We study the problem of optimal leader selection in consensus networks under two performance measures (1) formation coherence when subject to additive perturbations, as quantified by the steady-state variance of the deviation from the desired trajectory, and (2) convergence rate to a consensus value. The objective is to identify the set of k leaders that optimizes the chosen performance measure. In both cases, an optimal leader set can be found by an exhaustive search over all possible leader sets; however, this approach is not scalable to large networks. In recent years, several works have proposed approximation algorithms to the k-leader selection problem, yet the question of whether there exists an efficient, non-combinatorial method to identify the optimal leader set remains open. This work takes a first step towards answering this question. We show that, in one-dimensional weighted graphs, namely path graphs and ring graphs, the k-leader selection problem can be solved in polynomial time (in both k and the network size n). We give an O(n 3 ) solution for optimal k-leader selection in path graphs and an O(kn 3 ) solution for optimal k-leader selection in ring graphs.

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We study the problem of optimal leader selection in consensus networks with noisy relative information. The objective is to identify the set of k leaders that minimizes the formation's deviation from the desired trajectory established by the leaders. An optimal leader set can be found by an exhaustive search over all possible leader sets; however, this approach is not scalable to large networks. In recent years, several works have proposed approximation algorithms to the k-leader selection problem, yet the question of whether there exists an efficient, non-combinatorial method to identify the optimal leader set remains open. This work takes a first step towards answering this question. We show that, in one-dimensional weighted graphs, namely path graphs and ring graphs, the k-leader selection problem can be solved in polynomial time (in both k and the network size n). We give an O(n 3 ) solution for optimal k-leader selection in path graphs and an O(kn 3 ) solution for optimal k-leader selection in ring graphs.

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Neuromorphic computing is a broad category of non–von Neumann architectures that mimic biological nervous systems using hardware. Current research shows that this class of computing can execute data classification algorithms using only a tiny fraction of the power conventional CPUs require. This raises the larger research question: How might neuromorphic computing be used to improve application performance, power consumption, and overall system reliability of future supercomputers? To address this question, an open-source neuromorphic processor architecture simulator called NeMo is being developed. This effort will enable the design space exploration of potential heterogeneous compute systems that combine traditional CPUs, GPUs, and neuromorphic hardware. This article examines the design, implementation, and performance of NeMo . Demonstration of NeMo ’s efficient execution using 2,048 nodes of an IBM Blue Gene/Q system, modeling 8,388,608 neuromorphic processing cores is reported. The peak performance of NeMo is just over ten billion events-per-second when operating at this scale.