Optimal algorithms for broadcast and gossip in the edge-disjoint path modes

Extended abstract
  • Juraj Hromkovič
  • Ralf Klasing
  • Walter Unger
  • Hubert Wagener
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 824)


The communication power of the one-way and two-way edge-disjoint path modes for broadcast and gossip is investigated. The complexity of communication algorithms is measured by the number of communication steps (rounds). The main results achieved are the following:
  1. 1.

    For each connected graph Gn of n nodes, the complexity of broadcast in Gn, Bmin(Gn), satisfies [log2n]≤Bmin(Gn)≤[log2n]+1. The complete binary trees meet the upper bound, and all graphs containing a Hamiltonian path meet the lower bound.

  2. 2.
    For each connected graph Gn of n nodes, the one-way (two-way) gossip complexity R(Gn) (R2(Gn)) satisfies
    $$\begin{gathered}\left\lceil {\log _2 n} \right\rceil \leqslant R^2 (G_n ) \leqslant 2 \cdot \left\lceil {\log _2 n} \right\rceil + 1, \hfill \\1.44...\log _2 n \leqslant R(G_n ) \leqslant 2 \cdot \left\lceil {\log _2 n} \right\rceil + 2. \hfill \\\end{gathered}$$
    . All these lower and upper bounds are tight.
  3. 3.

    All planar graphs of n nodes and degree h have a two-way gossip complexity of at least 1.5log2n−log2log2n−0.5log2h−2, and the two-dimensional grid of n nodes has the gossip complexity 1.5log2n−log2log2n±O(1), i.e. two-dimensional grids are optimal gossip structures among planar graphs. Similar results are obtained for one-way mode too.


Moreover, several further upper and lower bounds on the gossip complexity of fundamental networks are presented.


communication algorithms parallel computations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [DDSV93]
    K. Diks, H.N. Djidjev, O. Sýkora, I. Vrťo, ”Edge separators of planar and outerplanar graphs with applications”, Journal of Algorithms 14 (1993), pp. 258–279.Google Scholar
  2. [EM89]
    S. Even, B. Monien, ”On the number of rounds necessary to disseminate information”, Proc. 1st ACM Symp. on Parallel Algorithms and Architectures (SPAA'89), 1989, pp. 318–327.Google Scholar
  3. [Fa80]
    A.M. Farley, “Minimum-Time Line Broadcast Networks”, Networks 10 (1980), pp. 59–70.Google Scholar
  4. [FHMMM92]
    R. Feldmann, J. Hromkovic, S. Madhavapeddy, B. Monien, P. Mysliwietz, ”Optimal algorithms for dissemination of information in generalized communication modes”, Proc. Parallel Architectures and Languages Europe (PARLE'92), Lecture Notes in Computer Science 605, Springer Verlag 1992, pp. 115–130.Google Scholar
  5. [HJM90]
    J. Hromkovič, C. D. Jeschke, B. Monien, ”Optimal algorithms for dissemination of information in some interconnection networks (extended abstract)”, Proc. MFCS'90, Lecture Notes in Computer Science 452, Springer Verlag 1990, pp. 337–346.Google Scholar
  6. [HKMP93]
    J. Hromkovič, R. Klasing, B. Monien, R. Peine, “Dissemination of Information in Interconnection Networks (Broadcasting and Gossiping)”, manuscript, University of Paderborn, Germany, Feb. 1993, to appear as a book chapter in: F. Hsu, D.-Z. Du (Eds.), Combinatorial Network Theory, Science Press & AMS, 1994.Google Scholar
  7. [HKS93]
    J. Hromkovič, R. Klasing, E.A. Stöhr, ”Gossiping in vertex-disjoint paths mode in interconnection networks”, Proc. 19th Int. Workshop on Graph-Theoretic Concepts in Computer Science (WG '93), Lecture Notes in Computer Science, Springer Verlag 1993, to appear.Google Scholar
  8. [HKSW93]
    J. Hromkovič, R. Klasing, E.A. Stöhr, H. Wagener, ”Gossiping in Vertex-Disjoint Paths Mode in d-Dimensional Grids and Planar Graphs”, Proc. of the First Annual European Symposium on Algorithms (ESA '93), Lecture Notes in Computer Science 726, Springer Verlag 1993, pp. 200–211.Google Scholar
  9. [KCV92]
    D.W. Krumme, G. Cybenko, K.N. Venkataraman, ”Gossiping in minimal time”, SIAM J. Comput. 21 (1992), pp. 111–139.MathSciNetGoogle Scholar
  10. [KMPS92]
    R. Klasing, B. Monien, R. Peine, E. Stöhr, ”Broadcasting in Butterfly and DeBruijn networks”, Proc. STACS'92, Lecture Notes in Computer Science 577, Springer Verlag 1992, pp. 351–362.Google Scholar
  11. [Kn75]
    W. Knödel, ”New gossips and telephones”, Discrete Math. 13 (1975), p. 95.Google Scholar
  12. [Le92]
    F.T. Leighton, “Introduction to Parallel Algorithms and Architectures: Array, Trees, Hypercubes”, Morgan Kaufmann Publishers (1992).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Juraj Hromkovič
    • 1
  • Ralf Klasing
    • 1
  • Walter Unger
    • 1
  • Hubert Wagener
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of PaderbornPaderbornGermany

Personalised recommendations