon, SE., Chwa, KY. (2009). Bounds on the Geometric Mean of Arc Lengths for Bounded-Degree Planar Graphs. In: Deng, X., Hopcroft, J.E., Xue, J. (eds) Frontiers in Algorithmics. FAW 2009. Lecture Notes in Computer Science, vol 5598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02270-8_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02270-8_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02269-2

  • Online ISBN: 978-3-642-02270-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics