In this paper we proposed a new Minimum Connected Dominating Set [MCDS] algorithm. This algorithm achieves energy efficiency by minimizing the Broadcast Storm Problem[1]. The connected dominating set (CDS) is widely used as a virtual backbone in mobile ad-hoc networks. Here the MCDS is a distributed algorithm based on Unit Disk Graph[7]. The node's mobility and residual energy are considered as parameters in construction of stable MCDS. The time complexity of this algorithm is O(n) and the message complexity is O(n). The performance evaluation of this algorithm yields better results in dense networks as well as sparse networks. Size of the MCDS is also small compared to other distributed algorithms[8][9][10].
For a simple, undirected, connected graph [Formula: see text], a function [Formula: see text] which satisfies the following conditions is called a total Roman {3}-dominating function (TR3DF) of [Formula: see text] with weight [Formula: see text]: (C1) For every vertex [Formula: see text] if [Formula: see text], then [Formula: see text] has [Formula: see text] ([Formula: see text]) neighbors such that whose sum is at least 3, and if [Formula: see text], then [Formula: see text] has [Formula: see text] ([Formula: see text]) neighbors such that whose sum is at least 2. (C2) The subgraph induced by the set of vertices labeled one, two or three has no isolated vertices. For a graph [Formula: see text], the smallest possible weight of a TR3DF of [Formula: see text] denoted [Formula: see text] is known as the total Roman[Formula: see text]-domination number of [Formula: see text]. The problem of determining [Formula: see text] of a graph [Formula: see text] is called minimum total Roman {3}-domination problem (MTR3DP). In this paper, we show that the problem of deciding if [Formula: see text] has a TR3DF of weight at most [Formula: see text] for chordal graphs is NP-complete. We also show that MTR3DP is polynomial time solvable for bounded treewidth graphs, chain graphs and threshold graphs. We design a [Formula: see text]-approximation algorithm for the MTR3DP and show that the same cannot have [Formula: see text] ratio approximation algorithm for any [Formula: see text] unless NP [Formula: see text]. Next, we show that MTR3DP is APX-complete for graphs with [Formula: see text]. We also show that the domination and total Roman {3}-domination problems are not equivalent in computational complexity aspects. Finally, we present an integer linear programming formulation for MTR3DP.
In this paper a new Hybrid Minimum ConnectedDominating Set IMCDSI algorithm is proposed. This algorithm achieves energy efficiency by minimizing the Broadcast Storm Problem [I]. The minimum connected dominating set (MCDS) is widely used as a virtual spine for mobile ad-hoc networks. Here the MCDS is a mixture of Centralized and Distributed approaches based on Unit Disk Graph [2]. The node's mobility and energy are also considered in the maintenance of MCDS. The time complexity of this algorithm is 0 (n) and the message complexity is 0 (n). The performance evaluation of this algorithm yields better results in both dense and sparse networks. Size of the MCDS is also optimal compared to other MCDS algorithms [3] [4] [5]. Index Terms-MANET, Minimum connected Dominating Set (MCDS), Broadcast Storm Problem, Mobility, Energy. I. [NTRODUCT[ON Mobile wireless ad-hoc networks have predominant applications in military battle field, disaster relief, surveillance, sensing and monitoring, Instantaneous Networks etc, Mobi[e ad hoc network (MANET) is a special kind of wireless network environment. [t is different from the traditional wireless networks. Ad-hoc network is a collection of autonomous arbitrarily located wireless nodes. It is an infrastructure less network with dynamic topology. The nodes should be complex to act as sender, receiver and intermediate forwarder. Because of dynamic topology they frequently advertises the control information which is a flooding (or) broadcasting. Considering the environment mentioned above, several ad hoc routing protocols were proposed in order to find out and maintain the multi-hop route with packet delivery reliability in MANETs. Generally the routing protocols are classified into two types reactive and proactive. These routing generally expect the shortest route from the source to destination. For instance, in the case of on-demand ad hoc routing protocols such as DSR[7] and AODV[8][9], whenever the source wishes to communicate with the destination, the source initiates the route discovery procedure by broadcasting route request (RREQ) packets to the network. These control packets are delivered to the destination using a number of nodes in the 978-1-4799-3448-5/13/$31.00 network. These routing protocols allow the source to dynamically establish a route consisting of several intermediate relaying nodes to the destination. [n proactive routing, tables are maintained and updated frequently, like DSDV. A. Broadcast Storm ProblemBroadcasting is the basic operation in ad-hoc routing protocols both proactive and reactive. A host, on receiving a broadcast message for the first time will rebroadcast the message into network. Proactive routing protocols disseminate control information like routing table updates throughout the ad-hoc network using simple flooding, example Destination Sequenced Distance Vector (DSDV) [24]. In Reactive routing protocol route discovery requires that a "route request"(RREQ) packet be blindly flooded throughout the network.When the destination or a node with an acti...
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