Abstract
Broadcasting is the process of transmitting a message from a node to all other nodes in a network. The problem of constructing sparse graphs in which the broadcast could be accomplished in minimum time has been investigated in several papers. However, the proposed graphs may have nodes of high degree that could be unacceptable from a network designer's point of view. In this paper we consider the problem of broadcasting on bounded degree graphs. We provide a lower bound on the time necessary to accomplish the broadcast when the maximum node degree is fixed. Moreover, we propose a method to construct bounded degree graphs in which the time to complete the broadcast from any node is of the same order as the lower bound. We also obtain the only known families of graphs having exactly minimum broadcast time.
This work was supported in part by the Italian Ministry of Education, Project: Algoritmi e Sistemi di Calcolo
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Bermond, J.C., Hell, P., Liestman, A.L., and Peters, J.G., “Broadcasting in Bounded Degree Graphs”, Technical Report 88-5, Simon Fraser University (1988).
Bermond, J.C., and Peyrat, C., “Broadcasting in De Bruijn Networks”, Technical Report 88-4, Simon Fraser University (1988).
Capocelli, R.M. and Cull, P., “Generalized Fibonacci Numbers Are Rounded Powers”, to appear in Proceedings of Third Int. Conf. on Fibonacci Numbers and Their Applications, Pisa, Italy, (1988)
Chau, S. and Liestman, A. L., “Constructing Minimal Broadcast Networks”, J. Combin., Inform. & System Sci. 10 (1985), 110–122.
Farley, A. M., “Minimal Broadcast Networks”, NETWORKS 9 (1979), 313–332.
Farley, A.M., “Broadcast Time in Communication Networks”, SIAM J. Appl. Math. 39 (1980), 385–390.
Farley, A. M., Hedetniemi, S. T., Proskurowski, A. and Mitchell, S., “Minimum Broadcast Graphs”, Discrete Math. 25 (1979), 189–193.
Gargano, L., and Vaccaro, U., “On the Construction of Minimal Broadcast Networks”, NETWORKS, to appear.
Hedetniemi, S.T., Hedetniemi, S.M., and Liestman, A.L., “A Survey of Broadcasting and Gossiping in Communication Networks”, NETWORKS, 18, (1988), 319–351.
Liestman, A.L., and Peters, J.G., “Broadcast Networks of Bounded Degree”, SIAM J. Disc. Math., 1, (1988), 531–540.
Miles, E.P., Jr., “Generalized Fibonacci Numbers and Matrices”, Amer. Math. Monthly. 67, (1960), 745–757.
Mitchell, S. and Hedetniemi, S. T., “A Census of Minimum Broadcast Graphs”, J. Combin., Inform. & Systems Sci. 9 (1980), 119–129.
Peleg, D., “Tight Bounds on Minimum Broadcast Graphs”, SIAM J. Disc. Math., to appear.
Tanebaum, A. S., “Computer Networks”, Prentice-Hall, Englewood Cliffs, N.J., (1981).
Bermond, J.C., Hell, P., Liestman, A.L., and Peters, J.G., “New Minimum Broadcast Graphs and Sparse Broadcast Graphs”, Technical Report 88-4, Simon Fraser University (1988).
G. Sabidussi, “Graph Multiplication”, Math. Zeitschr., 72, (1960), 446–457.
C. von Conta, “Torus and Other Networks as Communication Networks with up to some Hundred Points”, IEEE Trans. Comp., C-32, (1983), 657–666.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Capocelli, R.M., Gargano, L., Vaccaro, U. (1990). Time bounds for broadcasting in bounded degree graphs. In: Nagl, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 1989. Lecture Notes in Computer Science, vol 411. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52292-1_2
Download citation
DOI: https://doi.org/10.1007/3-540-52292-1_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52292-8
Online ISBN: 978-3-540-46950-6
eBook Packages: Springer Book Archive