Abstract. In this paper we present a novel approach to the graph isomorphism problem. We combine a direct approach, that tries to find a mapping between the two input graphs using backtracking, with a (possibly partial) automorphism precomputing that allows to prune the search tree. We propose an algorithm, conauto, that has a space complexity of O(n 2 log n) bits. It runs in time O(n 5 ) with high probability if either one of the input graphs is a G(n, p) random graph, for p ∈ [ω(ln 4 n/n ln ln n), 1 − ω(ln 4 n/n ln ln n)]. We compare the practical performance of conauto with other popular algorithms, with an extensive collection of problem instances. Our algorithm behaves consistently for directed, undirected, positive, and negative cases. Additionally, when it is slower than any of the other algorithms, it is only by a small factor.

Interest in multirobot systems is rising rapidly both in academia and in industry. The use of multiple robots working in a coordinated way, rather than a single robot, has several advantages in a diverse range of applications. However, few studies have focused on operations in which robots can behave maliciously and alter the outcome of the collective mission. In this article, we present a set of Byzantine Follow The Leader (BFTL) problems, in which a subset of robots in the system shows unintended or inconsistent behavior (i.e., Byzantine robots). In the BFTL problems, leaders discover routes from their starting positions to specific destinations and guide the followers, while Byzantine robots try to hinder the leaders and mislead the followers. In this research, blockchain technology is used as a communication tool within multirobot systems, for leaders to broadcast directions to the whole group. We propose algorithms to tackle the BFTL problems, prove their correctness, and validate them in simulated experiments of realistic scenarios. Results show that the proposed algorithms mitigate the impact of Byzantine robots in multirobot systems conducting a BFTL mission. Our analysis provides minimum and maximum boundary calculations for important metrics including number of robots reaching their destination, number of steps taken, and weight requirements of the chain used during the mission. Our results provide a path toward the deployment of byzantine-resistant real-world multirobot systems.

In this paper, a method of verification of the power performance of a wind farm is presented. This method is based on the Friedman’s test, which is a nonparametric statistical inference technique, and it uses the information that is collected by the SCADA system from the sensors embedded in the wind turbines in order to carry out the power performance verification of a wind farm. Here, the guaranteed power curve of the wind turbines is used as one more wind turbine of the wind farm under assessment, and a multiple comparison method is used to investigate differences between pairs of wind turbines with respect to their power performance. The proposed method says whether the power performance of the specific wind farm under assessment differs significantly from what would be expected, and it also allows wind farm owners to know whether their wind farm has either a perfect power performance or an acceptable power performance. Finally, the power performance verification of an actual wind farm is carried out. The results of the application of the proposed method showed that the power performance of the specific wind farm under assessment was acceptable.

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