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Relations Between Two Common Types of Rectangular Tilings

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Algorithms and Computation (ISAAC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4288))

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Abstract

Partitioning a multi-dimensional data set (array) into rectangular regions subject to some constraints (error measures) is an important problem arising from applications in parallel computing, databases, VLSI design, and so on. In this paper, we consider two most common types of partitioning used in practice: the Arbitrary partitioning and (p×p) partitioning, and study their relationships under three widely used error metrics: Max-Sum, Sum-SVar and Sum-SLift.

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References

  1. Anily, S., Federgruen, A.: Structured partitioning problems. Operations Research, 130–149 (1991)

    Google Scholar 

  2. Berman, P., Dasgupta, B., Muthukrishnan, S.: Exact size of binary space partitionings and improved rectangle tiling algorithms. SIAM J. Discrete Math. 15(2), 252–267 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Berman, P., DasGupta, B., Muthukrishnan, S., Ramaswami, S.: Efficient approximation algorithms for tiling and packing problems with rectangles. J. Algorithms 41(2), 443–470 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bokhari, S.: Partitioning problems in paralle, pipelined, and distributed computing. IEEE Transactions on Computers 37, 38–57 (1988)

    Article  MathSciNet  Google Scholar 

  5. Fox, G., Johnson, M., Lyzenga, G., Otto, S., Salmon, J., Walker, D.: Solving problems on concurrent processors, vol. 1. Prentice-Hall, Englewood Cliffs (1998)

    Google Scholar 

  6. Grigni, M., Manne, F.: On the complexity of the generalized block distribution. In: Saad, Y., Yang, T., Ferreira, A., Rolim, J.D.P. (eds.) IRREGULAR 1996. LNCS, vol. 1117, pp. 319–326. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  7. Khanna, S., Muthukrishnan, S., Paterson, M.: On approximating rectangle tiling and packing. In: SODA 1998: Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms, pp. 384–393 (1998)

    Google Scholar 

  8. Khanna, S., Muthukrishnan, S., Skiena, S.: Efficient array partitioning. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256, pp. 616–626. Springer, Heidelberg (1997)

    Google Scholar 

  9. Lackey, D.E., Zuchowski, P.S., Bednar, T.R., Stout, D.W., Gould, S.W., Cohn, J.M.: Managing power and performance for system-on-chip designs using voltage islands. In: Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design table of contents, pp. 195–202 (2002)

    Google Scholar 

  10. Lorys, K., Paluch, K.E.: New approximation algorithm for RTILE problem. Theor. Comput. Sci. 2-3(303), 517–537 (2003)

    Article  MathSciNet  Google Scholar 

  11. Manne, F.: Load Balancing in Parallel Sparse Matrix Computations. PhD thesis, Dept. of Informatics, Univ. of Bergen, Norway (1993)

    Google Scholar 

  12. Manne, F., Sorevik, T.: Partitioning an array onto a mesh of processors. In: Workshop on Applied Parallel Computing in Industrial Problems (1996)

    Google Scholar 

  13. Muthukrishnan, S., Poosala, V., Suel, T.: On rectangular partitionings in two dimensions: Algorithms, complexity, and applications. In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 236–256. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  14. Muthukrishnan, S., Suel, T.: Approximation algorithms for array partitioning problems. Journal of Algorithms 54, 85–104 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Poosala, V.: Histogram-based estimation techniques in databases. PhD thesis, Univ. of Wisconsin-Madison (1997)

    Google Scholar 

  16. Sharp, J.P.: Tiling multi-dimensional arrays. In: International Symposium on Fundamentals of Computation Theory, pp. 500–511 (1999)

    Google Scholar 

  17. Smith, A., Suri, S.: Rectangular tiling in multi-dimensional arrays. In: ACM/SIAM Symposium on Discrete Algorithms (SODA), pp. 786–794 (1999)

    Google Scholar 

  18. Wu, H., Liu, I., Wong, M.D.F., Wang, Y.: Post-placement voltage island generation under performance requirement. In: IEEE/ACM International Conference on Computer-Aided Design (ICCAD), pp. 309–316 (2005)

    Google Scholar 

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Wang, Y. (2006). Relations Between Two Common Types of Rectangular Tilings. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_21

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  • DOI: https://doi.org/10.1007/11940128_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49694-6

  • Online ISBN: 978-3-540-49696-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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