We propose a fast silent self-stabilizing building a k-independent dominating set, named FID. The convergence of protocol FID, is established for any computation under the unfair distributed scheduler. FID reaches a terminal (also legitimate) configuration in at most 4n+k rounds, where n is the network size. FID requires (k + 1)log(n+ 1) bits per node. keywords distributed computing, fault tole...

For a positive integer k, a k-rainbow dominating function of a digraph D is a function f from the vertex set V (D) to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex v ∈ V (D) with f(v) = ∅ the condition u∈N−(v) f(u) = {1, 2, . . . , k} is fulfilled, where N−(v) is the set of in-neighbors of v. A set {f1, f2, . . . , fd} of k-rainbow dominating functions on D with t...

We present an algorithm that constructively produces a solution to the k-dominating set problem for planar graphs in time O(c √ n), where c = 36 √ 34. To obtain this result, we show that the treewidth of a planar graph with domination number γ(G) is O( √ γ(G)), and that such a tree decomposition can be found in O( √ γ(G)n) time. The same technique can be used to show that the k-face cover probl...

Given a graph G, a k-dominating set of G is a subset S of its vertices with the property that every vertex of G is either in S or has at least k neighbors in S. We present a new incremental local algorithm to construct a k-dominating set. The algorithm constructs a monotone family of dominating sets D1 ⊆ D2 . . . ⊆ Di . . . ⊆ Dk such that each Di is an i-dominating set. For unit disk graphs, th...

We propose a memory efficient self-stabilizing protocol building k-independent dominating sets. A k-independent dominating set is a k-independent set and a kdominating set. A set of nodes, I, is k-independent if the distance between any pair of nodes in I is at least k + 1. A set of nodes, D, is a k-dominating if every node is within distance k of a node of D. Our algorithm, named SID, is silen...

We propose a memory efficient self-stabilizing protocol building k-independent dominating sets. A k-independent dominating set is a k-independent set and a kdominating set. A set of nodes, I, is k-independent if the distance between any pair of nodes in I is at least k + 1. A set of nodes, D, is a k-dominating if every node is within distance k of a node of D. Our algorithm, named SID, is silen...

We propose a memory efficient self-stabilizing protocol building k-independent dominating sets. A k-independent dominating set is a k-independent set and a kdominating set. A set of nodes, I, is k-independent if the distance between any pair of nodes in I is at least k + 1. A set of nodes, D, is a k-dominating if every node is within distance k of a node of D. Our algorithm, named SID, is silen...

We propose a fast, silent self-stabilizing protocol building a distance-k independent dominating set, named FID. The convergence of the protocol FID is established for any computation under the unfair distributed scheduler. The protocol FID reaches a terminal (also legitimate) configuration in at most 4n+k rounds, where n is the network size; it requires (k + 1)log(n + 1) bits per node. keyword...