Equal Number Of Nodes Research Articles

Networks and their degree distribution, leading to a new concept of small worlds

The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order.Next, we introduce a new class of small worlds, namely those based on the degrees of nodes in a network. Similar to a previous study, small worlds are defined as sequences of networks with certain limiting properties. We distinguish between three types of small worlds: those based on the highest degree, those based on the average degree, and those based on the median degree. We show that these new classes of small worlds are different from those introduced previously based on the diameter of the network or the average and median distance between nodes. However, there exist sequences of networks that qualify as small worlds in both senses of the word, with stars being an example. Our approach enables the comparison of two networks with an equal number of nodes in terms of their “small-worldliness”.Finally, we introduced neighboring arrays based on the degrees of the zeroth and first-order neighbors.

Virtual Coordinate System Based on a Circulant Topology for Routing in Networks-On-Chip

In this work, the circulant topology as an alternative to 2D mesh in networks-on-chip is considered. A virtual coordinate system for numbering nodes in the circulant topology is proposed, and the principle of greedy promotion is formulated. The rules for constructing the shortest routes between the two nodes based on coordinates are formulated. A technique for calculating optimal network configurations is described. Dense states of the network when all neighborhoods of the central node are filled with nodes and the network has the smallest diameter are defined. It is shown that with an equal number of nodes, the diameter of the circulant is two times smaller than the diameter of the 2D mesh. This is due to the large number of symmetries for the circulant, which leave the set of nodes unchanged. A comparison of communication stability in both topologies in the conditions of failure of network nodes is made, the network behavior under load and failures is modeled, and the advantages of the circulant topology are presented.

Lengthening of average path length in social networks due to the effect of community structure

Community structure is a common phenomenon observed in various social networks. In this work, a novel community detection algorithm is proposed by estimating the effect of community structure on the average path length of a network. The Erdos-Renyi graph model is used as a reference to compute the change in the average path length of a network due to community formation. By experimenting with artificial networks, it is found that community structure in a social network contributes towards the lengthening of the average shortest path length. A random graph is found to have a lesser average shortest path length than a social network with community structure. As the size of individual communities increases, there is a decrease in the difference of average shortest path lengths, compared with a random graph containing an equal number of nodes and edges. This relationship is used to predict the average community size and their numbers in a network. The findings mentioned above are applied to the proposed algorithm. The proposed community detection algorithm is an enhancement over Fire Spread community detection algorithm (Pattanayak, 2019), in which the value of R for the R-radius neighborhood subgraph is automatically calculated.

Comparison of Some Approximate Algorithms Proposed for Traveling Salesmen and Graph Partitioning Problems

In computation theory, the complexity class NP-complete is one of the most studied classes of decision problem. We can verify any given solution to such a problem, but the most important characteristic of NP-complete problems is that no fast solution to them is known. Time required to solve the problem using any currently known algorithm increases very quickly as the size of the problem grows. So, NP-complete problems like traveling salesman and graph partitioning have various heuristic algorithms to find the optimal solution of these problems in much lesser time. Out of all the algorithms none of them will provide the exact solution of the problem. In this paper, we have considered two of graph based NP-complete problem (Traveling Salesmen Problem (Single and Multiple Salesman) and Graph Partitioning Problem). In TSP, the aim is to minimize the total distance travelled covering all the cities exactly once. In graph partitioning, the aim to partition the graph into smaller subset with each subset has almost equal number of nodes with minimized number of edges whose vertices are in different sets. To achieve these goals, we have implemented various heuristic algorithms of both of the problems. In addition to these, comparison of various algorithms on basis of cost and time of each problem is performed on a range of data set.

Enhanced Balanced Cluster Lifetime Prolonging Protocol for Wireless Sensor Network

In enhanced balanced cluster lifetime prolonging protocol we investigate that how balance cluster approach work in heterogeneous environment by applying same network structure in heterogeneous environment. Dividing network in four equal static balanced cluster so that all the clusters have almost equal number of nodes. This will help in even load distribution of network and this will increase the network lifetime and energy of the network. Simulation-based evaluations are performed to compare the performance of EBCLPP against BCLPP balanced cluster lifetime prolonging protocol and EDDEEC Enhanced Developed Distributed Energy-Efficient Clustering for Heterogeneous Wireless Sensor .Our experiment results show that EBCLPP outperforms BCLPP and EDDEEC in terms of network lifetime and power consumption minimization. In heterogeneous wireless sensor network optimization of energy is the main issue. In previous scheme the clusters where formed dynamically and the cluster head selection was based on the probability. Formation of clusters dynamically lead to loss of energy in every round which affected the network lifetime and energy of every node. We investigate that how balance cluster approach work for heterogeneous wireless sensor network in this scheme we are forming the balance cluster in the start of network operation in order to reduce the overhead of cluster formation after every round. We divide sensor nodes in four cluster and all the cluster have almost equal number of nodes. And by doing so the cluster does not even get unbalanced as nodes in all the clusters are almost same. Cluster head selection is mapped to homogenous network that is done by finding the weight of nodes in the cluster and so the node having highest energy will become cluster head for the round. In this case all the nodes whether they are super nodes or normal nodes all the nodes get the chance to become the cluster head. This will increase the number of nodes alive over time and also the average energy per node.

Balanced Cluster Lifetime Prolonging Protocol for Wireless Sensor Network

sensor network with a large number of tiny sensor nodes can be used as an effective tool for gathering data in diverse conditions. One of the crucial matter in wireless sensor networks is developing an energy-efficient routing protocol which has a significant impact on the overall lifetime of the sensor network. In this paper, we propose a balanced cluster routing protocol called balance cluster lifetime prolonging protocol (BCLPP). In BCLPP, we divide the network into four static quadrants which have almost equal number of nodes, which reduce the overhead of dynamic clustering thus increase the lifetime of our network. Simulation-based evaluations are performed to compare the performance of BCLPP against Energy-Efficient Protocol with Static Clustering for Wireless Sensor Networks (EEPSC) Our experiment results show that BCLPP outperforms EEPSC in terms of network lifetime and power consumption minimization. Keywordstechnique, Energy efficiency, network lifetime and wireless sensor network.

AN EFFICIENT LOAD BALANCING CLUSTERING SCHEME FOR DATA CENTRIC WIRELESS SENSOR NETWORKS

Clustering is an efficient approach to capitalize the energy of energy constraint sensor nodes in wireless sensor networks. Clustering schemes do not guarantee formation of clusters with equal number of nodes. So data frames transmitted by the nodes vary. TDMA schedule of nodes of smaller cluster is smaller than others that results more number of data frames and hence more energy consumption. The non uniform energy consumption of nodes affects the load balancing of network and these nodes are more prone to die earlier than others. In this paper, an improved scheme for cluster head selection is proposed. Clusters having variable frame slots for nodes are applied to E-LEACH and improved E-LEACH to make the cluster more load balanced. Simulation is carried out in NS-2 to analyze the performance of E-LEACH and improved E-LEACH with variable frame length. Variable frame slot scheme for clusters is also measured with the varying distance of base station from the field. Simulation results show that clustering with variable frame length has an improvement of 7% in node death rate over E-LEACH and an improvement of 9% in node death rate over improved ELEACH. Results suggest that variable frame length scheme improves the performance of clustering schemes for WSNs and have most significant result at base station located at 75m from the field.

Tree Routing Protocol with Location-based Uniformly Clustering Strategy in WSNs

In WSNs, energy efficiency and low latency are considered as two key issues in designing routing protocol. This paper introduces a two layer hierarchical tree routing protocol with location-based uniformly clustering strategy in WSNs (TRPLUCS), which can gives a good compromise between energy consumption and delay. First, TRPLUCS makes balanced clustering based on geographic regions. That is to say, all the clusters are uniformly distributed in WSNs with approximately equal number of nodes in each cluster. Second, TRPLUCS computes a spanning tree inside the cluster. Each node in cluster transmits data to its cluster-head along the spanning tree. Third, TRPLUCS constructs an optimal tree among all the cluster-heads. The data packets are then routed to the sink along the optimal tree. Simulation results show that TRPLUCS performs better than PEGASIS and LEACH in terms of energy*delay cost metric.

A Clustering Protocol Using Multiple Chain Strategy in WSNs

In W SNs, e nergy efficiency and low latency are considered as two key issues in designing routing protocol . This paper introduces two schemes to combine clustering strategy with chain routing algorithm in order to satisfy both energy and delay constraints in WSNs. Furthermore by one scheme, we propose a two layer hierarchical routing protocol called Chain Routing B ased on Coordinates-oriented Clustering Strategy ( CRBCC ), which gives a good compromise between energy consumption and delay . First, CRBCC makes balanced clustering according to y coordinates. That is to say, each cluster has approximately equal number of nodes . Second, CRBCC makes chain routing by simulated annealing algorithm (SA) inside the cluster and elects chain leader in the order of x coordinates. Third, CRBCC makes chain routing again by SA method among chain leaders. Simulation results show that CRBCC performs better than PEGASIS in terms of energy efficiency and network delay.

Optimal Clustering of Hierarchical Hyper-Ring Multicomputers

The Hyper-Ring (HR) is presented as a hierarchical and scalable ring-based topology for small-scale to massively parallel systems which eliminates the major disadvantages of large-scale rings. With a fixed node degree, a low cost, symmetric properties, and a simple routing scheme, the HR topology is very suitable for small-scale to large-scale multicomputer systems. Assuming pipelined communication, the performance of 4- and 5-dimensional HR multicomputers is modeled, the performance model is evaluated, and the results of the performance model evaluation are analyzed. Moreover, the impact of the traffic load and message length on the system performance is analyzed. The major objective of this work is to shed light on how to cluster HRs in order to optimize the system efficiency. Assuming a uniform message arrival rate into the nodes of the HR, the results show that the efficiency of HR topologies with an equal number of nodes is best when the topologies are perfectly balanced. The next best-performing HRs are those with larger rings at the lower (outer) levels and smaller rings at the higher levels (near the root ring). The results confirm that the HR topology is suitable for massively parallel and scalable multicomputer systems as well as for networks of workstations.

The bisection width of grid graphs

A solid grid graph is a finite induced subgraph of the infinite grid that has no holes. We present a polynomial algorithm for computing the minimum number of edges we need to delete in order to divide a given solid grid graph into two parts containing an equal number of nodes. The algorithm is based on dynamic programming, and it extends to several related problems, including grid graphs with a bounded number of holes.