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**1 - 2**of**2**### Abstract Bounded-distance multi-clusterhead formation in wireless ad hoc networks

, 2006

"... We present a clustering technique addressing redundancy for bounded-distance clusters, which means being able to determine the minimum number of cluster-heads per node, and the maximum distance from nodes to their cluster-heads. This problem is similar to computing a (k,r)-dominating set,(k,r)-DS, o ..."

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We present a clustering technique addressing redundancy for bounded-distance clusters, which means being able to determine the minimum number of cluster-heads per node, and the maximum distance from nodes to their cluster-heads. This problem is similar to computing a (k,r)-dominating set,(k,r)-DS, of the network. (k,r)-DS is defined as the problem of selecting a minimum cardinality vertex set D of the network such that every vertex u not in D is at a distance smaller than or equal to r from at least k vertices in D. In mobile ad hoc networks (MANETs), clusters should be computed distributively, because the topology may change frequently. We present the first centralized and distributed solutions to the (k,r)-DS problem for arbitrary topologies. The centralized algorithm computes a (k Æ lnD)-approximation, where D is the largest cardinality among all r-hop neighborhoods in the network. The distributed approach is extended for clustering applications, while the centralized is used as a lower bound for comparison purposes. Extensive simulations are used to compare the distributed solution with the centralized one. As a case study, we propose a novel multi-core multicast protocol that applies the distributed solution for the election of cores. The new protocol is compared against PUMA, one of the best performing multicast protocols for MANETS. Simulation results show that the new protocol outperforms PUMA on

### Delay Preserving Substructures in Wireless Networks Using Edge Difference between a

"... Abstract—In practice, wireless networks has the property that the signal strength attenuates with respect to the distance from the base station, it could be better if the nodes at two hop away are considered for better quality of service. In this paper, we propose a procedure to identify delay prese ..."

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Abstract—In practice, wireless networks has the property that the signal strength attenuates with respect to the distance from the base station, it could be better if the nodes at two hop away are considered for better quality of service. In this paper, we propose a procedure to identify delay preserving substructures for a given wireless ad-hoc network using a new graph operation G 2 – E (G) = G * (Edge difference of square graph of a given graph and the original graph). This operation helps to analyze some induced substructures, which preserve delay in communication among them. This operation G * on a given graph will induce a graph, in which 1-hop neighbors of any node are at 2-hop distance in the original network. In this paper, we also identify some delay preserving substructures in G*, which are (i) set of all nodes, which are mutually at 2-hop distance in G that will form a clique in G*, (ii) set of nodes which forms an odd cycle C2k+1 in G, will form an odd cycle in G* and the set of nodes which form a even cycle C2k in G that will form two disjoint companion cycles ( of same parity odd/even) of length k in G*, (iii) every path of length 2k+1 or 2k in G will induce two disjoint paths of length k in G*, and (iv) set of nodes in G*, which induces a maximal connected sub graph with radius 1 (which identifies a substructure with radius equal 2 and diameter at most 4 in G). The above delay preserving sub structures will behave as good clusters in the original network. Keywords—Clique, cycles, delay preserving substructures, maximal connected sub graph. A I.