Self-stabilizing algorithms for {k}-domination

  • Authors:

  • Martin Gairing;Stephen T. Hedetniemi;Petter Kristiansen;Alice A. McRae

  • Affiliations:

  • Faculty of Computer Science, Electrical Engineering and Mathematics, University of Paderborn, Paderborn, Germany;Department of Computer Science, Clemson University, Clemson, SC;Department of Informatics, University of Bergen, Norway;Department of Computer Science, Appalachian State University, Boone, NC

  • Venue:
  • SSS'03 Proceedings of the 6th international conference on Self-stabilizing systems
  • Year:
  • 2003

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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 Σj∈N[i] f(j) ≥ k for all i ∈ 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.