International audienceA p-star is a complete bipartite graph K 1,p with one center node and p leaf nodes. In this paper we propose the first distributed self-stabilizing algorithm for graph decomposition into p-stars. For a graph G and an integer p ≥ 1, this decomposition provides disjoint components of G where each component forms a p-star. We prove convergence and correctness of the algorithm under an unfair distributed daemon. The stabilization time is 2⌊n/(p+1)⌋+2 rounds
In computer networks area, the minimal dominating sets (MDS) and maximal independent sets (MIS) structures are very useful for creating virtual network overlays. Often, these set structures are used for designing efficient protocols in wireless sensor and ad-hoc networks. In this paper, we give a particular interest to one kind of these sets, called Independent Strong Dominating Set (ISD-set). In addition to its domination and independence properties, the ISD-set considers also node’s degrees that make it very useful in practical applications where nodes with larger degrees play important role in the networks. For example, some network clustering protocols chose nodes with large degrees to be cluster-heads, which is exactly the result obtained by an ISD-set algorithm. Thence, we propose the first distributed self-stabilizing algorithm for computing an ISD-set of an arbitrary graph (called ISDS). Then, we prove that ISDS algorithm operates under the unfair distributed scheduler and converges after at most [Formula: see text] rounds requiring only [Formula: see text] space memory per node where Δ is the maximum node degree. The complexity of ISDS algorithm in rounds has the same order as the best known self-stabilizing algorithms for finding MDS and MIS. Moreover, performed simulations and comparisons with well-known self-stabilizing algorithms for MDS and MIS problems showed the efficiency of ISDS, especially for reducing the cardinality of dominating sets founded by the algorithms.
International audienceSelf-monitoring is a simple and effective mechanism for the security of wireless sensor networks (WSNs), especially to cope against compromised nodes. A node v can monitor an edge e if both end-nodes of e are neighbors of v; i.e., e together with v forms a triangle in thegraph. Moreover, some edges need more than one monitor. Finding a set of monitoring nodes satisfying all monitoring constraints is called the edge-monitoring problem. The minimum edge-monitoring problem is long known to be NP-complete. In this paper, we present a novelsilent self-stabilizing algorithm for computing a minimal edge-monitoring set. Correctness and termination are proven for the unfair distributed scheduler
The triangle partition problem is a generalization of the well-known graph matching problem consisting of finding the maximum number of independent edges in a given graph, i.e., edges with no common node. Triangle partition instead aims to find the maximum number of disjoint triangles. The triangle partition problem is known to be NP-complete. Thus, in this paper, the focus is on the local maximization variant, called maximal triangle partition (MTP). Thus, paper presents a new self-stabilizing algorithm for MTP that converges in O(m) moves under the unfair distributed daemon.
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