Abstract
In the self-stabilizing algorithmic paradigm for distributed computing each node has only a local view of the system, yet in a finite amount of time the system converges to a global state, satisfying some desired property. A function f : V (G) → {0, 1, 2, . . . , k} is a {k}-dominating function if Σ jεN[i] f(j) ≥ k for all i ε V (G). In this paper we present self-stabilizing algorithms for finding a minimal {k}-dominating function in an arbitrary graph. Our first algorithm covers the general case, where k is arbitrary. This algorithm requires an exponential number of moves, however we believe that its scheme is interesting on its own, because it can insure that when a node moves, its neighbors hold correct values in their variables. For the case that k = 2 we propose a linear time self-stabilizing algorithm.
Supported by the IST Program of the EU under contract numbers IST-1999-14186 (ALCOM-FT) and IST-2001-33116 (FLAGS).
Research supported in part by NSF Grant CCR-0222648.
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Gairing, M., Hedetniemi, S.T., Kristiansen, P., McRae, A.A. (2003). Self-Stabilizing Algorithms for {k}-Domination. In: Huang, ST., Herman, T. (eds) Self-Stabilizing Systems. SSS 2003. Lecture Notes in Computer Science, vol 2704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45032-7_4
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DOI: https://doi.org/10.1007/3-540-45032-7_4
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