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Effective systolic algorithms for gossiping in cycles and two-dimensional grids

Extended abstract
  • Juraj Hromkovič
  • Ralf Klasing
  • Dana Pardubská
  • Walter Unger
  • Juraj Waczulik
  • Hubert Wagener
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 965)

Abstract

The complexity of systolic dissemination of information in one-way (telegraph) and two-way (telephone) communication mode is investigated. The following main results are established:
  1. (i)

    tight lower and upper bounds on the complexity of one-way systolic gossip in cycles for any length of the systolic period,

     
  2. (ii)

    optimal one-way and two-way systolic gossip algorithms in 2-dimensional grids whose complexity (the number of rounds) meets the trivial lower bound (the sum of the sizes of its dimensions).

     

The second result (ii) shows that we can systolically gossip in grids with the general gossip complexity, i.e., we do not need to pay for the systolization in grids. Opposed to this, the first result (i) shows that the complexity of systolic gossip in cycles is greater than the gossip complexity in cycles for any systolic period length independent of the size of the cycle.

Keywords

Interconnection Network Communication Mode Communication Step Discrete Apply Mathematic Broadcast Algorithm 
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.

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References

  1. [BHMS90]
    A. Bagchi, S. L. Hakimi, J. Mitchem, E. Schmeichel: Parallel algorithms for gossiping by mail. Information Process. Letters 34 (1990), 197–202.CrossRefGoogle Scholar
  2. [CC84]
    C. Choffrut, K. Culik II: On real-time cellular automata and trellis automata. Acta Informatica 21 (1984), 393–407.CrossRefGoogle Scholar
  3. [CGS83]
    K. Culik II, J. Gruska, A. Salomaa: Systolic automata for VLSI on balanced trees. Acta Informatica 18 (1983), 335–344.CrossRefGoogle Scholar
  4. [CGS84]
    K. Culik II, I. Gruska, A. Salomaa: Systolic trellis automata. Part I. Intern. J. Comput. Math. 15 (1984), 195–212.Google Scholar
  5. [CSW84]
    K. Culik II, A. Salomaa, D. Wood: Systolic tree acceptors. R.A.I.R.O. Theoretical Informatics 18 (1984), 53–69.Google Scholar
  6. [FL94]
    P. Fraigniaud, E. Lazard, Methods and problems of communication in usual networks. Discrete Applied Mathematics, special issue on Broad-casting and Gossiping (DAM-BG), Vol. 53 Nos. 1–3, September 1994, pp. 79–134.Google Scholar
  7. [FP80]
    A.M. Farley, A. Proskurowski, Gossiping in grid graphs. J. Combin. Inform. System Sci. 5 (1980), pp. 161–172.Google Scholar
  8. [HJM94]
    J. Hromkovič, C.-D. Jeschke, B. Monien: Note on Optimal Gossiping in some Weak-Connected Graphs. Theoretical Computer Science 127 (1994), No. 2, 395–402.Google Scholar
  9. [HHL88]
    S. M. Hedetniemi, S. T. Hedetniemi, A. L. Liestmann: A survey of gossiping and broadcasting in communication networks. Networks 18 (1988), 319–349.Google Scholar
  10. [HKMP95]
    J. Hromkovič, R. Klasing, B. Monien, R. Peine: Dissemination of information in interconnection networks (broadcasting & gossiping). In: Combinatorial Network Theory (Frank Hsu, Ding-Zhu Du, Eds.), Science Press & AMS, 1994, to appear.Google Scholar
  11. [HKPUW94]
    J. Hromkovič, R. Klasing, D. Pardubská, W. Unger, H. Wagener: The complexity of systolic dissemination of information in interconnection networks. In: Proc. of the 1st Canada-France Conference on Parallel Computing (CFCP '94), Springer LNCS 805, pp. 235–249. R.A.I.R.O. Theoretical Informatics and Applications, Vol. 28 Nos. 3–4, 1994, pp. 303–342.Google Scholar
  12. [KCV92]
    D.W. Krumme, G. Cybenko, K.N. Venkataraman: Gossiping in minimal time. SIAM J. Comput. 21 (1992), pp. 111–139.MathSciNetGoogle Scholar
  13. [KP94]
    G. Kortsarz, D. Peleg: Traffic-light scheduling on the grid. Discrete Applied Mathematics, special issue on Broadcasting and Gossiping (DAM-BG), Vol. 53 Nos. 1–3, September 1994, pp. 211–234.Google Scholar
  14. [Ku79]
    H.T. Kung: Let's design algorithms for VLSI systems. In: Proc. of the Caltech Conference of VLSI (CL.L. Seifz Ed.), Pasadena, California 1979, pp. 65–90.Google Scholar
  15. [LHL94]
    R. Labahn, S.T. Hedetniemi, R. Laskar, Periodic gossiping on trees. Discrete Applied Mathematics, special issue on Broadcasting and Gossiping (DAM-BG), Vol. 53 Nos. 1–3, September 1994, pp. 235–246.Google Scholar
  16. [LR93a]
    A.L. Liestman, D. Richards: Network communication in edge-colored graphs: Gossiping. IEEE Trans. Par. Distr. Syst. 4 (1993), 438–445.Google Scholar
  17. [LR93b]
    A.L. Liestman, D. Richards: Perpetual gossiping. Parallel Processing Letters 3 (1993), No. 4, 347–355.Google Scholar
  18. [LR94]
    R. Labahn, A. Raspaud: Periodic gossiping in back-to-back trees. Technical Report, Universität Rostock, Germany, 1994.Google Scholar
  19. [XL92]
    Cheng-Zhong Xu, Francis C.M. Lau: Distributed termination detection of loosely synchronized computations. In: Proc. 4th IEEE Symp. on Parallel and Distr. Processing, Texas 1992, pp. 196–203.Google Scholar
  20. [XL94]
    Cheng-Zhong Xu, Francis C.M. Lau: Efficient distributed termination detection for synchronous computations in multicomputers. Technical Report TR-94-04, Department of Computer Science, The University of Hong Kong, March 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Juraj Hromkovič
    • 1
  • Ralf Klasing
    • 2
  • Dana Pardubská
    • 3
  • Walter Unger
    • 2
  • Juraj Waczulik
    • 3
  • Hubert Wagener
    • 2
  1. 1.Institut für Informatik und Praktische MathematikUniversität zu KielKielGermany
  2. 2.Department of Mathematics and Computer ScienceUniversity of PaderbornPaderbornGermany
  3. 3.Faculty of Mathematics and PhysicsComenius UniversityBratislavaSlovakia

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