Article

Free access

An optimal upper bound on the minimal completion time in distributed supercomputing

Authors:

Lars Lundberg,

Håkan LennerstadAuthors Info & Claims

ICS '94: Proceedings of the 8th international conference on Supercomputing

Pages 196 - 203

https://doi.org/10.1145/181181.181339

Published: 16 July 1994 Publication History

PDF eReader

Abstract

We first consider an MIMD multiprocessor configuration with n processors. A parallel program, consisting of n processes, is executed on this system—one process per processor. The program terminates when all processes are completed. Due to synchronizations, processes may be blocked waiting for events in other processes. Associated with the program is a parallel profile vector v¯, index i (1≤i≤n) in this vector indicates the percentage of the total execution time when i processes are executing.

We then consider a distributed MIMD supercomputer with k clusters, containing u processors each. The same parallel program, consisting of n processes, is executed on this system. Each process can only be executed by processors in the same cluster. Finding a schedule with minimal completion time in this case is NP-hard.

We are interested in the gain of using n processors compared to using k clusters containing u processors each. The gain is defined by the ratio between the minimal completion time using processor clusters and the completion time using a schedule with one process per processor. We present the optimal upper bound for this ratio in the form of an analytical expression in n, v¯, k and u. We also demonstrate how this result can be used when evaluating heuristic scheduling algorithms.

References

[1]

G.E. Anderson, An Ada Multitask Solution for the Sieve of Erathosthenes, ACM, Ada Letters Vol 7 September/ October 1988.

Digital Library

Google Scholar

[2]

S.H. Bokhari, Partitioning Problems in Parallel Pipelined, and Distributed Computing, IEEE Transactions on Computers, Vol. 37, No.1, January 1988, pp. 48-57.

Digital Library

Google Scholar

[3]

E.G. Coffman Jr., M. R. Garey and D. S. Johnson, An Application of Bin Packing to Multiprocessor Scheduling, SIAM Journal of Computing, Vol. 7, No. 1, February 1978, pp. 1-17.

Crossref

Google Scholar

[4]

R.L. Graham, Bounds on Multiprocessor Timing Anomalies, SIAM Journal of Applied Mathematics, 17, 2 (1969), pp 416-429.

Crossref

Google Scholar

[5]

D.K. Friesen, Tighter bounds for the multifit processor scheduling algorithm, SIAM Journal of Computing, 13 (1984), pp. 170-181.

Crossref

Google Scholar

[6]

M. Garey and D. Johnson, Computers and Intractability, W.H. Freeman and Company, 1979.

Digital Library

Google Scholar

[7]

D.S. Hochbaum and D. B. Shmoys, Using Dual Approximation Algorithms for Scheduling Problems: Theoretical and Practical Results, Journal of the ACM, Vol. 34, No. 1, 1987, pp 144-162.

Digital Library

Google Scholar

[8]

M.A. Langston, Processor scheduling with improved heuristic algorithms, Ph.D. thesis Texas University, Collage Station Texas, 1981.

Digital Library

Google Scholar

[9]

H. Lennerstad and L. Lundberg, An Optimal Execution Time Estimate of Static versus Dynamic Allocation in Multiprocessor Systems, SIAM Journal of Computing, to appear.

Digital Library

Google Scholar

[10]

L. Lundberg, Predicting the Speedup of Parallel Ada Programs, In Proceedings of the Ada Europe Conference, Amsterdam, June, 1992.

Digital Library

Google Scholar

[11]

H.S. Stone, Multiprocessor Scheduling with the Aid of Network Flow Algorithms, IEEE Transactions on Software Engineering, Vol. SE-3, No. 1. January 1977, pp. 85-93.

Google Scholar

[12]

P. Tang, P-C Yew, and C-Q Zhu, Impact of Self-Scheduling Order on Peformance of Multiprocessor systems, In 1988 International Conference on Supercomputing, St. Malo, France, July, 1988.

Digital Library

Google Scholar

Cited By

View all

Lundberg LLennerstad H(2018)Bounding the gain of changing the number of memory modules in shared memory multiprocessorsNordic Journal of Computing10.5555/640130.6401314:3(233-258)Online publication date: 21-Dec-2018
https://dl.acm.org/doi/10.5555/640130.640131
Lundberg L(2005)Bounding the minimal completion time of static mappings of multithreaded solaris programsEuro-Par'97 Parallel Processing10.1007/BFb0002849(1034-1038)Online publication date: 26-Sep-2005
https://doi.org/10.1007/BFb0002849
Lennerstad HLundberg L(2005)Combinatorics for multiprocessor scheduling optimization and other contexts in computer architectureCombinatorics and Computer Science10.1007/3-540-61576-8_94(341-347)Online publication date: 2-Jun-2005
https://doi.org/10.1007/3-540-61576-8_94
Show More Cited By

Index Terms

Recommendations

Minimizing Total Completion Time Subject to Job Release Dates and Preemption Penalties

Extensive research has been devoted to preemptive scheduling. However, little attention has been paid to problems where a certain time penalty must be incurred if preemption is allowed. In this paper, we consider the single-machine scheduling problem of ...
Minimizing Total Completion Time on Parallel Machines with Deadline Constraints

Consider n independent jobs and m identical machines in parallel. Job j has a processing time p_j and a deadline $\bar{d}_j$. It must complete its processing before or at its deadline. All jobs are available for processing at time t=0 and preemptions are ...
Preemptive Weighted Completion Time Scheduling of Parallel Jobs

We present a new algorithm for the preemptive offline scheduling of independent jobs on a system consisting of m identical machines. The jobs can be parallel; that is, they may need the concurrent availability of several machines for their execution. To ...

Comments

Information & Contributors

Information

Published In

ICS '94: Proceedings of the 8th international conference on Supercomputing

July 1994

452 pages

ISBN:0897916654

DOI:10.1145/181181

Chairmen:
John Gurd
Univ. of Manchester, Manchester, UK
,
William Jalby
Univ. de Versailles, France

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 16 July 1994

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Conference

ICS94

Sponsor:

SIGARCH

ICS94: International Conference on Supercomputing '94

July 11 - 15, 1994

Manchester, England

Acceptance Rates

ICS '94 Paper Acceptance Rate 45 of 114 submissions, 39%;

Overall Acceptance Rate 629 of 2,180 submissions, 29%

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

11
Total Citations
View Citations
185
Total Downloads

Downloads (Last 12 months)24
Downloads (Last 6 weeks)8

Reflects downloads up to 12 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Lundberg LLennerstad H(2018)Bounding the gain of changing the number of memory modules in shared memory multiprocessorsNordic Journal of Computing10.5555/640130.6401314:3(233-258)Online publication date: 21-Dec-2018
https://dl.acm.org/doi/10.5555/640130.640131
Lundberg L(2005)Bounding the minimal completion time of static mappings of multithreaded solaris programsEuro-Par'97 Parallel Processing10.1007/BFb0002849(1034-1038)Online publication date: 26-Sep-2005
https://doi.org/10.1007/BFb0002849
Lennerstad HLundberg L(2005)Combinatorics for multiprocessor scheduling optimization and other contexts in computer architectureCombinatorics and Computer Science10.1007/3-540-61576-8_94(341-347)Online publication date: 2-Jun-2005
https://doi.org/10.1007/3-540-61576-8_94
Lennerstad HLundberg L(2003)Chapter 7: Memory modulesElectronic Notes in Discrete Mathematics10.1016/S1571-0653(04)80606-114(131-154)Online publication date: May-2003
https://doi.org/10.1016/S1571-0653(04)80606-1
Lennerstad HLundberg L(2003)Chapter 6: Parallel program scheduling using test executionsElectronic Notes in Discrete Mathematics10.1016/S1571-0653(04)80605-X14(113-130)Online publication date: May-2003
https://doi.org/10.1016/S1571-0653(04)80605-X
Lennerstad HLundberg L(2003)Chapter 5: Parallel program scheduling with given parallel profileElectronic Notes in Discrete Mathematics10.1016/S1571-0653(04)80604-814(97-111)Online publication date: May-2003
https://doi.org/10.1016/S1571-0653(04)80604-8
Lennerstad HLundberg L(2003)Chapter 4: General parallel program schedulingElectronic Notes in Discrete Mathematics10.1016/S1571-0653(04)80603-614(67-96)Online publication date: May-2003
https://doi.org/10.1016/S1571-0653(04)80603-6
Lennerstad HLundberg L(2003)Chapter 3: Present approach to scheduling analysisElectronic Notes in Discrete Mathematics10.1016/S1571-0653(04)80602-414(35-63)Online publication date: May-2003
https://doi.org/10.1016/S1571-0653(04)80602-4
Lundberg LBroberg MKlonowska K(2003)Evaluating Heuristic Scheduling Algorithms for High Performance Parallel ProcessingHigh Performance Computing10.1007/978-3-540-39707-6_12(160-173)Online publication date: 2003
https://doi.org/10.1007/978-3-540-39707-6_12
Lundberg LLennerstad H(1998)Using Recorded Values for Bounding the Minimum Completion Time in MultiprocessorsIEEE Transactions on Parallel and Distributed Systems10.1109/71.6678969:4(346-358)Online publication date: 1-Apr-1998
https://dl.acm.org/doi/10.1109/71.667896
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

Minimizing Total Completion Time Subject to Job Release Dates and Preemption Penalties

Minimizing Total Completion Time on Parallel Machines with Deadline Constraints

Preemptive Weighted Completion Time Scheduling of Parallel Jobs

Comments

Published In

Sponsors

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Conference

Acceptance Rates

Other Metrics

Article Metrics

Other Metrics

Cited By

PDF

eReader

Login options

Full Access

Abstract

References

Cited By

Index Terms

Recommendations

Minimizing Total Completion Time Subject to Job Release Dates and Preemption Penalties

Minimizing Total Completion Time on Parallel Machines with Deadline Constraints

Preemptive Weighted Completion Time Scheduling of Parallel Jobs

Comments

Information

Published In

Sponsors

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Conference

Acceptance Rates

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations