Advertisement

Periodic and non-periodic min-max equations

  • Uwe Schwiegelshohn
  • Lothar Thiele
Session 9: Algorithms II
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1256)

Abstract

In this paper we address min-max equations for periodic and non-periodic problems. In the non-periodic case a simple algorithm is presented to determine whether a graph has a potential satisfying the min-max equations. This method can also be used to solve a more general quasi periodic min-max problem on periodic graphs. Also some results regarding the uniqueness of solutions in the latter case are given.

Keywords

Static Graph Dynamic Graph Cycle Graph Discrete Event Dynamic System Periodic Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ahuja, R. K., Magnanti, T. L., and Orlin, J. Network Flows. Prentice Hall, 1993.Google Scholar
  2. 2.
    Baccelli, F., Cohen, G., Olsder, G., and Quadrat, J.-P.Synchronization and Linearity. John Wiley, Sons, New York, 1992.Google Scholar
  3. 3.
    Backes, W., Schwiegelshohn, U., and Thiele, L. Analysis of free schedule in periodic graphs. In 4th Annual ACM Symposium on Parallel Algorithms and Architectures, San Diego, CA, USA, June 1992, pp. 333–342.Google Scholar
  4. 4.
    Cohen, G., Dubois, D., Quadrat, J. P., and Viot, M. A linear-systemtheoretic view of discrete-event processes and its use for performance evaluation in manufacturing. IEEE Transactions on Automatic Control AC-30, No. 3, March 1985, 210–220.CrossRefGoogle Scholar
  5. 5.
    Cunninghame-Green, R. Describing industrial processes and approximating their steady-state behaviour. Opt. Res. Quart. 13, 1962, 95–100.Google Scholar
  6. 6.
    Gunawardena, J. Timing analysis of digital circuits and the theory of min-max functions. In TAU'93, ACM International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems, September 1993.Google Scholar
  7. 7.
    Gunawardena, J. Min-max functions. Tech. Rep. to be published in Discrete Event Dynamic Systems, Department of Computer Science, Stanford University, Stanford, CA 94305, USA, March 1994.Google Scholar
  8. 8.
    Karp, R. A characterization of the minimum cycle mean in a digraph. Discrete Mathematics 23, 1978, 309–311.Google Scholar
  9. 9.
    Kosaraju, S. R., and Sullivan, G. F. Detecting cycles in dynamic graphs in polynomial time. In 20th Annual ACM Symposium on Theory of Computing, 1988, pp. 398–406.Google Scholar
  10. 10.
    Lawler, E. Optimal cycles in doubly weighted directed linear graphs. In Thèorie des Graphes, 1966, P. Rosenstiehl, Ed., pp. 209–213.Google Scholar
  11. 11.
    McMillan, K., and Dill, D. Algorithms for interface timing verification. In IEEE Int. Conference on Computer Design, 1992, pp. 48–51Google Scholar
  12. 12.
    Olsder, G. Eigenvalues of dynamic max-min systems. Discrete Event Dynamic Systems: Theory and Applications, 1991, 1:177–207.CrossRefGoogle Scholar
  13. 13.
    Olsder, G. Analyse de systèmes min-max. Tech. Rep. 1904, Institute National de Recherche en Informatique et en Automatique, May 1993.Google Scholar
  14. 14.
    Orlin, J. Some problems in dynamic and periodic graphs. In Progress in Combinatorial Optimization, Academic Press, Orlando, Florida, 1984, W.R. Pulleyblank, Ed., pp. 215–225.Google Scholar
  15. 15.
    Ramamoorthy, C. Performance evaluation of asynchronous concurrent systems using Petri nets. IEEE Transactions on Software Engineering, 1980, 440–449.Google Scholar
  16. 16.
    Reiter, R. Scheduling parallel computations. Journal of the Association for Computing Machinery 15, No. 4, October 1968, 590–599.Google Scholar
  17. 17.
    Walkup, E., and Borriello, G. Interface timing verification with application to synthesis. In IEEE/ACM Design Automation Conference, 1994, pp. 106–112.Google Scholar
  18. 18.
    Schwiegelshohn, U., and Thiele, L. Dynamic min max problems. Technical Report ETH Zurich, Computer Engineering and Networks Laboratory, January 1997.Google Scholar
  19. 19.
    Yen, T., Ishii, A., Casavant, A., and Wolf, W. Efficient algorithms for interface timing verification. Technical Report Princeton University, June 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Uwe Schwiegelshohn
    • 1
  • Lothar Thiele
    • 2
  1. 1.Computer Engineering InstituteUniversity DortmundDortmundGermany
  2. 2.Computer Engineering and Communications LaboratorySwiss Federal Institute of Technology (ETH)ZürichSwitzerland

Personalised recommendations