Maintenance of a Spanning Tree For Dynamic Graphs by Mobile Agents and Local Computations

Ktari, Mouna; Haddar, Mohamed Amine; Mosbah, Mohamed; Hadj Kacem, Ahmed

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 51 (2017) no. 2, pp. 51-70.

The problem of constructing and maintaining a spanning tree in dynamic networks is important in distributed systems. Trees are essential structures in various communication protocols such as information broadcasting, routing, etc. In a distributed computing environment, the solution of this problem has many practical motivations. To make designing distributed algorithm easier, we model this latter with a local computation model. Based on the mobile agent paradigm, we present in this paper a distributed algorithm that maintain a hierarchical spanning tree in dynamic networks. We study all topological events that may affect the structure of the spanning tree: we address the appearance and the disappearance of places and communication channels.

A. Renyi and P. Erdos, On the evolution of random graphs, In Publication of the Mathematical Institute of the Hungarian Academy of Sciences (1960) 17–61. | MR | Zbl

B. Yener and C.C. Bilgin, Dynamic network evolution: Models, clustering, anomaly detection. IEEE Networks (2006).

F. Chung, L. Lu and W. Aeillo, A Random Graph Model for Massive Graphs, In Proceedings of the Thirty-second Annual ACM Symposium on Theory of Computing, ser. Portland, Oregon, USA (2000) 171–180. | MR | Zbl

A.L. Barabasi and R. Albert, Emergence of Scaling in Random Networks. Science 286 (1999) 509–512. | DOI | MR | Zbl

A. Ferreria, On models and algorithms for dynamic communication networks: The case for evolving graphs, In $4^e$ rencontres francophones sur les Aspects Algorithmiques des Telecommunications (ALGOTEL), Mèze, France (2002).

E. Sopena, I. Litovsky and Y. Métivier, Handbook of graph grammars and computing by graph transformation. World Scientific Publishing Co., Inc (1999).

A. Sellami, M. Bauderon, M. Mosbah, S. Gruner and Y. Métivier, Visualization of Distributed Algorithms Based on Graph Relabelling Systems. Electron. Notes Theoret. Comput. Sci. 50 (2001) 227–237. | Zbl

A. Hadj Kacem, M.A. Haddar, M. Mosbah, M. Jmail and Y. Métivier, A Distributed Computational Model for Mobile Agents. In Agent Computing and Multi-Agent Systems, 10th Pacific Rim International Conference on Multi-Agents, PRIMA (2007) 416–421.

A. Hadj Kacem, M.A. Haddar, M. Mosbah and Y. Métivier, Proving Distributed Algorithms for Mobile Agents: Examples of Spanning Tree Computation in Anonymous Networks. In Distributed Computing and Networking, 9th International Conference, ICDCN (2008) 286–291. | Zbl

M.A. Haddar, Codage d’algorithmes distribués d’agents mobiles à l’aide de calculs locaux. Ph.D. thesis. University of Bordeaux 1, France (2011).

D.B. Lange and M. Oshima, Seven good reasons for mobile agents. Commun. ACM (1999) 88–89.

A. Hadj Kacem, M. Ktari, M.A. Haddar and M. Mosbah, Proving Distributed Algorithms for Mobile Agents: Examples of Spanning Tree Computation in Dynamic Networks. In 12th ACS/IEEE International Conference on Computer Systems and Applications AICCSA (2015).

A. Hadj Kacem, M. Ktari, M.A. Haddar and M. Mosbah, Distributed Computation and Maintenance of a Spanning Tree in Dynamic Netrworks by Mobile Agents. In The 30th IEEE International Conference on Advanced Information Networking and Applications AINA (2016).

I. Litovsky and Y. Métivier, Computing trees with graph rewriting systems with priorities. Tree Automata and Languages (1992) 115–140. | MR | Zbl

M. Yamashita and T. Kameda, Computing on anonymous networks: Part I-characterizing the solvable cases. IEEE Transactions on Parallel and Distributed Systems (1996).

M. Yamashita and T. Kameda, Computing on Anonymous Networks: Part II Decision and Membership Problems. In IEEE Trans. Parallel Distrib. Syst. IEEE Press (1996).

I. Litovsky and Y. Métivier, Computing with graph rewriting systems with priorities. Theoretical Computer Science (1993). | MR | Zbl

A. Muscholl, E. Godard and Y. Métivier, The power of local computations in graphs with initial knowledge. In Theory and applications of graph transformations, Vol. 1764 of Lecture notes in computer science (2000). | MR | Zbl

A. Casteigts, C. Johnen, M. Bargon, S. Chaumette and Y.M. Neggaz, Maintaining a spanning forest in highly dynamic networks: The synchronous case. In vol. 8878 of Lecture Notes in Computer Science. Springer (2014) | MR

H. Baala, J. Gaber, M. Bui, O. Flauzac and T. El-Ghazawi, A self-stabilizing distributed algorithm for spanning tree construction in wireless ad hoc networks. J. Parallel Distrib. Comput. 63 (2003) 97–104. | DOI | Zbl

A. Casteigts, F. Guinand, S. Chaumette and Y. Pigne, Distributed maintenance of anytime available spanning trees in dynamic networks. In ADHOC-NOW. In vol. 7960 of Lecture Notes in Computer Science. Springer, Berlin, Heidelberg (2013).

E. Sopena and I. Litovsky, Graph relabelling systems and distributed algorithms. In Handbook of graph grammars and computing by graph transformation. World scientific (2001) 1–56.

A. Zemmari, M. Mosbah and S. Abbas, Distributed Computation of a Spanning Tree in a Dynamic Graph by Mobile Agents. In IEEE International Conference on Engineering of Intelligent Systems ICEIS (2006).

F. Kuhn, N.A. Lynch and R. Oshman, Distributed computation in dynamic networks. In Proc. of the 42nd ACM Symposium on Theory of Computing, STOC (2010) 513–522. | MR | Zbl

M.R. Henzinger and V. King, Maintaining minimum spanning trees in dynamic graphs. In Automata, Languages and Programming: 24th International Colloquium (1997) 594–604. | MR

R.E. Tarjan and R.F. Werneck, Dynamic Trees in Practice. In Experimental Algorithms: 6th International Workshop (2007) 80–93. | MR

S. Kutten and A. Porat, Maintenance of a Spanning Tree in Dynamic Networks. In Proc. of the 13th International Symposium on Distributed Computing (1999) 342–355.