Abstract
Considerable attention in recent theoretical computer science is devoted to parallel computing. Here, we would like to present a special part of this large topic, namely, the part devoted to an abstract study of the dissemination of information in interconnection networks. The importance of this research area lies in the fact that the ability of a network to effectively disseminate information is an important qualitative measure for the suitabilty of the network for parallel computing. This follows simply from the observation that the communication among processes working in parallel is one of the main parts of the whole parallel computation. So, the effectivity of information exchange among processors essentially influences the effectivity of the whole computation process.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S.B. Akers, B. Krishnamurthy, “A group-theoretic model for symmetric interconnection networks” , IEEE Transactions on Computers, Vol. 38, No. 4, pp. 555–566, 1989.
F. Annexstein, M. Baumslag, A.L. Rosenberg, “Group action graphs and parallel architectures” , SIAM J. Comput., Vol. 19, No. 3, pp. 544–569, 1990.
P. Berthomé, A. Ferreira, S. Perennes, “Optimal information dissemination in star and pancake networks” , In: Proc. 5th IEEE Symp. on Parallel and Distributed Processing (SPDP ‘93), 1993, 720–724.
J.-C. Bermond, P. Hell, A.L. Liestman, J.G. Peters, “Broadcasting in bounded degree graphs” , SIAM Journal on Discrete Maths. 5, pp. 10–24, 1992.
A. Bagchi, S.L. Hakimi, J. Mitchem, E. Schmeichel, “ Parallel algorithms for gossiping by mail” , Inform. Proces. Letters 34 (1990), No. 4, pp. 197–202.
C.A. Brown, P.W. Purdom, The Analysis of Algorithms, Holt, Rinehart and Winston, New York, 1985, p 5.3.
J.-C. Bermond, C. Peyrat, “Broadcasting in deBruijn networks” , Proc. 19th Southeastern Conference on Combinatorics, Graph Theory and Computing, Congressus Numerantium 66, pp. 283–292, 1988.
J.C. Bermond, C. Peyrat, “De Bruijn and Kautz networks: a competitor for the hypercube?” , In F. Andre, J.P. Verjus, editors, Hypercube and Distributed Computers, pp. 279–294, North-Holland, 1989.
B. Baker, R. Shostak: “Gossips and Telephones”, Discr. Mathem. 2 (1972), pp. 191–193.
R.M. Capocelli, L. Gargano, U. Vaccaro, “Time Bounds for Broadcasting in Bounded Degree Graphs” , 15th Int. Workshop on Graph- Theoretic Concepts in Computer Science (WG 89), LNCS 411, pp. 19–33, 1989.
G. Cybenko, D.W. Krumme, K.N. Venkataraman, “Simultaneous broadcasting in multiprocessor networks”, Proc. International Conference on Parallel Processing (1986), pp. 555–558.
G. Cybenko, D.W. Krumme, K.N. Venkataraman, “Gossiping in minimal time” , SIAM J. Comput. 21 (1992), pp. 111–139.
N.G. De Bruijn, “A combinatorial problem” , Koninklijke Nederlandsche Akademie van Wetenschappen Proc., Vol. 49, pp. 758–764, 1946.
S. Even, B. Monien, “On the number of rounds necessary to disseminate information”, Proc. 1 st A CM Symp. on Parallel Algorithms and Architectures, Santa Fe, June 1989, pp. 318–327.
R.C. Entringer, P.J. Slater, “ Gossips and telegraphs” , J. Franklin Institute 307 (1979), pp. 353–360.
A.M. Farley, “Minimum-Time Line Broadcast Networks” , Networks, Vol. 10 (1980), pp. 5 9–70.
R. Feldmann, J. Hromkovič, S. Madhavapeddy, B. Monien, P. Mysliwietz, “ Optimal algorithms for dissemination of information in generalized communication modes”, Proc. PARLE’92, Lecture Notes in Computer Science 605, Springer Verlag 1992, pp. 115–130.
P. Fraigniaud, E. Lazard, “Methods and problems of communication in usual networks”, Discrete Applied Mathematics 53 (1994), No. 1–3, 79–133.
A.M. Farley, A. Proskurowski, “Gossiping in grid graphs”, J. Combin. Inform. System Sci. 5 (1980), pp. 161–172.
R. Feldmann, W. Unger, “The Cube-Connected Cycles Network is a Subgraph of the Butterfly Network”, Parallel Processing Letters, Vol. 2, No. 1 (1992), pp. 13–19.
C. Gowrisankaran, “Broadcasting in recursively decomposable Cayley graphs”, Discrete Applied Mathematics 53 (1994), No. 1–3, 171–182.
S.M. Hedetniemi, S.T. Hedetniemi, A.L. Liestman, “A survey of gossiping and broadcasting in communication networks”, Networks, Vol. 18, pp. 319–349, 1988.
J. Hromkovič, C. D. Jeschke, B. Monien, “Optimal algorithms for dissemination of information in some interconnection networks”, extended abstract in Proc. MFCS’90, Lecture Notes in Computer Science 452, Springer Verlag 1990, pp. 337–346; full version in: Algorithmica 10 (1993), 24–40.
J. Hromkovič, C.D. Jeschke, B. Monien, “ Optimal algorithms for dissemination of information in some interconnection networks” , Theoretical Computer Science 127 (1994), No. 2, 395–402.
A. Hajnal, E.C. Milner, E. Szemeredi, “A cure for the telephone disease”, Can. Math. Bull. 15 (1972), pp. 447–450.
M.C. Heydemann, J. Opatrny, D. Sotteau, “Broadcasting and spanning trees in de Bruijn and Kautz networks” , Discrete Applied Mathematics 37/38 (1992), 297–317.
R. Klasing, R. Lüling, B. Monien, “Compressing cube-connected cycles and butterfly networks” , extended abstract in Proc. 2nd IEEE Symposium on Parallel and Distributed Processing, pp. 858–865, 1990; full version in Discrete Applied Mathematics 53 (1994), No. 1–3, 183–197.
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.
D.E. KnuthThe art of computer programming, Vol. 1, Addison-Wesley, Reading-Massachusetts, 1968.
W. Knödel, “New gossips and telephones” , Discrete Math. 13 (1975), p. 95.
D.W. Krumme, “Fast gossiping for the hypercube” , SIAM J. Comput. 21 (1992), to appear.
A.L. Liestman, J.G. Peters, “ B roadcast networks of bounded degree” , SIAM Journal on Discrete Maths, Vol. 1, No. 4, pp. 531–540, 1988.
R. Labahn, I. Warnke, “ Quick gossiping by multi-telegraphs” , In R. Bodendiek, R. Henn (Eds.), Topics in Combinatorics and Graph Theory, pp. 451–458, Physica-Verlag Heidelberg, 1990.
B. Monien, I.H. Sudborough, “Embedding one Interconnection Network in Another”, Computing Supplementum7 (1990), 257–282.
V.E. Mendia, D. Sarkar, “ Optimal broadcasting on the star graph” , IEEE Transactions on Parallel and Distributed Systems 3 (1992), No. 4, 389–396.
M.G. Pease, “An adaptation of the Fast Fourier transform for parallel processing”, Journal ACM, Vol. 15, pp. 252–264, April 1968.
D. Richards, A.L. Liestman, “Generalization of broadcasting and gossiping”, Networks 18 (1988), pp. 125–138.
M.R. Samatham, D.K. Pradhan, “The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI” , IEEE Transactions on Computers, Vol. 38, No. 4, pp. 567–581, 1989.
E.A. Stöhr, “Broadcasting in the butterfly network” , Information Processing Letters 39 (1991), pp. 41–43.
E.A. Stöhr, “On the broadcast time of the butterfly network”, Proc. 17th Int. Workshop on Graph-Theoretic Concepts in Computer Science (WG 91), LNCS 570, pp. 226–229, 1991.
E.A. Stöhr, “An upper bound for broadcasting in the butterfly network”, manuscript, University of Manchester, United Kingdom.
V.S. Sunderam, P. Winkler, “Fast information sharing in a distributed system”, Discrete Applied Mathematics 42 (1993), pp. 75–86.
I.H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Hromkovič, J., Klasing, R., Monien, B., Peine, R. (1996). Dissemination of Information in Interconnection Networks (Broadcasting & Gossiping). In: Du, DZ., Hsu, D.F. (eds) Combinatorial Network Theory. Applied Optimization, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2491-2_5
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2491-2_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4752-9
Online ISBN: 978-1-4757-2491-2
eBook Packages: Springer Book Archive