Sharif Digital Repository

Although many complex real-world networks are weighted, unweighted networks are used in many applications such as sensor networks. In this Letter it is shown using properly weighted networks the performance can be greatly enhanced by reducing the time necessary for the average consensus. Random geographical models are adapted as network models and a method based on mutually coupled phase oscillators is used for providing average consensus over the network. The consensus time is calculated by numerically solving the network's differential equations and monitoring the average error. The simulation results on some sample networks show that the consensus time is dramatically reduced when the... 

'Help bits' are some limited trusted information about an instance or instances of a computational problem that may reduce the computational complexity of solving that instance or instances. Assume that we can efficiently solve k instances of a decision problem using some help bits whose entropy is less than k when the k instances are drawn independently from a particular distribution. Then there is an upper bound on the average-case complexity of the problem, namely we can efficiently solve an instance drawn from that distribution correctly with probability better than 1/2  

Random geographical networks are realistic models for wireless sensor networks which are used in many applications. Achieving average consensus is very important in sensor networks and the faster the consensus is, the durable the sensors' life, and thus, the better the performance of the network. In this paper we compared the performance of a number of linear consensus algorithms with application to distributed averaging in random geographical networks. Interestingly, the simplest algorithm - where only the degree of receiving nodes is needed for the averaging - had the best performance in terms of the consensus time. Furthermore, we proved that the network has guaranteed convergence with... 

Sensor networks are increasingly employed in many applications ranging from environmental to military cases. The network topology used in many sensor network applications has a kind of geographical structure. A graph weighting method for reducing consensus time in random geographical networks is proposed in this paper. We consider a method based on the mutually coupled oscillators for providing general consensus in the network. In this way, one can relate the consensus time to the properties of the Laplacian matrix of the connection graph, i.e. to the second smallest eigenvalue (algebraic connectivity). Our weighting algorithm is based on the node and edge between centrality measures. The...