Broadcast Networks with Near Optimal Cost

  • Hovhannes A. Harutyunyan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8546)


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.


Broadcast minimum broadcast graph optimal networks 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bermond, J.-C., Fraigniaud, P., Peters, J.: Antepenultimate broadcasting. Networks 26, 125–137 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    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)CrossRefzbMATHGoogle Scholar
  3. 3.
    Bermond, J.-C., Hell, P., Liestman, A.L., Peters, J.G.: Sparse broadcast graphs. Discrete Appl. Math. 36, 97–130 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    Elkin, M., Kortsarz, G.: Sublogarithmic approximation for telephone multicast: path out of jungle. In: SODA 2003, Baltimore, pp. 76–85 (2003)Google Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    Farley, A.M.: Minimal broadcast networks. Networks 9, 313–332 (1979)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Farley, A.M., Hedetniemi, S.T., Mitchell, S., Proskurowski, A.: Minimum broadcast graphs. Discrete Math. 25, 189–193 (1979)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Fertin, G., Raspaud, A.: Survey on Knödel Graphs. Discrete Appl. Math. 137, 173–195 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Fraigniaud, P., Lazard, E.: Methods and problems of communication in usual networks. Discrete Appl. Math. 53, 79–133 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Gargano, L., Vaccaro, U.: On the construction of minimal broadcast networks. Networks 19, 673–689 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Harutyunyan, H.A.: An Efficient Vertex Addition Method for Broadcast Networks. Internet Mathematics 5(3), 211–225 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Harutyunyan, H.A., Liestman, A.L.: More broadcast graphs. Discrete Applied Math. 98, 81–102 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Harutyunyan, H.A., Liestman, A.L.: On the monotonicity of the broadcast function. Discrete Math. 262(1-3), 149–157 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Harutyunyan, H.A., Liestman, A.L.: Upper bounds on the broadcast function using minimum dominating sets. Discrete Math 312(20), 2992–2996 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Harutyunyan, H.A., Morosan, C.D.: On the minimum path problem in Kndel graphs. Networks 50(1), 86–91 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Harutyunyan, H.A., Morosan, C.D.: The spectra of Knödel graphs. Informatica (Slovenia) 30(3), 295–299 (2006)zbMATHMathSciNetGoogle Scholar
  18. 18.
    Hedetniemi, S.M., Hedetniemi, T., Liestman, A.L.: A Survey of Gossiping and Broadcasting in Communication Networks. Networks 18, 319–349 (1988)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Johnson, D., Garey, M.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)zbMATHGoogle Scholar
  20. 20.
    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)Google Scholar
  21. 21.
    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)Google Scholar
  22. 22.
    Knödel, W.: New gossips and telephones. Discrete Math. 13, 95 (1975)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Labahn, R.: A minimum broadcast graph on 63 vertices. Discrete Appl. Math. 53, 247–250 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    Labahn, R.: Extremal broadcasting problems. Discrete Applied Mathematics 23(2), 139–155 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    Middendorf, M.: Minimum broadcast time is NP-complete for 3-regular planar graphs and deadline 2. Inf. Proc. Lett. 46, 281–287 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    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)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Hovhannes A. Harutyunyan
    • 1
  1. 1.Department of Computer Science and Software EngineeringConcordia UniversityMontrealCanada

Personalised recommendations