Abstract
Broadcasting is a basic problem of communication in usual networks. Many papers have investigated the construction of minimum broadcast networks, the cheapest possible network architecture (having the fewest communication lines), in which broadcasting can be accomplished as fast as theoretically possible from any vertex. Other papers considered the problem of determining the minimum broadcast time of a given vertex in an arbitrary network. In this paper, for given n we construct optimal networks on n vertices which we define to be the product of the broadcast time and the number of edges of the network. On the way we start the study of an interesting problem, the problem of minimum time broadcasting in networks with given number of vertices and edges.
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
Bermond, J.-C., Fraigniaud, P., Peters, J.: Antepenultimate broadcasting. Networks 26, 125–137 (1995)
Bermond, J.-C., Harutyunyan, H.A., Liestman, A.L., Perennes, S.: A note on the dimensionality of modified Knödel graphs. Int. J. Found. Comp. Sci. 8, 109–117 (1997)
Bermond, J.-C., Hell, P., Liestman, A.L., Peters, J.G.: Sparse broadcast graphs. Discrete Appl. Math. 36, 97–130 (1992)
Dinneen, M.J., Fellows, M.R., Faber, V.: lgebraic constructions of efficient broadcast networks. In: Mattson, H.F., Rao, T.R.N., Mora, T. (eds.) AAECC 1991. LNCS, vol. 539, pp. 152–158. Springer, Heidelberg (1991)
Elkin, M., Kortsarz, G.: Sublogarithmic approximation for telephone multicast: path out of jungle. In: SODA 2003, Baltimore, pp. 76–85 (2003)
Elkin, M., Kortsarz, G.: A combinatorial logarithmic approximation algorithm for the directed telephone broadcast problem. In: Proc. of ACM Symp. on Theory of Computing, pp. 438–447 (2002)
Farley, A.M.: Minimal broadcast networks. Networks 9, 313–332 (1979)
Farley, A.M., Hedetniemi, S.T., Mitchell, S., Proskurowski, A.: Minimum broadcast graphs. Discrete Math. 25, 189–193 (1979)
Fertin, G., Raspaud, A.: Survey on Knödel Graphs. Discrete Appl. Math. 137, 173–195 (2004)
Fraigniaud, P., Lazard, E.: Methods and problems of communication in usual networks. Discrete Appl. Math. 53, 79–133 (1994)
Gargano, L., Vaccaro, U.: On the construction of minimal broadcast networks. Networks 19, 673–689 (1989)
Harutyunyan, H.A.: An Efficient Vertex Addition Method for Broadcast Networks. Internet Mathematics 5(3), 211–225 (2008)
Harutyunyan, H.A., Liestman, A.L.: More broadcast graphs. Discrete Applied Math. 98, 81–102 (1999)
Harutyunyan, H.A., Liestman, A.L.: On the monotonicity of the broadcast function. Discrete Math. 262(1-3), 149–157 (2003)
Harutyunyan, H.A., Liestman, A.L.: Upper bounds on the broadcast function using minimum dominating sets. Discrete Math 312(20), 2992–2996 (2012)
Harutyunyan, H.A., Morosan, C.D.: On the minimum path problem in Kndel graphs. Networks 50(1), 86–91 (2007)
Harutyunyan, H.A., Morosan, C.D.: The spectra of Knödel graphs. Informatica (Slovenia) 30(3), 295–299 (2006)
Hedetniemi, S.M., Hedetniemi, T., Liestman, A.L.: A Survey of Gossiping and Broadcasting in Communication Networks. Networks 18, 319–349 (1988)
Johnson, D., Garey, M.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)
Khachatrian, L.H., Haroutunian, H.S.: Construction of new classes of minimal broadcast networks. In: Proceedings 3rd International Colloquium on Coding Theory, Dilijan, Armenia, pp. 69–77 (1990)
Khachatrian, L.H., Haroutunian, H.S.: Minimal broadcast trees. In: XIV All-Union School of Computer Networks, Minsk, USSR, pp. 36–40 (1989) (in Russian)
Knödel, W.: New gossips and telephones. Discrete Math. 13, 95 (1975)
Labahn, R.: A minimum broadcast graph on 63 vertices. Discrete Appl. Math. 53, 247–250 (1994)
Labahn, R.: Extremal broadcasting problems. Discrete Applied Mathematics 23(2), 139–155 (1989)
Middendorf, M.: Minimum broadcast time is NP-complete for 3-regular planar graphs and deadline 2. Inf. Proc. Lett. 46, 281–287 (1993)
Ravi, R.: Rapid rumor ramification: Approximating the minimum broadcast time. In: Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS 1994), pp. 202–213 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Harutyunyan, H.A. (2014). Broadcast Networks with Near Optimal Cost. In: Gu, Q., Hell, P., Yang, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2014. Lecture Notes in Computer Science, vol 8546. Springer, Cham. https://doi.org/10.1007/978-3-319-07956-1_28
Download citation
DOI: https://doi.org/10.1007/978-3-319-07956-1_28
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07955-4
Online ISBN: 978-3-319-07956-1
eBook Packages: Computer ScienceComputer Science (R0)