Abstract
Mobile ad hoc networks as well as grid platforms are distributed, changing and error prone environments. Communication costs within such infrastructures can be improved, or at least bounded, by using k-clustering. A k-clustering of a graph, is a partition of the nodes into disjoint sets, called clusters, in which every node is distance at most k from a designated node in its cluster, called the clusterhead. A self-stabilizing asynchronous distributed algorithm is given for constructing a k-clustering of a connected network of processes with unique IDs and weighted edges. The algorithm is comparison-based, takes O(nk) time, and uses O(logn + logk) space per process , where n is the size of the network. To the best of our knowledge, this is the first distributed solution to the k-clustering problem on weighted graphs.
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Caron, E., Desprez, F.: DIET: A scalable toolbox to build network enabled servers on the grid. Int. Jour. of HPC Applications 20(3), 335–352 (2006)
YarKhan, A., Dongarra, J., Seymour, K.: GridSolve: The Evolution of Network Enabled Solver. In: Patrick Gaffney, J.C.T.P. (ed.) Grid-Based Problem Solving Environments: IFIP TC2/WG 2.5 Working Conference on Grid-Based Problem Solving Environments, Prescott, AZ, July 2006, pp. 215–226. Springer, Heidelberg (2007)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)
Amis, A.D., Prakash, R., Vuong, T.H., Huynh, D.T.: Max-min d-cluster formation in wireless ad hoc networks. In: IEEE INFOCOM, pp. 32–41 (2000)
Spohn, M., Garcia-Luna-Aceves, J.: Bounded-distance multi-clusterhead formation in wireless ad hoc networks. Ad Hoc Networks 5, 504–530 (2004)
Fernandess, Y., Malkhi, D.: K-clustering in wireless ad hoc networks. In: ACM Workshop on Principles of Mobile Computing POMC 2002, pp. 31–37 (2002)
Datta, A.K., Larmore, L.L., Vemula, P.: A self-stabilizing O(k)-time k-clustering algorithm. Computer Journal (2008)
Dolev, S.: Self-stabilization. MIT Press, Cambridge (2000)
Dolev, S., Israeli, A., Moran, S.: Uniform dynamic self-stabilizing leader election. IEEE Trans. Parallel Distrib. Syst. 8(4), 424–440 (1997)
Caron, E., Datta, A.K., Depardon, B., Larmore, L.L.: A self-stabilizing k-clustering algorithm using an arbitrary metric. Technical Report RR2008-31, Laboratoire de l’Informatique du Parallélisme, LIP (2008)
Datta, A.K., Larmore, L.L., Vemula, P.: Self-stabilizing leader election in optimal space. In: 10th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), Detroit, MI (November 2008)
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Caron, E., Datta, A.K., Depardon, B., Larmore, L.L. (2009). A Self-stabilizing K-Clustering Algorithm Using an Arbitrary Metric. In: Sips, H., Epema, D., Lin, HX. (eds) Euro-Par 2009 Parallel Processing. Euro-Par 2009. Lecture Notes in Computer Science, vol 5704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03869-3_57
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DOI: https://doi.org/10.1007/978-3-642-03869-3_57
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