Abstract
Broadcasting is an information dissemination problem in a connected graph in which one vertex, called the originator, must distribute a message to all other vertices by placing a series of calls along the edges of the graph. Every time the informed vertices aid the originator in distributing the message. Finding the broadcast time of any vertex in an arbitrary graph is NP-complete. The problem is NP-Complete for even more restricted classes of graphs, such as for 3-regular planar graphs. The best approximation algorithm for broadcast problem is \(O( \frac{\log(|V|)}{\log \log(|V|)}b(G))\). The polynomial time solvability is shown only for certain tree-like graphs; trees, unicyclic graphs, tree of cycles. The problem becomes very difficult when cycles intersect. In this paper we study the broadcast problem in a simple cactus graph called k-cycle graph. For any originator we present a (2 − ε)-approximation algorithm in the arbitrary k-cycle graph. We also prove that our algorithm generates the optimal broadcast time for some subclasses of this graph.
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.: Multicasting in heterogeneous networks. In: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing (STOC 1998), pp. 448–453 (1998)
Beier, R., Sibeyn, J.F.: A powerful heuristic for telephone gossiping. In: Proceedings of the 7th International Colloquium on Structural Information Communication Complexity (SIROCCO 2000), pp. 17–36 (2000)
Bhabak, P., Harutyunyan, H.A.: Approximation algorithm for the broadcast time in k-path graph (abstract only). In: 3rd International Symposium on Combinatorial Optimization (ISCO 2014), p. 83 (2014)
Elkin, M., Kortsarz, G.: Combinatorial logarithmic approximation algorithm for directed telephone broadcast problem. In: Proceedings of the thirty-fourth Annual ACM Symposium on Theory of Computing (STOC 2002), pp. 438–447 (2002)
Elkin, M., Kortsarz, G.: Sublogarithmic approximation for telephone multicast: path out of jungle (extended abstract). In: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2003), pp. 76–85 (2003)
Fraigniaud, P., Vial, S.: Approximation algorithms for broadcasting and gossiping. J. Parallel and Distrib. Comput. 43(1), 47–55 (1997)
Fraigniaud, P., Vial, S.: Heuristic algorithms for personalized communication problems in point-to-point networks. In: Proceedings of the 4th Colloquium on Structural Information Communication Complexity (SIROCCO 1997), pp. 240–252 (1997)
Fraigniaud, P., Vial, S.: Comparison of heuristics for one-to-all and all-to-all communication in partial meshes. Parallel Processing Letters 9, 9–20 (1999)
Harutyunyan, H.A., Maraachlian, E.: On broadcasting in unicyclic graphs. J. Comb. Optim. 16(3), 307–322 (2008)
Harutyunyan, H.A., Maraachlian, E.: Broadcasting in fully connected trees. In: Proceedings of the 2009 15th International Conference on Parallel and Distributed Systems (ICPADS 2009), pp. 740–745 (2009)
Harutyunyan, H.A., Shao, B.: An efficient heuristic for broadcasting in networks. J. Parallel Distrib. Comput. 66(1), 68–76 (2006)
Harutyunyan, H.A., Wang, W.: Broadcasting algorithm via shortest paths. In: Proceedings of the 2010 IEEE 16th International Conference on Parallel and Distributed Systems (ICPADS 2010), pp. 299–305 (2010)
Jansen, K., Muller, H.: The minimum broadcast time problem for several processor networks. Theoretical Computer Science 147, 69–85 (1995)
Kortsarz, G., Peleg, D.: Approximation algorithms for minimum time broadcast. SIAM J. Discrete Math. 8, 401–427 (1995)
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 35th Annual Symposium on Foundations of Computer Science (FOCS 1994), pp. 202–213 (1994)
Scheuermann, P., Wu, G.: Heuristic algorithms for broadcasting in point-to-point computer networks. IEEE Trans. Comput. 33(9), 804–811 (1984)
Schindelhauer, C.: On the inapproximability of broadcasting time. In: Jansen, K., Khuller, S. (eds.) APPROX 2000. LNCS, vol. 1913, pp. 226–237. Springer, Heidelberg (2000)
Slater, P.J., Cockayne, E.J., Hedetniemi, S.T.: Information dissemination in trees. SIAM J. Comput. 10(4), 692–701 (1981)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Bhabak, P., Harutyunyan, H.A. (2015). Constant Approximation for Broadcasting in k-cycle Graph. In: Ganguly, S., Krishnamurti, R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2015. Lecture Notes in Computer Science, vol 8959. Springer, Cham. https://doi.org/10.1007/978-3-319-14974-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-14974-5_3
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-14973-8
Online ISBN: 978-3-319-14974-5
eBook Packages: Computer ScienceComputer Science (R0)