AN EVOLUTIONARY ALGORITHMIC APPROACH TO CONSTRUCT CONNECTED DOMINATING SET IN MANETS

D.Manohari1 , Dr. G.S. Anandha Mala2

1Associate Professor, St. Joseph’s College of Engineering, Chennai Email id: mano_thosh @yahoo.com

2 Professor, St. Joseph’s College of Engineering, Chennai Email id: gs.anandhamala@gmail.com

Keywords : MANETs, Connected Dominating Set, Genetic Algorithm, Evolutionary Algorithm. Abstract A virtual backbone of a MANETs is typically the Connected Dominating Set (CDS) of the graph representation of the network. The CDS in the MANETs helps to increase the efficiency of the network and extends the life span of the network. While existing CDS protocols are successful in constructing CDS of s mall size, they either require localized informat ion beyond immediate neighbors, lack the mechanism to properly handle nodal mobility, o r involve lengthy recovery procedure when CDS becomes corrupted. In general, the smaller the CDS is, the less communicat ion and storage overhead the protocols making use of CDS will incur. Hence, it is desired that the size of the CDS for mobile ad hoc networks to be as small as possible. On the other hand, it is known that the problem of finding the Minimum Connected Dominating Set (MCDS) is NP-hard. As the construction of MCDS is an NP-hard problem, this proposed work incorporates an evolutionary algorithmic approach using Genetic algorithm to minimize the number of nodes in the CDS.

1. Introduction 1.1 Mobile Ad Hoc Networks – MANETs

A mobile ad hoc network (MANET) consists of many mobile nodes that can communicate with each other directly or through intermediate nodes. Often, hosts in a MANET operate with batteries and can roam freely, and thus, a host may exhaust its power or move away, giving no notice to its neighboring nodes, causing changes in network topology [3]. One of the important and challenging problems in the design of ad hoc networks is the development of an efficient routing protocol that can provide high-quality communications among mobile hosts.

1.2 Connected Dominating set Given an undirected graph G =(V ,E) a subset C V is a Connected Dominating Set (CDS) of G if, for each node

u V , u is either in C or there exists a node v C such that uv E and the sub graph induced by C, i.e., G(C), is connected. The nodes in the CDS are called dominators and other nodes are called dominatees. The CDS has been extensively used for routing and broadcasting in wireless adhoc networks. This Connected Dominating Set helps in efficient transmission of the data. Every other node in the network is d irectly adjacent to at least one node in the CDS. The node in the CDS has the information about its neighbors which helps in efficient transmission. The key to scalability and efficiency in traditional computer networks is the organization of the network infrastructure into a hierarch ical structure. However, due to the lack of a network infrastructure, sensor networks and MANETs are inherently flat. Hence to overcome this problem connected dominating sets are used. The fo llowing Table 1.1 depicts the applicat ions of CDS.

Table 1.1 Applications of CDS

Figure 1.1 Structure of CDS

CDS as virtual back bone.

Reduction of communication Overhead and reliability.

CDS – in Broadcast.

Only nodes in CDS relay messages . Thus Reduce communication cost and reduce redundant traffic.

CDS- in Unicast.

Only the nodes in CDS maintain routing tables. Routing information is localized. Save storage space.

Connected Dominating Set, C is a dominating set of G which induces a connected sub graph of G. One approach to constructing a CDS is to find a Maximal Independent Set (MIS), and then add additional vertices as needed to connect the nodes in the MIS.

1.3 Genetic algorithm

An evolutionary algorithm Genetic Algorithm (GA) is applied in this work to find the Minimum Connected Dominating Set (MCDS). It can quickly adapt to environmental changes (i.e., the network topology changes) and produce high-quality solutions after each change. Crossover simply takes two genomes, splits them at some point and produces two new genomes by swapping the end parts as shown in the Fig. 1.2.

Figure 1.2 Example for single point cross over

The split occurs at a randomly chosen point along the length of the genome, and the split only occurs if a probability test is passed. This is typically set quite high which reflects what happens in nature. The representation of chromosomes differs for each prob lem [6]. The Table 1.2 shows how the terms of genetic algorithm are represented.

Table 1.2 Representation of nature in GA

2. Literature survey

There had been a lot of issues that were causing few discrepancies in the CDS. Most of these issues were resolved in the works which were done later and few are still on process. Topology control or topology management has always been a hot topic in MANETs since it has close relat ion

to the performance of the control algorithms used in networks for scheduling of transmissions, routing, and broadcasting [4]. Bao and Garcia -Luna-Aceves divided topology control into two categories—one is power control and the other one is hierarchical topology organization. Power control adjusts the power on every node to ensure the connectivity of the network and balance the one-hop neighbor connectivity. Hierarch ical topology control aims to select a subset of nodes in the network serving as backbone over which essential network control functions are supported. In hierarchical topology organization, CDS acts well as a backbone. The research work on selecting a MCDS has never been interrupted because of its dramat ic contributions to wireless networks [5]. It is also well known that computation of a MCDS in a general graph is an NP-hard problem and it is even an NP-hard problem in Unit Disk Graph (UDG) [8]. Thus, much work has been devoted to achieving a better approximat ion ratio in polynomial time. CDS algorithms can be categorized into two types , one is 2-stage and the other one is 1-stage. The 2-stage algorithms can also be div ided into two categories. The main idea of the first category is to construct a Dominating Set (DS) and add more nodes to make the selected DS connected. As a result, a CDS is constructed. In another work, a 2-stage strategy is proposed yielding an approximation ratio of 2H (∂) + 2, where H is a harmonic function. Based on the ideas of Independent Set and Steiner Tree, Min et al proposed an algorithm for constructing a MCDS. The other category is to construct a redundant CDS first, then remove some nodes to get a smaller CDS. The main idea of 1-stage algorithms is to construct a CDS directly skipping any intermediate step. A 1-stage strategy is proposed with approximation rat io of 2H (∂) + 2. Based on the main idea of the 2-stage algorithm, Ruan et al. had modified the selection standard of DS. Therefore, 2-stage is reduced to 1-stage, with approximat ion ratio of 3 +ln (∂).

2.1 Drawbacks

The time taken for data transfer and recovery procedure are too long because the energy associated with the nodes in Connected Dominating Set is not considered so the node might have less power. Since the number of nodes in CDS is not minimized it reduces the efficiency of CDS.

3. Proposed system

The proposed system finds MCDS in two steps. First step finds the CDS using dying algorithm. The categorization of nodes in CDS are dominator node and dominatee node. Second step finds MCDS using an evolutionary algorithmic approach. The evolutionary algorithmic approach used in the proposed system is Genetic algorithm. The informat ion about the immediate neighbors is sufficient for the CDS protocol. In general, nodes in the CDS consume more energy in order to

Nature Genetic algorithm

Chromosomes String

Gene Character

Locus String position

Genotype Population

Phenotype Decoded structure

handle various bypass traffics than nodes outside the set. To prolong the life span of each node, and hence, the network by balancing the energy consumption in the network, nodes should be alternated in being chosen to form a connected dominating set. The reference energy associated with each node is taken into account and plays a major role during the application of genetic algorithm. Since the number of nodes in the CDS is min imized the time taken for convergence and recovery procedure is minimized. Reference energy is associated with each node in the proposed system. Since the energy factor is considered while constructing the CDS it makes the network more energy efficient. The target of power control is to adjust nodes’ transmission range to achieve balanced connectivity, while hierarchical topology organization aims to find a communication backbone from the orig inal network in charge of all forwarding in the network. Routing information is only kept in the virtual backbone, so that routing path search time and communication cost will decrease greatly. The CDS constructed here is a distributed CDS this is more efficient than the centralized CDS. Even if the network size is large this CDS works efficiently as it prohibits centralized computation.

3.1 CDS_Construction

The network of twenty nodes is given as the input to construct CDS. The CDS is constructed from this network. The dying and deleting process is used to construct the CDS and MCDS. This process of constructing CDS is as depicted in the CDS- Construction Algorithm. CDS construction Algorithm will take the set of mobile nodes as the input and the outcome is CDS. In the dying process the node with the h ighest number of neighboring nodes is colored b lack and all its neighbors are colored grey [7]. Next the grey node with the highest number of neighbors is colored black and all its neighbors are colored grey. This process is repeated until all the nodes in the network are colored either black are grey. In the final network all the nodes that are black in color are the dominating nodes while the other grey nodes are non dominating nodes. Now all the black nodes together form the CDS. Fig. 3.1 shows the sample CDS of size 4 for eight mobile nodes. Black colored nodes are dominating nodes and they form the CDS. Thus the backbone that is required for data transfer is constructed. The next section describes the construction of MCDS using GA.

Figure 3.1 Structure of Connected Dominating Set

CDS- Construction Algorithm

Input : Mobile nodes

Output : Connected Dominating Set

STEPS

1. For each node u

1- Hop neighbors N (u) are co llected using

HELLO message periodically.

2. N (u) values of each node are broadcasted so that 2- Hop neighbors for each node will be calculated. 3. In itially all the nodes are colored WHITE. Later the nodes with larger 1-hop neighbor value will be colored BLACK to indicate those nodes as the dominating node and the neighboring nodes are colored grey. 4. Dying process is repeated until no WHITE Nodes

are left.

3.2 MCDS_Construction The number of nodes in the CDS is minimized for MCDS construction. This minimization is done using the Genetic algorithm [11]. With each node there is associated an initial energy and reference energy [7]. The chromosome is the set of nodes in the CDS and the reference energy of each node in a chromosome is added to calculate the total reference energy which is used as fitness value to select the parents for constructing new population. The chromosomes with the highest reference energy are chosen as the parents. Parent selection is done using Roulette Wheel selection. Parent with highest reference energy and the parent with next higher energy will be chosen for producing new off springs. Crossover is applied on the elected parents. In the crossover the first half o f the first parent is taken and the second parent is scanned starting from the left. The alleles that are not present in the first half of the first parent are taken and this makes the second half of the new offspring. These new off springs will form a new population. The process will be repeated either for the specified number of iterations or until the diversity of population is maintained. For each chromosome (chr), p roposed work define Fitness (chr) 0.8 VERTICES (chr) 0.2 MAX-SIZE (chr) fitnessPower (chr) = rfenergy (x) × fitness (chr)

xx chr VERTICES (chr)- Number of nodes in the chromosome. MAX-SIZE (chr) - Max size of connected components of chromosome.

MCDS – Construction Algori thm Input : Nodes in CDS Output : MCDS STEPS 1. Select candidate solution by randomly delet ing any one of

the dominating node in CDS, the set of remaining nodes will be formed as a candidate solution which is referred as chromosome.

2. Init ial population Step 1 will be repeated so that the population set of chromosomes of required size is obtained. 3. Fitness value –calculation Calculate the fitness value, total reference energy of each chromosome. 4. Repeat the following sub steps until the new Population of the required size is generated.

a) Select a pair of parent chromosomes those have higher reference energy from the current population.

b) Cross over the pair at a randomly chosen

point (chosen with uniform probability) to form two offspring. 5. Rep lace the current population with the new Population. Go to step 3

Figure 3.2 MCDS Using GA

The deleting algorithm is applied to min imize the number of nodes in CDS. The node that has the least reference energy in the new offspring chromosome is deleted and not included in the new population. The new set of population is formed likewise. Then the genetic algorithm is applied again to the new population. Th is process is repeated until the number of nodes in the CDS is min imized as much as possible. But the MCDS network should satisfy the condition that every non

dominating node in the Network should directly connect to any one of the dominating node.

Figure 3.3 Sample network with MCDS

3.3 Data Transfer

The MCDS thus obtained as explained in section B makes the data transfer more efficient and reliable. Since the network is dynamic it cannot be assured that message will first reach a node in CDS. If the message reaches a node in CDS then that node transfers the message to all its direct neighbors and also to the next nearest dominating node. Then again that dominating node transfers the data to all its direct neighbors to and also to the nearest dominating node. Likewise the message is transferred to the whole network. But if the message reaches a non dominating node then the message is first sent to a dominating node and from here the data transfer is done in the same way as mentioned above.

3.4 Recovery Procedure

In MANETS the nodes are dynamic so the nodes may move out of transmission range. If message is sent to a node that has moved out of range then the message will be lost and the data is not transferred to any other node. But if the node that went out of range comes again into the network range it cannot be restored as a dominating node because the energy value of that node may not be the same. Notice that the topology change can be the result of node mobility, the power outage of some nodes in the network, the deployment of additional nodes to the network, or the combination of the aforementioned cases. If a dominating node moves out of range then the neighboring grey node that has the highest number of neighbor with the highest reference energy is chosen by invoking MCDS - construction algorithm to replace the black dominating node that went out of range. The reconstruction of CDS from scratch can keep the CDS from being unavailab le for service for an extended period of t ime. In an environment with mobile hosts as routers, convergence to new, stable routes after dynamic changes in network topology may be slow and this process could be expensive due to low bandwidth. Routing informat ion has to be localized to adapt quickly to changes such as host movements. Otherwise there are chances for the message sent to get lost without reaching the destination.

4. Experimental Study

This work is simulated using twenty nodes and is distributed over an area of 3 kms. The MCDS is constructed from these twenty nodes. Table 4.1 shows the parameters needed for the construction of CDS and MCDS. By this proposed work CDS of size 12 for 20 nodes has been achieved which is depicted in Fig. 4.1. By using GA, MCDS of size 6 has been achieved and is shown in Fig. 4.2.

Table 4.1 Parameters and Strategies used for GA

Parameter / Strategy Settings

Population size 10

Population type Generational

Initializat ion Random

Selection Roulette Wheel

Crossover Two parents (single point cross

over)

Bit Swap Inversion 0.1 % probability

Replacement St rategy Keep 80% best

Fig. 4.2 that is generated by the proposed Genetic Algorithm shows the reduction in the number of nodes in CDS. So it takes the less time and energy and thus proving more efficient. The energy consumed is evaluated by considering the number of total nodes and percentage of nodes in CDS as illustrated in Fig. 4.3. It clearly depicts that when the percentage of number of nodes in CDS is high the energy consumed is also high thus reducing the energy efficiency. For example if the number of nodes is 20, then if only 0.4 % of total nodes are in MCDS then the energy consumed for t ransmission will be less. Hence it is always good to keep the number of nodes in the CDS as minimum as possible.

Figure 4.1 – CDS of size 12 for 20 nodes using CDS- Construction Algorithm

Figure 4.2 – MCDS of size 6 using GA

Figure 4.3 – Energy Efficiency Evaluation

5. Conclusion and future work The number of nodes in the CDS is min imized as much as possible. The nodes in the MCDS are more active and efficient as they have the highest reference energy. The data transfer is done more efficiently and reliably. The GA is applied to minimize the number of nodes in the CDS. The data transferred is not secure hence security can be enhanced by encrypting the data being sent. The GA applied here uses chromosome of fixed length. When messy GA is used chromosome of varied length can be used. Future work includes to find the reaffiliation count for each node, and to reduce disconnections in the CDS. Techniques can be adopted to reduce the signal interference problem in MANETs. Further techniques for efficient use of available band width can be adopted. Improvements can be made in the construction of MCDS by applying probability values for assessing the suitability of the dominating nodes. Since the nodes are battery powered, predicting the life t ime of dominating nodes can also be included as further enhancement.

References

[1] J. Blum, M. Ding, A. Thaeler, and X. Cheng, “Connected Dominating Set in Sensor Networks and MANETs,” Handbook of Combinatorial Optimization. [2] Dai F, Wu J. “An extended localized algorithm for Connected dominating set format ion in ad hoc Wireless Networks. ”IEEE Transactions on Parallel and distributed Systems 2004; 15(10):908–920.

[3] B. Chen, K. Jamieson, H. Balakrishnan, and R. Morris, “Span: An Energy Efficient Coordination Algorithm for Topology Maintenance in Ad Hoc Wireless Networks,” Proc. ACM MobiCom, July 2001. [4] Kazuya sakai, C.H. huang, Wei-shinn ku “Timer-Based CDS construction in wireless Ad Hoc Networks” IEEE Trans Mobile computing, vol. 10, Oct 2011. [5] Jeremy Blum, Min Ding, Andrew Thaeler “Connected Dominating Set in Sensor Networks and MANETs” Kluwer Academic Publishers 2004. [6] T.Ho.meister F. and Schwefel H.P “ A survey of evolution strategies In RK Belew and L B Booker eds – Proceedings of the Fourth International Conference on Genetic Algorithms 2-9. San Francisco_ CA Morgan Kaufmann. [7] Yajie Ma, Yike Guo and Moustafa Ghanem, “RECA: Referenced energy-based CDS algorithm“Int. J. Commun. Syst. 2010; 23:125–138 in wireless sensor networks. [8] Garey ML, Johnson DS. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H.Freeman: San Francisco, 1979. [9] Yuanyuan Z, Xiaohua J, and Yanxuag H. “A distributed algorithm for constructing energy- balanced connected dominating set in wireless sensor networks. International Journal of Sensor Networks 2007; 2(1/2):68– 76.

[10] Wu J, Dai F, GAO M. On calculating power- aware Connected dominating sets for efficient routing in adhoc wireless networks. Journal of Communication and Networks 2002; 4(1):59–70. [11] Melanie Mitchell,”An introduction to genetic algorithm". A Bradford Book the MIT PressCambridge, Massachusetts • London, England Fifth printing, 1999. pp. 8–10. [12] K.E.Kinnear,” The evolution of evolvability in genetic programming”. 1994 M.I.T. Press pp. 47-74.