We present a new tool called the ”mv- decomposition”, and we describe some interesting algorithmic properties about it. We propose an algorithm with a complexity of $O(m)$ to build a mv-decomposition for each bipartite graph. We use this mv-decomposition to propose a solution to the distance-2 broadcast problem in a synchronous multi-hops radio networks where adjacent transmissions are subject to interferences. More precisely, we propose two algorithms of resolution: the first one guarantees a complete distance-2 broadcast scheme using $O((log n )2)$ slots for a time complexity of $O (m (log n)2)$, while the second builds a solution with a minimal number of transmissions for a time complexity of $O(m)$.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
N. Alon, A. Bar-Noy, N. Linial, and D. Peleg. A lower bound for radio broadcast. J. Comput. Syst. Sci., 43(2):290–298, 1991.
R. Bar-Yehuda, O. Goldreich, and A. Itai. On the time-complexity of broadcast in multi-hop radio networks: An exponential gap between determinism and randomization. J. Comput. Syst. Sci., 45(1):104–126, 1992.
D. Bruschi and M. Del Pinto. Lower bounds for the broadcast problit in mobile radio networks. Distrib. Comput., 10(3):129–135, 1997.
I. Chlamtac and S. Kutten. On broadcasting in radio networks - Problit analysis and protocol design. IEEE Transactions on Communications, 33:1240–1246, December 1985.
I. Chlamtac and O. Weinstein. The wave expansion approach to broadcasting in multihop radio network. IEEE Transaction Communication, (39):426–433, 1991.
B. Chlebus, L. G¸sieniec, A. Gibbons, A. Pelc, and W. Rytter. Deterministic broadcasting in unknown radio networks. In SODA ’00: Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms, pages 861–870, Philadelphia, PA, USA, 2000. Society for Industrial and Applied Mathitatics.
B. Chlebus, L. G¸sieniec, A. Östlin, and J.M. Robson. Deterministic radio broadcasting. In ICALP ’00: Proceedings of the 27th International Colloquium on Automata, Languages and Programming, pages 717–728, London, UK, 2000. Springer-Verlag.
M. Chrobak, L. Gasieniec, and W. Rytter. Fast broadcasting and gossiping in radio networks. J. Algorithms, 43(2):177–189, 2002.
I. Gaber and Y. Mansour. Broadcast in radio networks. In SODA ’95: Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms, pages 577–585, Philadelphia, PA, USA, 1995. Society for Industrial and Applied Mathitatics.
G. Kortsarz and M. Elkin. An improved algorithm for radio broadcast (submitted), 2005.
D. R. Kowalski and A. Pelc. Centralized deterministic broadcasting in undirected multi-hop radio networks. In APPROX-RANDOM, pages 171–182, 2004.
G. De Marco and A. Pelc. Faster broadcasting in unknown radio networks. Inf. Process. Lett., 79(2):53–56, 2001.
D. Peleg. Deterministic radio broadcast with no topological knowledge, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 IFIP International Federation for Information Processing
About this paper
Cite this paper
Cogis, O., Darties, B., Durand, S., König, JC., Simonet, G. (2008). The mv-decomposition: definition and application to the distance-2 broadcast problem in multi-hops radio networks. In: Ausiello, G., Karhumäki, J., Mauri, G., Ong, L. (eds) Fifth Ifip International Conference On Theoretical Computer Science – Tcs 2008. IFIP International Federation for Information Processing, vol 273. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09680-3_8
Download citation
DOI: https://doi.org/10.1007/978-0-387-09680-3_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-09679-7
Online ISBN: 978-0-387-09680-3
eBook Packages: Computer ScienceComputer Science (R0)