Abstract
A p-star is a complete bipartite graph K 1,p with one center node and p leaf nodes. In this paper we propose the first distributed self-stabilizing algorithm for graph decomposition into p-stars. For a graph G and an integer pāā„ā1, this decomposition provides disjoint components of G where each component forms a p-star. We prove convergence and correctness of the algorithm under an unfair distributed daemon. The stabilization time is \(2\lfloor \frac{n}{p+1}\rfloor +2\) rounds.
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References
Andreev, K., RƤcke, H.: Balanced graph partitioning. In: Proceedings 16th Annual ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2004, pp. 120ā124 (2004)
Bein, D., Datta, A.K., Jagganagari, C.H., Villain, V.: A self-stabilizing link-cluster algorithm in mobile ad hoc networks. In: ISPAN, pp. 436ā441 (2005)
Belkouch, F., Bui, M., Chen, L., Datta, A.: Self-stabilizing deterministic network decomposition. J. Parallel Distrib. Comput.Ā 62(4), 696ā714 (2002)
Bendjoudi, A., Melab, N., Talbi, E.-G.: P2p design and implementation of a parallel branch and bound algorithm for grids. Int. J. Grid Util. Comput.Ā 1(2), 159ā168 (2009)
Blin, L., Potop-Butucaru, M.G., Rovedakis, S., Tixeuil, S.: Loop-free super-stabilizing spanning tree construction. In: Dolev, S., Cobb, J., Fischer, M., Yung, M. (eds.) SSS 2010. LNCS, vol.Ā 6366, pp. 50ā64. Springer, Heidelberg (2010)
Bryant, D., El-Zanati, S., Eynden, C.H.: Star factorizations of graph products. J. Graph. TheoryĀ 36(2), 59ā66 (2001)
Cain, P.: Decomposition of complete graphs into stars. Bull. Austral. Math. Soc.Ā 10, 23ā30 (1974)
Caron, E., Datta, A.K., Depardon, B., Larmore, L.L.: A self-stabilizing K-clustering algorithm using an arbitrary metric. In: Sips, H., Epema, D., Lin, H.-X. (eds.) Euro-Par 2009. LNCS, vol.Ā 5704, pp. 602ā614. Springer, Heidelberg (2009)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACMĀ 17(11), 643ā644 (1974)
Dolev, S.: Self-stabilization. MIT Press (2000)
Dubois, S., Tixeuil, S.: A taxonomy of daemons in self-stabilization. CoRR, abs/1110.0334 (2011)
Gnanadhas, N., Ebin Raja Merly, E.: Linear star decomposition of lobster. Int. J. of Contemp. Math. SciencesĀ 7(6), 251ā261 (2012)
Goddard, W., Hedetniemi, S., Jacobs, D., Srimani, K.: Self-stabilizing protocols for maximal matching and maximal independent sets for ad hoc networks. In: Proceedings of the 17th International Symposium on Parallel and Distributed Processing, IPDPS, p. 162.2 (2003)
Guellati, N., Kheddouci, H.: A survey on self-stabilizing algorithms for independence, domination, coloring, and matching in graphs. J. Parallel Distrib. Comput.Ā (4), 406ā415 (2010)
Johnen, C., Nguyen, L.H.: Robust self-stabilizing clustering algorithm. In: Shvartsman, A. (ed.) OPODIS 2006. LNCS, vol.Ā 4305, pp. 410ā424. Springer, Heidelberg (2006)
Kirkpatrick, D., Hell, P.: On the completeness of a generalized matching problem. In: STOC, pp. 240ā245. ACM, New York (1978)
Kirkpatrick, D., Hell, P.: On the complexity of general graph factor problems. SIAM Journal on ComputingĀ 12(3), 601ā609 (1983)
Lee, H., Lin, C.H.: Balanced star decompositions of regular multigraphs and Ī»-fold complete bipartite graphs. Discrete MathematicsĀ 301(2-3), 195ā206 (2005)
Lemmouchi, S., Haddad, M., Kheddouci, H.: Study of robustness of community emerged from exchanges in networks communication. In: Proceedings 11th International ACM Conference on Management of Emergent Digital EcoSystems, MEDES, pp. 189ā196 (2011)
Lemmouchi, S., Haddad, M., Kheddouci, H.: Robustness study of emerged communities from exchanges in peer-to-peer networks. Computer CommunicationsĀ 36(1011), 1145ā1158 (2013)
Lin, C., Shyu, T.: A necessary and sufficient condition for the star decomposition of complete graphs. J. Graph TheoryĀ 23(4), 361ā364 (1996)
Manne, F., Mjelde, M., Pilard, L., Tixeuil, S.: A new self-stabilizing maximal matching algorithm. Theor. Comput. Sci.Ā 410(14), 1336ā1345 (2009)
Mezmaz, M., Melab, N., Talbi, E.-G.: A Grid-based Parallel Approach of the Multi-Objective Branch and Bound. In: Proceedings 15th Euromicro International Conference on Parallel, Distributed and Network-Based Processing, PDP, pp. 23ā30 (2007)
Neggazi, B., Haddad, M., Kheddouci, H.: Self-stabilizing algorithm for maximal graph partitioning into triangles. In: Richa, A.W., Scheideler, C. (eds.) SSS 2012. LNCS, vol.Ā 7596, pp. 31ā42. Springer, Heidelberg (2012)
Pothen, A.: Graph partitioning algorithms with applications to scientific computing. Technical report, Norfolk, VA, USA (1997)
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Neggazi, B., Turau, V., Haddad, M., Kheddouci, H. (2013). A Self-stabilizing Algorithm for Maximal p-Star Decomposition of General Graphs. In: Higashino, T., Katayama, Y., Masuzawa, T., Potop-Butucaru, M., Yamashita, M. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2013. Lecture Notes in Computer Science, vol 8255. Springer, Cham. https://doi.org/10.1007/978-3-319-03089-0_6
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DOI: https://doi.org/10.1007/978-3-319-03089-0_6
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