Advertisement

Acyclic orientations for deadlock prevention in interconnection networks

extended abstract
  • Jean-Claude Bermond
  • Miriam Di Ianni
  • Michele Flammini
  • Stephane Perennes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1335)

Abstract

In this paper we extend some of the computational results presented in [6] on finding an acyclic orientation of a graph which minimizes the maximum number of changes of orientations along the paths connecting a given subset of source-destination couples. The corresponding value is called rank of the set of paths. Besides its theoretical interest, the topic has also practical applications. In fact, the existence of a rank r acyclic orientation for a graph implies the existence of a deadlock-free routing strategy for the corresponding network which uses at most r buffers per vertex.

We first show that the problem of minimizing the rank is NP-hard if all shortest paths between the couples of vertices wishing to communicate have to be represented and even not approximable within an error in O(k1−ε) for any ε > 0, where k is the number of source-destination couples wishing to communicate, if only one shortest path between each couple has to be represented.

We then improve some of the known lower and upper bounds on the rank of all possible shortest paths between any couple of vertices for particular topologies, such as grids and hypercubes, and we find tight results for tori.

Keywords

computational and structural complexity graph theory parallel algorithms routing communication in interconnection networks 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. Awerbuch, S. Kutten, and D. Peleg. Efficient deadlock-free routing. In 10th Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 177–188, Montreal, Canada, 1991.Google Scholar
  2. 2.
    P.E. Berman, L. Gravano, G.D. Pifarré, and J.L.C. Sanz. Adaptive deadlock and livelock-free routing with all minimal paths in torus networks. In 4th Symposium on Parallel Algorithms and Architectures (SPAA), pages 3–12, June 1992.Google Scholar
  3. 3.
    J.C. Bermond and M. Syska. Routage wormhole et canaux virtuel. In M. Cosnard M. Nivat and Y. Robert, editors, Algorithmique Parallèle, pages 149–158. Masson, 1992.Google Scholar
  4. 4.
    Robert Cypher and Luis Gravano. Requirements for deadlock-free, adaptive packet routing. In 11th Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 25–33, 1992.Google Scholar
  5. 5.
    W. J. Dally and C. L. Seitz. Deadlock-free message routing in multiprocessor interconnection networks. IEEE Trans. Comp., C-36, N.5:547–553, May 1987.Google Scholar
  6. 6.
    M. Di Ianni, M. Flammini, R. Flammini, and S. Salomone. Systolic acyclic orientations for deadlock prevention. In 2nd Colloquium on Structural Information and Communication Complexity (SIROCCO), pages 1–12. Carleton University Press, 1995.Google Scholar
  7. 7.
    J. Duato. Deadlock-free adaptive routing algorithms for multicomputers: evaluation of a new algorithm. In 3rd IEEE Symposium on Parallel and Distributed Processing, 1991.Google Scholar
  8. 8.
    J. Duato. On the design of deadlock-free adaptive routing algorithms for multicomputers: theoretical aspects. In 2nd European Conference on Distributed Memory Computing, volume 487 of Lecture Notes in Computer Science, pages 234–243. Springer-Verlag, 1991.Google Scholar
  9. 9.
    E. Fleury and P. Fraigniaud. Deadlocks in adaptive wormhole routing. Research Report, Laboratoire de l'Informatique du Parallélisme, LIP, École Normale Supérieure de Lyon, 69364 Lyon Cedex 07, France, March 1994.Google Scholar
  10. 10.
    M.R. Garey and D.S. Johnson. Computers and Intractability. A Guide to the Theory of NP-completeness. W.H. Freeman, 1977.Google Scholar
  11. 11.
    K.D. Gunther. Prevention of deadlock in packet-switched data transport system. IEEE Trans. on Commun., COM-29:512–514, May 1981.Google Scholar
  12. 12.
    P.M. Merlin and P.J. Schweitzer. Deadlock avoidance in store-and-forward networks: Store and forward deadlock. IEEE Trans. on Commun., COM-28:345–352, March 1980.Google Scholar
  13. 13.
    G.D. Pifarré, L. Gravano, S.A. Felperin, and J.L.C. Sanz. Fully-adaptive minimal deadlock-free packet routing in hypercube, meshes, and other networks. In 3rd Symposium on Parallel Algorithms and Architectures (SPAA), pages 278–290, June 1991.Google Scholar
  14. 14.
    A.G. Ranade. How to emulate shared memory. In Foundation of Computer Science, pages 185–194, 1985.Google Scholar
  15. 15.
    Gerard Tel. Introduction to Distributed Algorithms. Cambridge University Press, Cambridge, U.K., 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Jean-Claude Bermond
    • 1
  • Miriam Di Ianni
    • 2
  • Michele Flammini
    • 3
    • 1
  • Stephane Perennes
    • 4
    • 1
  1. 1.Project SLOOP 13S-CNRS/INRIA/Université de Nice-Sophia AntipolisSophia-Antipolis CedexFrance
  2. 2.Istituto di ElettronicaUniversity of PerugiaPerugiaItaly
  3. 3.Dipartimento di Maternatica Pura ed ApplicataUniversity of L'AquilaL'AquilaItaly
  4. 4.Dept. Math. and Computer ScienceTU DelftDelftThe Netherlands

Personalised recommendations