Skip to main content
SpringerLink
Log in

Optimal broadcasting in almost trees and partial k-trees

  • Algorithms and Data Structures IV
  • Conference paper
  • First Online:
STACS 98 (STACS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

Included in the following conference series:

Abstract

We consider message broadcasting in networks that have almost tree topology. The source node of the input network has a single message which has to be broadcasted to all nodes of the network. In every time unit each node that has already received the message can send it to one of its neighbors. A broadcasting scheme prescribes in which time unit a given node should send a message to which neighbor. It is minimum if it achieves the smallest possible time for broadcasting the message from the source to all nodes. We give the following algorithms to construct a minimum broadcasting scheme for different types of weakly cyclic networks:

  • A linear-time algorithm for networks whose cycles are node-disjoint and in which any simple path intersects at most O(1) cycles.

  • An O(nlogn)-time algorithm for networks whose cycles are edge-disjoint and in which a node can belong to at most O(1) cycles.

  • An O(nk log n) -time algorithm for networks whose each edge-biconnected component is convertible to a tree by removal of at most k edges.

  • We also present an O(n4k+s)-time algorithm for constructing a minimum broadcasting scheme for partial k-trees.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.V. Aho, J.E. Hopcroft and J.D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.

    MATH  Google Scholar 

  2. S. Arnborg, A. Proskurowski, Linear time algorithms for NP-hard problems on graphs embedded in k-trees. Discrete Applied Mathematics 23 (1989), pp. 11–24.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Bar-Noy and S. Kipnis, Designing broadcasting algorithms in the postal model for message passing systems, Proc. 5th Ann. ACM Symp. on Par. Alg. and Arch. (1992), 11–22.

    Google Scholar 

  4. A. Bar-Noy and S. Kipnis, Broadcasting multiple messages in simultaneous send/receive systems, Discr. Appl. Math. 53 (1994), 95–105.

    Article  MathSciNet  Google Scholar 

  5. D. Barth and P. Fraigniaud, Approximation algorithms for Structured communication problems, Proc. 9th Ann. ACM Symp. on Par. Alg. and Arch. (1997), 180–188.

    Google Scholar 

  6. D.P. Bertsekas and J.N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, (1989).

    MATH  Google Scholar 

  7. H. Bodlaender. A linear time algorithm for finding tree-decompositions of small treewidth. Proc. 33rd ACM STOC, pp. 226–234.

    Google Scholar 

  8. A. Dessmark, A. Lingas, H. Olsson and H. Yamamoto, Optimal broadcasting in almost trees and partial k-trees, Technical Report, LU-EX-CS:97–193, Dept. Computer Science, Lund University, Sweden, 1997.

    Google Scholar 

  9. S. Even. Graph Algorithms. Computer Science Press, 1979.

    Google Scholar 

  10. G. Fox, M. Johnsson, G. Lyzenga, S. Otto, J. Salmon and D. Walker, Solving Problems on Concurrent Processors, Volume I, Prentice Hall, (1988).

    Google Scholar 

  11. P. Fraigniaud and E. Lazard, Methods and problems of communication in usual networks, Disc. Appl. Math. 53 (1994), 79–133.

    Article  MATH  MathSciNet  Google Scholar 

  12. M. Garey and D. Johnson, Computers and Intractability: a guide to the theory of NPcompleteness, Freeman and Co., San Francisco (1979).

    Google Scholar 

  13. S.M. Hedetniemi, S.T. Hedetniemi and A.L. Liestman, A survey of gossiping and broadcasting in communication networks, Networks 18 (1988), 319–349.

    Article  MATH  MathSciNet  Google Scholar 

  14. J. Hromkovič, R. Klasing, B. Monien and R. Peine, Dissemination of information in interconnection networks (broadcasting and gossiping), in: F. Hsu and D. Z. Du (Eds.), Combinatorial Network Theory, Kluwer Academic Publishers, 1995, 125–212.

    Google Scholar 

  15. A. Jacoby, R. Reischuk, Ch. Schindelhaner, The complexity of broadcasting in planar and decomposable graphs, Proc. 20th International Workshop WG'94, June 1994, LNCS 903, 219–231.

    Google Scholar 

  16. K. Jansen, H. Müller, The Minimum Broadcast Time Problem, Proc. 1st Canada-France Conference on Parallel Computing, Montreal, LNCS 805, 1994', 219–234.

    Google Scholar 

  17. S.L. Johnsson and C.T. Ho, Matrix multiplication on Boolean cubes using generic communication primitives, in: Parallel Processing and Medium-Scale Multiprocessors, A. Wouk (Ed.), SIAM, (1989), 108–156.

    Google Scholar 

  18. J. van Leeuwen. Graph Algorithms. Handbook of Theoretical Computer Science A, North Holland, Amsterdam 1990, pp. 527–631.

    Google Scholar 

  19. G. Kortsarz and D. Peleg, Approximation Algorithms for Minimum Time Broadcast, Proc. of the Israel Symposium on Theoretical Computer Science, LNCS 601, 1992.

    Google Scholar 

  20. R. Ravi, Rapid Rumour Ramification: Approximating tha minimum broadcast time, Proc. 35th IEEE Symposium on Foundations of Computer Science (1994), 202–213.

    Google Scholar 

  21. N. Robertson and P. Seymour. Graph Minors H. Algorithmic aspects of tree-width. J. Algorithms No. 7 (1986), pp. 309–322.

    Google Scholar 

  22. P.J. Slater, E. Cockayne and S.T. Hedetniemi, Information dissemination in trees, SIAM J. Comput. 10 (1981), 692–701.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Lund University, Box 118, S-22100, Lund, Sweden

    Anders Dessmark, Andrzej Lingas & Hans Olsson

  2. Department of Information Engineering, Shinshu University, 500 Wakasato, 380, Nagano-shi, Japan

    Hiroaki Yamamoto

Authors
  1. Anders Dessmark
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrzej Lingas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hans Olsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hiroaki Yamamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Michel Morvan Christoph Meinel Daniel Krob

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag

About this paper

Cite this paper

Dessmark, A., Lingas, A., Olsson, H., Yamamoto, H. (1998). Optimal broadcasting in almost trees and partial k-trees. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028579

Download citation

  • DOI: https://doi.org/10.1007/BFb0028579

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation