Robust Graphs Research Articles

An event‐triggered approach to quantized resilient consensus

SummaryWe consider an event‐triggered update scheme for the problem of multiagent consensus in the presence of faulty and malicious agents within the network. In particular, we focus on the case where the agents take integer (or quantized) values. To keep the regular agents from being affected by the behavior of faulty agents, algorithms of the mean subsequence reduced type are employed, where neighbors taking extreme values are ignored in the updates. Different from the real‐valued case, the quantized version requires the update rule to be randomized. We characterize the error bound on the achievable level of consensus among the agents as well as the necessary structure for the network in terms of the notion of robust graphs. We verify via a numerical example the effectiveness of the proposed algorithms.

Resilient Attitude Alignment in Multispacecraft Systems

Resilient attitude alignment of leaderless multispacecraft systems (MSSs) in the presence of cyberattacks is investigated. The main problem of resilient cooperative control schemes existing in the literature is their limitation to integrator linear systems. However, since real spacecraft are prone to uncertainties in model parameters, they may not be feedback linearizable to integrator models. Thus, the main contribution of the current study is to guarantee attitude alignment in MSSs in the presence of cyberattacks when the model parameters of the spacecraft are unknown. We propose a cooperative adaptive control scheme for a network of spacecraft, and based on the concept of robust graphs, we show that if the network connectivity is sufficiently robust with respect to the number of possible malicious spacecraft (spacecraft under cyberattacks), attitude alignment among the normal spacecraft can be guaranteed. The accuracy of the proposed control strategy is validated via a simulation example.

Leveraging Diversity for Achieving Resilient Consensus in Sparse Networks

A networked system can be made resilient against adversaries and attacks if the underlying network graph is structurally robust. A typical approach to making networks structurally robust is to strategically add extra links between nodes, which might be prohibitively expensive. In this paper, we propose an alternative way of improving network’s robustness, that is by considering heterogeneity of nodes. Nodes in a network can be of different types and can have multiple variants. As a result, different nodes can have disjoint sets of vulnerabilities, which means that an attacker can only compromise a particular type of nodes by exploiting a particular vulnerability. We show that, by such a diversification of nodes, attacker’s ability to change the underlying network structure can be reduced significantly. Consequently, even a sparse network with heterogeneous nodes can exhibit the properties of a structurally robust network. Using these ideas, we propose a distributed control policy that utilizes heterogeneity in the network to achieve resilient consensus in adversarial environment. We extend the notion of (r,s)-robustness to incorporate the diversity of nodes and provide necessary and sufficient conditions to guarantee resilient distributed consensus in heterogeneous networks. Finally we study the properties and construction of robust graphs with heterogeneous nodes.

Estimating Graph Robustness Through the Randic Index.

Graph robustness-the ability of a graph to preserve its connectivity after the loss of nodes and edges-has been extensively studied to quantify how social, biological, physical, and technical systems withstand to external damages. In this paper, we prove that graph robustness can be quickly estimated through the Randic index, a parameter introduced in chemistry to study organic compounds. We prove that Erdos-Renyj (ER) graphs are a good specimen of robust graphs because they lack of a clear modular structure; we derive an analytical expression for the Randic index of ER graphs and use ER graphs as an effective term of comparison to decide about graph robustness. Experiments on real datasets from different domains (scientific collaboration networks, content-sharing systems, co-purchase networks from an e-commerce platform, and a road network) show that real-life large graphs are more robust than ER ones with the same number of nodes and edges. We also observe that if node degree distribution closely follows a power law, then few edges contribute for more than half of the Randic index, thus indicating that the selective removal of those edges has devastating impact on graph robustness. Finally, we describe sampling-based algorithms to efficiently but accurately approximate the Randic index.

Formations for Resilient Robot Teams

All cooperative control algorithms for robot teams assume the ability to communicate without considering the possibility of a malicious or malfunctioning robot that may either communicate false information or take wrong actions. This paper addresses the development of formations that enable resilience, the ability to achieve consensus, and to cooperate in the presence of malicious or malfunctioning robots. Specifically, we use the notion of robust graphs to build resilient teams, and focus on the problem of designing robot formations with communication graphs (each edge models a bidirectional communication link) that are robust. We present algorithms to build robust graphs. Given a set of robots and the maximum number of malicious or malfunctioning robots, we are able to 1) state if it is possible to build a resilient team; 2) say what the proximity relationships that enable communication ought to be; 3) construct elemental resilient graphs; and 4) develop a framework for composing resilient teams to build larger resilient teams. We illustrate these algorithms by constructing resilient robot formations in the plane.

RGCLI: Robust Graph that Considers Labeled Instances for Semi-Supervised Learning

Graph-based semi-supervised learning (SSL) provides a powerful framework for the modeling of manifold structures in high-dimensional spaces. Additionally, graph representation is effective for the propagation of the few initial labels existing in training data. Graph-based SSL requires robust graphs as input for an accurate data mining task, such as classification. In contrast to most graph construction methods, which ignore the labeled instances available in SSL scenarios, a previous study proposed a graph-construction method, named GBILI, to exploit the informativeness conveyed by such instances available in a semi-supervised classification domain. Here, we have improved the method proposing an optimized algorithm referred to as Robust Graph that Considers Labeled Instances (RGCLI) for the generation of more robust graphs. The contributions of this paper are threefold: i) reduction of GBILI time complexity from quadratic to O(nklogn). This enhancement allows addressing large datasets; ii) demonstration of RGCLI mathematical properties, proving the constructed graph is an optimal graph to model the smoothness assumption of SSL; and iii) evaluation of the efficacy of the proposed approach in a comprehensive semi-supervised classification scenario with several datasets, including an image segmentation task, which needs a large graph to represent the image. Such experiments show the use of labeled vertices in the graph construction process improves the graph topology, hence, the learning task in which it will be employed.

Extraction of strokes in handwritten characters

Among the many handwritten character recognition algorithms that have been proposed in the past few years, few of them use models which are able to simulate handwriting. This can be explained by the fact that simulation models require the estimation of strokes starting from statistic images of letters, while crossing and overlapping strokes make this estimation difficult. The approach we suggest is to efficiently deal with crossing areas and overlaps using parametric representations of lines and thickness of stroke: a probabilistic model of strokes is described to extract non-overlapping strokes of the image. A bayesian approach using a statistical study and a model of stroke crossing is described that optimizes the reconstruction of crossings and permits to characterize image of letters by robust graphs of curves.