Self-Stabilizing Algorithms for {k}-Domination.

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 ΣjεN[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. [ABSTRACT FROM AUTHOR]