In this paper, we look at the problem of randomized leader election in synchronous distributed networks with a special focus on the message complexity. We provide an algorithm that solves the implicit version of leader election (where non-leader nodes need not be aware of the identity of the leader) in any general network with O( √ n log 7/2 n · t mix ) messages and in O(t mix log 2 n) time, where n is the number of nodes and t mix refers to the mixing time of a random walk in the network graph G. For several classes of well-connected networks (that have a large conductance or alternatively small mixing times e.g. expanders, hypercubes, etc), the above result implies extremely efficient (sublinear running time and messages) leader election algorithms. Correspondingly, we show that any substantial improvement is not possible over our algorithm, by presenting an almost matching lower bound for randomized leader election. We show that Ω( √ n/φ 3/4 ) messages are needed for any leader election algorithm that succeeds with probability at least 1 − o(1), where φ refers to the conductance of a graph. To the best of our knowledge, this is the first work that shows a dependence between the time and message complexity to solve leader election and the connectivity of the graph G, which is often characterized by the graph's conductance φ. Apart from the Ω(m) bound in [24] (where m denotes the number of edges of the graph), this work also provides one of the first non-trivial lower bounds for leader election in general networks.Leader election is one of the most classical and fundamental problem in the field of distributed computing having applications in numerous problems relating to synchronization, resource allocation, reliable replication, load balancing, job scheduling (in master slave environment), crash recovery, membership maintenance etc. Computing a leader can be thought of as a form of symmetry breaking, where exactly one special node or process (denoted as leader) is chosen to take some critical decisions.Loosely speaking, the problem of leader election requires a set of nodes in a distributed network to elect a unique leader among themselves, i.e., exactly one node must output the decision that it is the leader. There are two well known variants of this problem (cf. [3,27]), the explicit variant where at the end of the election process all the nodes are required to be aware of the identity of the leader and the implicit variant where the non-leader nodes need not be aware of the identity of the leader.Often, the implicit variant is sufficient for many practical applications, e.g. its original application for token generation in token ring environments [26] etc. This variant also allows us to clearly distinguish between the two aspects of explicit leader election and costs associated to each of them, i.e. electing a leader (implicitly) as compared to broadcasting the unique id of the leader to all the other nodes. Clearly, any solution for the explicit variant of leader election also solves the implicit variant. H...

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We study graph realization problems from a distributed perspective. The problem is naturally applicable to the distributed construction of overlay networks that must satisfy certain degree or connectivity properties, and we study it in the node capacitated clique (NCC) model of distributed computing, recently introduced for representing peer-to-peer networks.We focus on two central variants, degree-sequence realization and minimum threshold-connectivity realization. In the degree sequence problem, each node v is associated with a degree d(v), and the resulting degree sequence is realizable if it is possible to construct an overlay network in which the degree of each node v is d(v). The minimum threshold-connectivity problem requires us to construct an overlay network that satisfies connectivity constraints specified between every pair of nodes. Overlay network realizations can be either explicit or implicit. Explicit realizations require both endpoints of any edge in the realized graph to be aware of the edge. In implicit realizations, on the other hand, at least one endpoint of each edge of the realized graph needs to be aware of the edge. The main realization algorithms we present are the following.• An Õ(min{ √ m, ∆}) time algorithm for implicit realization of a degree sequence. Here, ∆ = max v d(v) is the maximum degree and m = (1/2) v d(v) is the number of edges in the final realization.• Õ(∆) time algorithm for an explicit realization of a degree sequence. We first compute an implicit realization and then transform it into an explicit one in Õ(∆) additional rounds.• An Õ(∆) time algorithm for the threshold connectivity problem that obtains an explicit solution and an improved Õ(1) algorithm for implicit realization when all nodes know each other's IDs. These algorithms are 2-approximations w.r.t. the number of edges.We complement our upper bounds with lower bounds to show that the above algorithms are tight up to factors of log n. Additionally, we provide algorithms for realizing trees and an Õ(1) round algorithm for approximate degree sequence realization.

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This paper proposes a simple, accurate, and easy to model approach for the simulation of photovoltaic (PV) array and also provides a comparative analysis of the same with two other widely used models. It is highly imperative that the maximum power point (MPP) is achieved effectively and thus a simple and robust mathematical model is necessary that poses less mathematical complexity as well as low data storage requirement, in which the maximum power point tracking (MPPT) algorithm can be realized in an effective way. Further, the resemblance of the P-V and I-V curves as obtained on the basis of experimental data should also be taken into account for theoretical validation. In addition, the study incorporates the root mean square deviation (RMSD) from the experimental data, the fill factor (FF), the efficiency of the model, and the time required for simulation. Two models have been used to investigate the I-V and P-V characteristics. Perturb and Observe method has been adopted for MPPT. The MPP tracking is realized using field programmable gate array (FPGA) to prove the effectiveness of the proposed approach. All the systems are modeled and simulated in MATLAB/Simulink environment.