Abstract
We consider the broadcasting problem in heterogeneous tree networks. A heterogeneous tree network is represented by a weighted tree Tâ=â(V,E) such that the weight of each edge denotes the communication time between the two end vertices. The broadcasting problem is to find a broadcast center such that the maximum communication time from the broadcast center to all vertices is minimized. In this paper, we propose a linear time algorithm for the broadcasting problem in a heterogeneous tree network following the postal model. As a byproduct of the algorithm, we can compute in linear time the broadcasting time of any vertex in the tree, i.e., the maximum time required to transmit messages from the vertex to every other vertex in the tree. Furthermore, an optimal sequence by which the broadcast center broadcasts its messages to all vertices in T can also be determined in linear time.
This work is partially supported by the National Science Council under the Grants No. NSC98-2221-E-001-007-MY3, NSC98-2221-E-001-008-MY3, and NSC-98-2221-E-019-029.
This is a preview of subscription content, log in via an institution to check access.
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
Bar-Noy, A., Guha, S., Naor, J., Schieber, B.: Message multicasting in heterogeneous networks. SIAM J. Comput. 30(2), 347â358 (2000)
Bar-Noy, A., Kipnis, S.: Designing broadcasting algorithms in the postal model for message-passing systems. Math. Systems Theory 27(5), 431â452 (1994)
Bar-Noy, A., Kipnis, S.: Multiple message broadcasting in the postal model. Networks 29(1), 1â10 (1997)
Elkin, M., Kortsarz, G.: An approximation algorithm for the directed telephone multicast problem. Algorithmica 45(4), 569â583 (2006)
Farley, A.M.: Broadcast time in communication networks. SIAM J. Appl. Math. 39(2), 385â390 (1980)
Hedetniemi, S.M., Hedetniemi, S.T., Liestman, A.L.: A survey of gossiping and broadcasting in communication networks. Networks 18(4), 319â349 (1988)
Khuller, S., Kim, Y.-A.: Broadcasting in heterogeneous networks. Algorithmica 48(1), 1â21 (2007)
Khuller, S., Kim, Y.-A., Wan, Y.-C.: On generalized gossiping and broadcasting. J. Algorithms 59(2), 81â106 (2006)
Khuller, S., Kim, Y.-A., Wan, Y.-C.: Broadcasting on networks of workstations. Algorithmica 52(3), 1â21 (2008)
Koh, J.-M., Tcha, D.-W.: Information dissemination in trees with nonuniform edge transmission times. IEEE Trans. Comput. 40(10), 1174â1177 (1991)
Lee, H.-M., Chang, G.J.: Set to set broadcasting in communication networks. Discrete Appl. Math. 40(3), 411â421 (1992)
Richards, D., Liestman, A.L.: Generalizations of broadcasting and gossiping. Networks 18(2), 125â138 (1988)
Slater, P.J., Cockayne, E.J., Hedetniemi, S.T.: Information dissemination in trees. SIAM J. Comput. 10(4), 692â701 (1981)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Âİ 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Su, YH., Lin, CC., Lee, D.T. (2010). Broadcasting in Heterogeneous Tree Networks. In: Thai, M.T., Sahni, S. (eds) Computing and Combinatorics. COCOON 2010. Lecture Notes in Computer Science, vol 6196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14031-0_40
Download citation
DOI: https://doi.org/10.1007/978-3-642-14031-0_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14030-3
Online ISBN: 978-3-642-14031-0
eBook Packages: Computer ScienceComputer Science (R0)