Given a graph, a connected dominating set is a subset of vertices such that every vertex is either in the subset or adjacent to a vertex in the subset and the subgraph induced by the subset is connected.A minimum connected dominating set is such a vertex subset with minimum cardinality. In this paper, we present a new one-step greedy approximation with performance ratio ln + 2 where is the maxi...

Let G = (V; E) be a /nite and undirected graph without loops and multiple edges. An edge is said to dominate itself and any edge adjacent to it. A subset D of E is called a perfect edge dominating set if every edge of E \ D is dominated by exactly one edge in D and an e cient edge dominating set if every edge of E is dominated by exactly one edge in D. The perfect (e cient) edge domination prob...

For a given graph G = (V,E), a set D ⊆ V (G) is said to be an outerconnected dominating set if D is dominating and the graph G−D is connected. The outer-connected domination number of a graph G, denoted by γ̃c(G), is the cardinality of a minimum outer-connected dominating set of G. We study several properties of outer-connected dominating sets and give some bounds on the outer-connected dominati...

We present an O∗(1.3160n)-time algorithm for the edge dominating set problem in an n-vertex graph, which improves previous exact algorithms for this problem. The algorithm is analyzed by using the “Measure and Conquer method.” We design new branching rules based on conceptually simple local structures, called “clique-producing vertices/cycles,” which significantly simplify the algorithm and its...

An edge dominating set D of graph G = (V; E) is a set of edges such that every edge not in D is adjacent to at least an edge in D. In this paper we develop polynomial time algorithms for nding a minimum edge dominating set for a cotriangulated graph and a bipartite permutation graph.

Many prominent applications in wireless sensor networks require collected information has to be routed to end nodes in an efficient manner. In general, Connected Dominating Set (CDS) based routing is a promising approach for enhancing the routing efficiency in sensor networks. Our idea is to generate a quality based CDS algorithm, which can resolve the standing issues like cardinality, risk fac...

Connected Dominating Set (CDS) has been a well known approach for constructing a virtual backbone to alleviate the broadcasting storm in wireless networks. Previous literature modeled the wireless network in a 2-dimensional plane and looked for the approximated Minimum CDS (MCDS) distributed or centralized to construct the virtual backbone of the wireless network. However, in some real situatio...

3 Energy efficient broadcasting without range adjustment 10 3.1 Clustering based broadcasting protocols . . . . . . . . . . . . . . . . 11 3.2 Neighbor elimination based broadcasting protocols . . . . . . . . . . 11 3.3 Distance-based and probabilistic protocols . . . . . . . . . . . . . . . 11 3.4 Coverage and connected dominating set based broadcasting . . . . . 12 3.5 Forwarding neighbors ba...

For any edge of an isolate free graph , , 〈 〉 is the subgraph induced by the vertices adjacent to u and v in G. We say that an edge x, edominates an edge y if ∈ 〈 〉 . A set ⊆ is an Edge-Edge Dominating Set (EED-set) if every edge in is e-dominated by an edge in L. The edgeedge domination number is the cardinality of a minimum EED-set. We find the relation ship between the new parameter and some...