[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content

Scheduling Dynamic Graphs

  • Conference paper
  • First Online:
STACS 99 (STACS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1563))

Included in the following conference series:

  • 1648 Accesses

Abstract

In parallel and distributed computing scheduling low level tasks on the available hardware is a fundamental problem. Traditionally, one has assumed that the set of tasks to be executed is known beforehand. Then the scheduling constraints are given by a precedence graph. Nodes represent the elementary tasks and edges the dependencies among tasks. This static approach is not appropriate in situations where the set of tasks is not known exactly in advance, for example, when different options how to continue a program may be granted.

In this paper a new model for parallel and distributed programs, the dynamic process graph, will be introduced, which represents all possible executions of a program in a compact way. The size of this representation is small - in many cases only logarithmically with respect to the size of any execution. An important feature of our model is that the encoded executions are directed acyclic graphs having a ”regular” structure that is typical of parallel programs. Dynamic process graphs embed constructors for parallel programs, synchronization mechanisms as well as conditional branches. With respect to such a compact representation we investigate the complexity of different aspects of the scheduling problem: the question whether a legal schedule exists at all and how to find an optimal schedule. Our analysis takes into account communication delays between processors exchanging data. Precise characterization of the computational complexity of various variants of this compact scheduling problem will be given in this paper. The results range from easy, that is \( \mathcal{N}\mathcal{L}\mathcal{O}\mathcal{G}\mathcal{S}\mathcal{P}\mathcal{A}\mathcal{C}\mathcal{E} \) -complete, to very hard, namely \( \mathcal{N}\mathcal{E}\mathcal{X}\mathcal{P}\mathcal{T}\mathcal{I}\mathcal{M}\mathcal{E} \) -complete.

Supported by DFG Research Grant Re 672/2.

On leave of Instytut Informatyki, Uniwersytet Wrocławski, Wrocław, Poland.

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

Access this chapter

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
GBP 19.95
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
GBP 71.50
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
GBP 89.99
Price includes VAT (United Kingdom)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

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. A. Burns, Programming in Occam 2, Addison-Wesley Publishing Company, 1988.

    Google Scholar 

  2. H. El-Rewini and H. H. Ali, Static Scheduling of Conditional Branches in Parallel Programs, J. Par. Distrib. Comput. 24, 1995, 41–54.

    Article  Google Scholar 

  3. H. Galperin, A. Wigderson, Succinct Representations of Graphs, Information and Control, 56, 1983, 183–198.

    MATH  MathSciNet  Google Scholar 

  4. S. Ha, E. Lee, Compile-time Scheduling and Assignment of Data-flow Program Graphs with Data-dependent Iteration, IEEE Trans. Computers 40, 1991, 1225–1238.

    Article  Google Scholar 

  5. A. Jakoby, M. Liśkiewicz, R. Reischuk, Scheduling Dynamic Graphs, Technischer Bericht, Institut für Theoretische Informatik, Med. Universität zu Lübeck, 1998.

    Google Scholar 

  6. A. Jakoby and R. Reischuk, The Complexity of Scheduling Problems with Communication Delay for Trees, Proc. 3. SWAT, 1992, 165–177.

    Google Scholar 

  7. H. Jung, L. Kirousis, P. Spirakis, Lower Bounds and Efficient Algorithms for Multiprocessor scheduling of DAG s with Communication Delays, Proc. 1. SPAA, 1989, 254–264.

    Google Scholar 

  8. R. Kieckhafer, Fault-Tolerant Real-Time Task Scheduling in the MAFT Distributed System, Proc. 22. Hawaii Int. Conf. on System Science, 1989, 145–151.

    Google Scholar 

  9. R. Kieckhafer, C. Walter, A. Finn, P. Thambidurai, The MAFT Architecture For Distributed Fault-Tolerance, IEEE Trans. Computers, April 1988, 398–405.

    Google Scholar 

  10. T. Lengauer, K. Wagner, The Correlation between the Complexities of the Nonhierarchical and Hierarchical Versions of Graph Problems, J. CSS 44, 1992, 63–93.

    MATH  Google Scholar 

  11. C. Papadimitriou and M. Yannakakis, A Note on Succinct Representations of Graphs, Information and Control, 71, 1986, 181–185.

    Article  MATH  MathSciNet  Google Scholar 

  12. C. Papadimitriou and M. Yannakakis, Towards an Architecture-Independent Analysis of Parallel Algorithms, Proc. 20. STOC, 1988, 510–513, see also SIAM J. Comput. 19, 1990, 322–328.

    Google Scholar 

  13. B. Veltman, Multiprocessor Scheduling with Communication Delays, Ph.D. Thesis, University of Technology Eindhoven, Department of Computer Science, Eindhoven, The Netherlands, 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jakoby, A., Liśkiewicz, M., Reischuk, R. (1999). Scheduling Dynamic Graphs. In: Meinel, C., Tison, S. (eds) STACS 99. STACS 1999. Lecture Notes in Computer Science, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49116-3_36

Download citation

  • DOI: https://doi.org/10.1007/3-540-49116-3_36

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65691-3

  • Online ISBN: 978-3-540-49116-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics