Abstract
We consider the problem of mapping an array onto a mesh of processors in such a way that locality is preserved. When the computational work associated with the array is distributed in an unstructured way the generalized block distribution has been recognized as an efficient way of achieving an even load balance while at the same time imposing a simple communication pattern.
In this paper we consider the problem of computing an optimal generalized block distribution. We show that this problem is NP-complete even for very simple cost functions. We also classify a number of variants of the general problem.
Preview
Unable to display preview. Download preview PDF.
References
B. Chapman, P. Mehrotra, and H. Zima, Programming in Vienna Fortran, Sci. Prog., 1 (1992), pp. 31–50.
-, High performance Fortran languages: Advanced applications and their implementation, Future Generation Computer Systems, (1995), pp. 401–407.
-, Extending HPF for advanced data parallel applications, IEEE Trans. Par. Dist. Syst., (Fall 1994), pp. 59–70.
G. Fox, M. Johnson, G. Lyzenga, S. Otto, J. Salmon, and D. Walker, Solving Problems on Concurrent Processors, vol. 1, Prentice-Hall, Englewood Cliffs, NJ, 1988.
M. R. Garey and D. S. Johnson, Computers and Intractability, Freeman, 1979.
M. Halldorsson and F. Manne. Private communications.
High Performance Fortran Forum, High performance language specification. Version 1.0, Sci. Prog., 1–2 (1993), pp. 1–170.
High Performance Fortran Forum Home Page. http://www.crpc.rice.edu/HPFF/home.html.
F. Manne, Load Balancing in Parallel Sparse Matrix Computations, PhD thesis, University of Bergen, Norway, 1993.
F. Manne and T. Sørevik, Structured partitioning of arrays, Tech. Rep. CS-96-119, Department of Informatics, University of Bergen, Norway, 1996.
B. Olstad and F. Manne, Efficient partitioning of sequences, IEEE Trans. Comput., 44 (1995), pp. 1322–1326.
M. Ujaldon, S. D. Sharma, J. Saltz, and E. Zapata, Run-time techniques for parallelizing sparse matrix problems, in Proceedings of 1995 Workshop on Irregular Problems, 1995.
M. Ujaldon, E. L. Zapata, B. M. Chapman, and H. P. Zima, Vienna-Fortran/HPF extensions for sparse and irregular problems and their compilation. Submitted to IEEE Trans. Par. Dist. Syst.
H. Zima, H. Bast, and M. Gerndt, Superb: A tool for semi-automatic MIMD/SIMD parallelization, Parallel Comput., (1986), pp. 1–18.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Grigni, M., Manne, F. (1996). On the complexity of the generalized block distribution. In: Ferreira, A., Rolim, J., Saad, Y., Yang, T. (eds) Parallel Algorithms for Irregularly Structured Problems. IRREGULAR 1996. Lecture Notes in Computer Science, vol 1117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030123
Download citation
DOI: https://doi.org/10.1007/BFb0030123
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61549-1
Online ISBN: 978-3-540-68808-2
eBook Packages: Springer Book Archive