research-article

A Partitioning Strategy for Nonuniform Problems on Multiprocessors

Authors:

S. H. BokhariAuthors Info & Claims

IEEE Transactions on Computers, Volume 36, Issue 5

Pages 570 - 580

https://doi.org/10.1109/TC.1987.1676942

Published: 01 May 1987 Publication History

Abstract

We consider the partitioning of a problem on a domain with unequal work estimates in different subdomains in a way that balances the workload across multiple processors. Such a problem arises for example in solving partial differential equations using an adaptive method that places extra grid points in certain subregions of the domain. We use a binary decomposition of the domain to partition it into rectangles requiring equal computational effort. We then study the communication costs of mapping this partitioning onto different multiprocessors: a mesh- connected array, a tree machine, and a hypercube. The communication cost expressions can be used to determine the optimal depth of the above partitioning.

References

[1]

L. Adams and H. Jordan, "Is SOR color-blind?," ICASE Rep. 84-14, May 1984.

[2]

S. Baden, "Dynamic load balancing of a vortex calculation running on multiprocessors," Ph.D. dissertation, Univ. California, Berkeley, in preparation.

[3]

D. Bai and A. Brandt, "Local mesh refinement multilevel techniques" Weizmann Instit. Sci. Rep. 1984.

[4]

R. Bank and A. Sherman, "Algorithmic aspects of the multi-level solution of finite element equations," CNA-144, Center Numer. Anal., Univ. Texas, Austin, Oct. 1978.

[5]

J. Bentley, "Multidimensional divide-and-conquer," Comm. ACM, vol. 23, 1980.

Digital Library

[6]

M. Berger and A. Jameson, "Automatic adaptive mesh refinement for the Euler equations," AIAA J., vol. 23, 1985.

[7]

M. Berger and J. Oliger, "Adaptive mesh refinement for hyperbolic partial differential equations," J. Comput. Phys., vol. 53, 1984.

[8]

S. Bokhari, "'On the mapping problem," IEEE Trans. Comput., vol. C-30, no. 3, 1981.

Digital Library

[9]

N. Deo, Graph Theory with Applications to Engineering and Computer Science. Englewood Cliffs, NJ: Prentice-Hall, 1974.

Digital Library

[10]

D. Gannon and J. Van Rosendale, "Parallel architectures for iterative methods on adaptive block structured grids," in Elliptic Problem Solvers II, G. Birkhoff and A. Schoenstadt, Ed. New York: Academic, 1984.

[11]

A. Gottlieb, R. Grishman, C. Kruskal, K. McAuliffe, L. Rudolph, and M. Snir, "The NYU Ultracomputer--Designing an MIMD shared memory parallel machine," IEEE Trans. Comput., vol. C-32, no. 2, 1983.

Digital Library

[12]

W. Gropp, "Local uniform mesh refinement on loosely-coupled parallel processors," Yale Rep. DCS/RR-352, Dec. 1984.

[13]

H. Jordan, "A special purpose architecture for finite element analysis," in Proc. 1978 Conf. Parallel Processing, Aug. 1978.

[14]

S. McCormick and J. Thomas, "The fast adaptive composite grid method for elliptic equations," Math. Comput., 1986.

Digital Library

[15]

C. Papadimitriou and J. Ullman, "A communication-time tradeoff," in Proc. 25th Annu. Symp. Foundations Comput. Sci., 1984.

Digital Library

[16]

G. Pfister et al., "The IBM research parallel processor prototype (RP3): Introduction and architecture," in Proc. 1985 Int. Conf. Parallel Processing, 1985.

[17]

J. Van Rosendale, "Rapid solution of finite element equations on locally refined grids by multi-level methods," Ph.D. dissertation, Univ. Illinois, May 1980.

Digital Library

[18]

A. Waksman, "A permutation network," J. Ass. Comput. Mach., vol. 15, no. 1, 1968.

Digital Library

[19]

P. Zave and W. Rheinboldt, "Design of an adaptive, parallel finite-element system," ACM Trans. Math. Software, vol. 5, 1979.

Digital Library

Cited By

Çatalyürek ÜDevine KFaraj MGottesbüren LHeuer TMeyerhenke HSanders PSchlag SSchulz CSeemaier DWagner D(2023)More Recent Advances in (Hyper)Graph PartitioningACM Computing Surveys10.1145/357180855:12(1-38)Online publication date: 2-Mar-2023
https://dl.acm.org/doi/10.1145/3571808
Qiu YReeve SLi MYang YSlattery SJiang C(2023)A Sparse Distributed Gigascale Resolution Material Point MethodACM Transactions on Graphics10.1145/357016042:2(1-21)Online publication date: 16-Jan-2023
https://dl.acm.org/doi/10.1145/3570160
Xu JGuo HShen HRaj MWurster SPeterka T(2023)Reinforcement Learning for Load-Balanced Parallel Particle TracingIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.314874529:6(3052-3066)Online publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1109/TVCG.2022.3148745
Show More Cited By

Index Terms

A Partitioning Strategy for Nonuniform Problems on Multiprocessors

Recommendations

The Banyan-Hypercube Networks

The authors introduce a family of networks that are a synthesis of banyans and hypercubes and are called the banyan-hypercubes (BH). They combine the advantageous features of banyans and hypercubes and thus have better communication capabilities.The ...
Automatic Domain Partitioning in Three Dimensions

The problem of automatically decomposing a mesh contained in a three-dimensional domain into p pieces is considered. This problem arises in the context of domain-decomposition solvers for partial differential equations (PDEs). Finite-difference meshes ...
Partitioning Algorithms Analysis for Heterogeneous NoC Based MPSoC
SBESC '12: Proceedings of the 2012 Brazilian Symposium on Computing System Engineering

Several new applications have high complexity degree, requiring high processing rate and memory usage. Multiprocessor System-on-Chip (MPSoC) is a promising architecture to fulfill these requirements, due to its high parallelism that enables several ...

Comments

Information & Contributors

Information

Published In

cover image IEEE Transactions on Computers

IEEE Transactions on Computers Volume 36, Issue 5

May 1987

134 pages

ISSN:0018-9340

Editor:
Bruce D. Shriver

Issue’s Table of Contents

Copyright © 1987.

Publisher

IEEE Computer Society

United States

Publication History

Published: 01 May 1987

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

125
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 27 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Çatalyürek ÜDevine KFaraj MGottesbüren LHeuer TMeyerhenke HSanders PSchlag SSchulz CSeemaier DWagner D(2023)More Recent Advances in (Hyper)Graph PartitioningACM Computing Surveys10.1145/357180855:12(1-38)Online publication date: 2-Mar-2023
https://dl.acm.org/doi/10.1145/3571808
Qiu YReeve SLi MYang YSlattery SJiang C(2023)A Sparse Distributed Gigascale Resolution Material Point MethodACM Transactions on Graphics10.1145/357016042:2(1-21)Online publication date: 16-Jan-2023
https://dl.acm.org/doi/10.1145/3570160
Xu JGuo HShen HRaj MWurster SPeterka T(2023)Reinforcement Learning for Load-Balanced Parallel Particle TracingIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.314874529:6(3052-3066)Online publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1109/TVCG.2022.3148745
Yaşar ABalin MAn XSancak KÇatalyürek Ü(2022)On Symmetric Rectilinear PartitioningACM Journal of Experimental Algorithmics10.1145/352375027(1-26)Online publication date: 31-Aug-2022
https://dl.acm.org/doi/10.1145/3523750
Verkaik JHughes Jvan Walsum POude Essink GLin HBierkens M(2021)Distributed memory parallel groundwater modeling for the Netherlands Hydrological InstrumentEnvironmental Modelling & Software10.1016/j.envsoft.2021.105092143:COnline publication date: 1-Sep-2021
https://dl.acm.org/doi/10.1016/j.envsoft.2021.105092
Barrios Molano HSepehrnoori K(2020)Development of a framework for parallel reservoir simulationInternational Journal of High Performance Computing Applications10.1177/109434201879271033:4(632-650)Online publication date: 17-Jun-2020
https://dl.acm.org/doi/10.1177/1094342018792710
Shan XShi XSong YZhang MSong B(2020)Dynamic Partition of Large Graphs Combining Local Nodes Exchange with Directed Dynamic MaintenanceWeb Information Systems and Applications10.1007/978-3-030-60029-7_40(441-453)Online publication date: 23-Sep-2020
https://dl.acm.org/doi/10.1007/978-3-030-60029-7_40
(2019)DBSCAN-PSMInternational Journal of High Performance Computing and Networking10.5555/3337625.333763113:4(417-426)Online publication date: 1-Jan-2019
https://dl.acm.org/doi/10.5555/3337625.3337631
Wang HChandramowlishwaran AEigenmann RDing CMcKee S(2019)Multi-criteria partitioning of multi-block structured gridsProceedings of the ACM International Conference on Supercomputing10.1145/3330345.3330369(261-271)Online publication date: 26-Jun-2019
https://dl.acm.org/doi/10.1145/3330345.3330369
Deveci MDevine KPedretti KTaylor MRajamanickam SÇatalyürek Ü(2019)Geometric Mapping of Tasks to Processors on Parallel Computers with Mesh or Torus NetworksIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2019.290004330:9(2018-2032)Online publication date: 1-Sep-2019
https://dl.acm.org/doi/10.1109/TPDS.2019.2900043
Show More Cited By

View Options

View options

Figures

Tables

Media

View Issue’s Table of Contents