Search

The vertices of a graph are to be labelled with 0 or 1 such that each edge gets the label as the product of its end vertices. If the number of vertices labelled with 0’s and 1’s differ by at most one and if the number of edges labelled with 0’s and 1’s differ by at most by one, then the labelling is called product cordial labelling. Complete characterizations of product cordial dragon graphs is given. We also characterize dragon graphs whose line graphs are product cordial. [ABSTRACT FROM AUTHOR]

Let G be a graph with vertex set V (G) and edge set E(G). Denote by dG(u) the degree of a vertex u ∈ V (G). The Sombor index of G is defined as SO(G) = Σuv∈E(G) √d²u + d²v , whereas, the inverse sum indeg (ISI) index is defined as ISI(G) = Σuv∈E(G) dudv/du+dv . In this paper, we compute the bounds in terms of maximum degree, minimum degree, order and size of the original graphs G and H for Sombor and ISI indices of several graph operations like corona product, cartesian product, strong product, composition and join of graphs. [ABSTRACT FROM AUTHOR]

Let G = (V (G), E(G)) be a simple graph. A set D ⊆ V (G) is a strong dominating set of G, if for every vertex x ∈ V (G) \ D there is a vertex y ∈ D with xy ∈ E(G) and deg(x) ≤ deg(y). The strong domination number γst(G) is defined as the minimum cardinality of a strong dominating set. In this paper, we examine the effects on γst(G) when G is modified by operations on edge (or edges) of G. [ABSTRACT FROM AUTHOR]

A signed graph is a graph whose edges are labeled either as positive or negative. The concepts of vector valued switching and balancing dimension of signed graphs were introduced by S. Hameed et al. In this paper, we deal with the balancing dimension of various products of signed graphs, namely the Cartesian product, the lexicographic product, the tensor product, and the strong product. [ABSTRACT FROM AUTHOR]

Topological indices play a significant role in crisp, fuzzy graphs and their real-life application. But to avoid the vagueness in the final result, these indices should be dealt with in the neutrosophic environment since it consolidates the uncertain quantity or values of an event in the name of "indeterminacy membership". Except for the wiener index, no other indices are introduced under the neutrosophic graphical setting. In this article, we consider the forgotten topological index (ToI) and the Edge forgotten index in the 3-valued logic neutrosophic graph and came up with some important theorem results and applications. [ABSTRACT FROM AUTHOR]

Let G = (V, E) be a simple connected graph. A perfect matching (or Kekulé structure in chemical literature) of G is a set of disjoint edges which covers all vertices of G. The anti-forcing number of G is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching and is denoted by af(G). For every m ∈ N, the mth power of G, denoted by Gm, is a graph with the same vertex set as G such that two vertices are adjacent in Gm if and only if their distance is at most m in G. In this paper, we study the anti-forcing number of the powers of some graphs. [ABSTRACT FROM AUTHOR]

This paper introduces certain relations between 1-edge contraction and the total vertex stress and the confluence number of a graph. A main result states that if a graph G with ζ(G) = k ≥ 2 has an edge vivj and a ζ-set CG such that vi, vj ∈ CG then, ζ(G/vivj ) = k − 1. In general, either S(G/ei) ≤ S(G/ej ) or S(G/ej ) ≤ S(G/ei) is true. This observation leads to an investigation into the question: for which edge(s) ei will S(G/ei) = max{S(G/ej ) : ej ∈ E(G)} and for which edge(s) will S(G/ej ) = min{S(G/el) : el∈ E(G)}? [ABSTRACT FROM AUTHOR]

A signed graph (G, σ) is called a parity signed graph if there exists a bijective mapping f : V (G) → {1, . . ., |V (G)|} such that for each edge uv in G, f(u) and f(v) have same parity if σ(uv) = +1, and opposite parity if σ(uv) = −1. The rna number σ−(G) of G is the least number of negative edges among all possible parity signed graphs over G. Equivalently, σ−(G) is the least size of an edge-cut of G that has nearly equal sides. In this paper, we show that for the generalized Petersen graph Pn,k, σ−(Pn,k) lies between 3 and n. Moreover, we determine the exact value of σ−(Pn,k) for k ∈ {1, 2}. The rna numbers of some famous generalized Petersen graphs, namely, Petersen graph, Dürer graph, Möbius-Kantor graph, Dodecahedron, Desargues graph and Nauru graph are also computed. Recently, Acharya, Kureethara and Zaslavsky characterized the structure of those graphs whose rna number is 1. We use this characterization to show that the smallest order of a (4n + 1)-regular graph having rna number 1 is 8n + 6. We also prove the smallest order of (4n − 1)-regular graphs having rna number 1 is bounded above by 12n − 2. In particular, we show that the smallest order of a cubic graph having rna number 1 is 10. [ABSTRACT FROM AUTHOR]

The harmonic status index of a simple connected graph G is defined as the sum of the weights 2 sG(u)+sG(v) over all edges uv of G, where sG(u) denotes the status of the vertex u in G which is the sum of distances between u and all other vertices of G. In this paper, we present upper bounds on the harmonic status index of some families of graph products in terms of certain structural invariants such as the order, size, maximum degree, inverse status and harmonic status index of their components. The graph products considered here are sum, disjunction, symmetric difference, Indu-Bala product, corona product, Cartesian product, lexicographic product, and strong product. Some applications of the obtained results are also presented as corollaries. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the subset-strong product of graphs and give a method for calculating the adjacency spectrum of this product. In addition, exact expressions for the first and second Zagreb indices of the subset-strong products of two graphs are reported. Examples are provided to illustrate the applications of this product in some growing graphs and complex networks. [ABSTRACT FROM AUTHOR]

We extend the notion of balance from the realm of signed and gain graphs to conjugate skew gain graphs which are skew gain graphs where the labels on the oriented edges get conjugated when we reverse the orientation. We characterize the balance in a conjugate skew gain graph in several ways especially by dealing with its adjacency matrix and the g -Laplacian matrix. We also deal with the concept of anti-balance in conjugate skew gain graphs. [ABSTRACT FROM AUTHOR]

Let tp (G) denote the number of paths in a graph G and let f: E → Z+ be an edge labeling of G. The weight of a path P is the sum of the labels assigned to the edges of P. If the set of weights of the paths in G is {1, 2, 3,..., tp (G)}, then f is called a Leech labeling of G and a graph which admits a Leech labeling is called a Leech graph. In this paper, we prove that the complete bipartite graphs K2, n and K3, n are not Leech graphs and determine the maximum possible value that can be given to an edge in the Leech labeling of a cycle. [ABSTRACT FROM AUTHOR]

This article successfully attempts to introduce the notion of Inverse Neutrosophic Mixed Graphs (INMG) together with its applications. This novel approach highlights the network modeling of real physical situations with indeterminacy. Here, INMG are developed with both directed and undirected relationships between nodes that express the circumstances where the truth membership degrees of the edges are superior or equivalent to the least of the truth membership degrees of the associated vertices and where false membership and indeterminacy values of the edges are inferior or equivalent to the maximum of false membership and indeterminacy values of the corresponding vertices. Furthermore, some fundamental functions and algebraic characteristics of INMG are examined to attain a profound insight into the properties and applications. To illustrate the application of INMG, the article provides a numerical example centered around social networks. By employing INMG in this context, the article demonstrates how the model can effectively capture and represent the complex relationships within social networks, taking into account the inherent uncertainties and indeterminacies present in such systems. [ABSTRACT FROM AUTHOR]

Recently, a serious problem in communications is security. Hiding data is one of the most important security techniques. Steganography is the art and science of hiding information in a cover media. Texts are the most usual method of communication and so they are very suitable for cover objects. In this paper, we give a new technique for text steganography. There exist different models, such as RGB, HSL, HSV to determine a color. The main goal of the proposed algorithm is the fact that some different but very similar colors in RGB have the same code in HSL. We use this fact to hide data. For this purpose, first we find a color B′ in RGB, which is very similar to black in such a way that they have the same code in HSL. Then, by changing the color of each character of the text to black or B′, we conceal the information. We will show that the capacity of this method is better than some other methods of text steganography, and then we show that the invisibility of this algorithm is very high, which is the most prominent feature of the proposed technique. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a notion of Connes biprojectivity for a dual Banach algebra A with respect to its w∗-closed ideal I, say I-Connes biprojectivity. Some Lipschitz algebras Lipα(X) and some matrix algebras are studied under this new notion. Also, with some mild assumptions, the relation between IConnes biprojectivity and left ϕ-contractibility is given, where ϕ is a ω∗-continuous multiplicative linear functional on A. As an application, we characterize Connes biprojectivity of some Lipschitz algebras. [ABSTRACT FROM AUTHOR]

Let G = (V,E) be a simple graph. A set D ⊆ V is a strong dominating set of G, if for every vertex x ∈ V \ D there is a vertex y ∈ D with xy ∈ E(G) and deg(x) ≤ deg(y). The strong domination number γst(G) is defined as the minimum cardinality of a strong dominating set. In this paper, we study the effects on γst(G) when G is modified by operations on vertices and edges of G. [ABSTRACT FROM AUTHOR]

Conditional Independence (CI) graphs are a type of Probabilistic Graphical Models that are primarily used to gain insights about feature relationships. Each edge represents the partial correlation between the connected features which gives information about their direct dependence. In this survey, we list different methods and study the advances in techniques developed to recover CI graphs. We cover traditional optimization methods as well as recently developed deep learning architectures along with their recommended implementations. To facilitate wider adoption, we include preliminaries that consolidate associated operations, for example techniques to obtain covariance matrix for mixed datatypes. [ABSTRACT FROM AUTHOR]

As the interdependence between arbitrary objects in the real world grows, it becomes gradually important to use chain graphs containing directed and undirected edges to learn the structure among objects. However, independence among some variables corresponds to multiple structures and the direction of edges among variables cannot be uniquely determined. This limitation restricts existing chain graphs structure learning algorithms to only learning their Markov equivalence class. To alleviate this limitation, we define the block domain knowledge and propose a block domain knowledge-driven learning chain graphs structure algorithm (KDLCG). The KDLCG algorithm learns the adjacencies and spouses of all variables, which are utilized to directly construct the skeleton and orient the edges of the complexes, thereby learning the Markov equivalence class of the chain graphs. Subsequently, the KDLCG algorithm then updates some edges with Meek rules, guided by block domain knowledge. Finally, the KDLCG algorithm directs some edges by estimating causal effects between two variables, driven by block domain knowledge. Meanwhile, we conduct theoretical analysis to prove the correctness of our algorithm and compare it with the LCD algorithm and MBLWF algorithm on synthetic and real-world datasets. The experimental results validate the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

We consider the problem of extending partial edge colorings of iterated cartesian products of even cycles and paths, focusing on the case when the precolored edges satisfy either an Evans-type condition or is a matching. In particular, we prove that if G = C d 2k is the dth power of the cartesian product of the even cycle C2k with itself, and at most 2d−1 edges of G are precolored, then there is a proper 2d-edge coloring of G that agrees with the partial coloring. We show that the same conclusion holds, without restrictions on the number of precolored edges, if any two precolored edges are at distance at least 4 from each other. For odd cycles of length at least 5, we prove that if G = C d 2k+1 is the dth power of the cartesian product of the odd cycle C2k+1 with itself (k ≥ 2), and at most 2d edges of G are precolored, then there is a proper (2d+1)-edge coloring of G that agrees with the partial coloring. Our results generalize previous ones on precoloring extension of hypercubes [Journal of Graph Theory 95 (2020) 410–444]. [ABSTRACT FROM AUTHOR]

An edge e of a matching covered graph G is removable if G − e is also matching covered. Carvalho, Lucchesi, and Murty showed that every brick G different from K4 and C6 has at least ∆ − 2 removable edges, where ∆ is the maximum degree of G. In this paper, we generalize the result to irreducible near-bricks, where a graph is irreducible if it contains no single ear of length three or more. [ABSTRACT FROM AUTHOR]

A harmonious coloring of a k-uniform hypergraph H is a vertex coloring such that no two vertices in the same edge have the same color, and each k-element subset of colors appears on at most one edge. The harmonious number h(H) is the least number of colors needed for such a coloring. The paper contains a new proof of the upper bound h(H) = O( k√k k!m) on the harmonious number of hypergraphs of maximum degree ∆ with m edges. We use the local cut lemma of A. Bernshteyn. [ABSTRACT FROM AUTHOR]

Graph and digraph decompositions are a fundamental part of design theory. Probably the best known decompositions are related to decomposing the complete graph into 3-cycles (which correspond to Steiner triple systems), and decomposing the complete digraph into orientations of a 3-cycle (the two possible orientations of a 3-cycle correspond to directed triple systems and Mendelsohn triple systems). Decompositions of the λ -fold complete graph and the λ -fold complete digraph have been explored, giving generalizations of decompositions of complete simple graphs and digraphs. Decompositions of the complete mixed graph (which contains an edge and two distinct arcs between every two vertices) have also been explored in recent years. Since the complete mixed graph has twice as many arcs as edges, an isomorphic decomposition of a complete mixed graph into copies of a sub-mixed graph must involve a sub-mixed graph with twice as many arcs as edges. A partial orientation of a 6-star with two edges and four arcs is an example of such a mixed graph; there are five such mixed stars. In this paper, we give necessary and sufficient conditions for a decomposition of the λ -fold complete mixed graph into each of these five mixed stars for all λ > 1 . [ABSTRACT FROM AUTHOR]

The concept of the Sombor indices of a graph was introduced by Gutman. A vertex-edge variant of the Sombor index of graphs is called the KG-Sombor index. Recently, the Sombor and KG-Sombor indices of Kragujevac trees were studied, and the extremal Kragujevac trees with respect to these indices were empirically determined. Here we give analytical proof of the results. [ABSTRACT FROM AUTHOR]

A graph is half-arc-transitive if its automorphism group acts transitively on its vertex set, edge set, but not its arc set. In this paper, we study all tetravalent half-arc-transitive graphs of order 12p, where p is a prime. [ABSTRACT FROM AUTHOR]

A defective vertex coloring of a graph is a coloring in which some adjacent vertices may have the same color. An edge whose adjacent vertices have the same color is called a bad edge. A defective coloring of a graph G with minimum possible number of bad edges in G is known as a near proper coloring of G. In this paper, we introduce the notion of equitable near proper coloring of graphs and determine the minimum number of bad edges obtained from an equitable near proper coloring of some graph classes. [ABSTRACT FROM AUTHOR]

Let S be a collection of elements in a vertex set V. If every vertex in a graph G falls on a geodesic connecting two vertices from S, then that graph is said to be a geodesic graph. g(G) is the smallest cardinality of the geodesic subset of a graph G and is known as the geodetic number. This study investigates how the removal of an edge affects the geodetic number of some unique families. [ABSTRACT FROM AUTHOR]

A type (1; 1; 1) face-magic labeling of a planar graph G = (V;E; F) is a bijection from V [E [F to the set of labels f1; 2;: :: ; jV j + jEj + jFjg such that the weight of every n-sided face of G is equal to the same fixed constant. The weight of a face F 2 F is equal to the sum of the labels of the vertices, edges, and face that determine F. It is known that the grid graph Pm-Pn admits a type (1; 1; 1) face-magic labeling, but the proof in the literature is quite lengthy. We give a simple proof of this result and show two more infinite families of gridded graphs admit type (1; 1; 1) face-magic labelings. [ABSTRACT FROM AUTHOR]

A facial total-coloring of a plane graph G is a coloring of the vertices and edges such that no facially adjacent edges, no adjacent vertices, and no edge and its endvertices are assigned the same color. A facial total-coloring of G is odd if for every face f and every color c, either no element or an odd number of elements incident with f is colored by c. In this note we prove that every cactus forest with an outerplane embedding admits an odd facial total-coloring with at most 16 colors. Moreover, this bound is tight. [ABSTRACT FROM AUTHOR]

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph G is a pair G = (V , E), where V and E are the vertex set and the edge set of G , respectively. The order and size of G is the number of vertices and edges of G , respectively. The degree or valency of a vertex u in a graph G (loopless), denoted by deg (u), is the number of edges meeting at u. If, for every vertex ν in G , deg (ν) = k , we say that G is a k -regular graph. The cycle of order n is denoted by Cn and is a connected 2-regular graph. The path graph of order n is denoted by Pn and obtain by deleting an edge of Cn. A tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected undirected graph without cycle. A leaf (or pendant vertex) of a tree is a vertex of the tree of degree 1. An edge of a graph is said to be pendant if one of its vertices is a pendant vertex. A complete bipartite graph is a graph G with and such that every vertex of the set (part) X is connected to every vertex of the set (part) Y. If , then this graph is denoted by Km,n. The complete bipartite graph K1,n is called the star graph which has n + 1 vertices. The distance between two vertices u and ν of G , denoted by d (u , ν), is defined as the minimum number of edges of the walks between them. The complement of graph G is denoted by and is a graph with the same vertices such that two distinct vertices of are adjacent if, and only if, they are not adjacent in G. For more information on graphs, refer to [1]. [ABSTRACT FROM AUTHOR]

The Sigma colouring (σ - colouring) of a graph σ with G vertices is an injection from V(G) to {1,2,...} such that the colour sums (adding the colours of the neighbouring vertices) of any two neighbouring vertices are different. The smallest number of colours needed to colour a graph G is represented by its Sigma Chromatic number, σ(G). In this article we obtain the σ-colouring of some graphs such as Barbell Graph, Twig graph, Shell graph, Tadpole, Lollipop, Fusing all the vertices of cycle and duplication of every edge by a vertex in Cn. [ABSTRACT FROM AUTHOR]

A function f: E (G) {0,1,2} is an edge Italian dominating function (EIDF) if it satisfies the rule that every edge with weight 0 is either adjacent to an edge with weight 2 or adjacent to at least two edges with weight 1 each. The weight of an EIDF is S. The minimum is the edge Italian domination number (EIDN). The symbol is used to denote the EIDN. In this paper, we obtain the EIDN of some wheel related graphs like gear graph, helm graph, flower graph, web graph etc. [ABSTRACT FROM AUTHOR]

Any line graph L(G), the vertices correspond to the edges of G(V, E) and two vertices in L(G) are adjacent if and only if the corresponding edges in G are adjacent". "If there are vertices u, v in x, y such that dg, G -[G,-] for any pair of vertices S, G in G, then the set G of vertices of f is said to be a double geodetic set of The lowest cardinality of a double geodetic set is represented by the double geodetic number. In this study, we determine double geodetic number of several line graphs. [ABSTRACT FROM AUTHOR]

Random hyper-network is an important hyper-network structure. Studying the structure and properties of random hyper-networks, which helps researchers to understand the influence of the hypernetwork structure on its properties. Currently, studies related to the influence of the internal structure of the hyper-edge on robustness have not been carried out for research on the robustness of hypernetworks. In this paper, we construct three k-uniform random hyper-networks with different structures inside hyper-edges. The nodes inside hyper-edges are connected in the ways randomly connected, preferentially connected and completely connected. Meanwhile, we propose a capacity-load model that can describe the relationship between the internal structure and the robustness of the hyper-edge, based on the idea of capacity-load model. The robustness of the three hyper-networks was obtained by simulation experiments. The results show the variation of the internal structure of hyper-edge has a large influence on the robustness of the k-uniform random hyper-network. In addition, the larger number of ordinary edges mk inside the hyper-edges and the size of the hyper-network k, the more robust the k-uniform random hyper-network is. [ABSTRACT FROM AUTHOR]

It was conjectured by Jaeger et al. that all 5-edge-connected graphs are Z3-connected. In this paper, we confirm this conjecture for all 5-edge-connected graphs with independence number at most 3. [ABSTRACT FROM AUTHOR]

The Sombor index of the graph G is a degree based topological index, deffned as SO =P uv2E(G) p dG(u)2 + dG(v)2, where dG(u) is the degree of the vertex u of G and E(G) is the edge set of G. In this paper we calculate SO of some graph transformations. [ABSTRACT FROM AUTHOR]

Let G = (V;E) be a given graph of order n. A function f: V ! f0; 1; 2g is an independent Roman dominating function (IRDF) on G if for every vertex v 2 V with f(v) = 0 there is a vertex u adjacent to v with f(u) = 2 and fv 2 V: f(v) > 0g is an independent set. The weight of an IRDF f on G is the value f(V) = P v2V f(v). The minimum weight of an IRDF among all IRDFs on G is called the independent Roman domination number of G. In this paper, we give algorithms for computing the independent Roman domination number of G in O(jV j) time when G = (V;E) is a tree, unicyclic graph or proper interval graph. [ABSTRACT FROM AUTHOR]

For a graph G with no isolated vertex, a covering total double Roman dominating function (CTDRD function) f of G is a total double Roman dominating function (TDRD function) of G for which the set fv 2 V (G)jf(v) 6= 0g is a vertex cover set. The covering total double Roman domination number ctdR(G) equals the minimum weight of an CTDRD function on G. An CTDRD function on G with weight ctdR(G) is called a ctdR(G)-function. In this paper, the graphs G with small ctdR(G) are characterised. We show that the decision problem associated with CTDRD is NP-complete even when restricted to planer graphs with maximum degree at most four. We then show that for every graph G without isolated vertices, oitR(G) < ctdR(G) < 2 oitR(G) and for every tree T, 2-(T) + 1 - ctdR(T) - 4-(T), where oitR(G) and -(T) are the outer independent total Roman domination number of G, and the minimum vertex cover number of T respectively. Moreover we investigate the ctdR of corona of two graphs. [ABSTRACT FROM AUTHOR]

We examine the classic game of Cops and Robbers played on dynamic graphs, that is, graphs evolving over discrete time steps. At each time step, a graph instance is generated as a subgraph of the (static) underlying graph. The cops and the robber take their turns on the current graph instance. The cops win if they can capture the robber at some point in time. Otherwise, the robber wins. In the offline case, the players are fully aware of the evolution sequence, up to some finite time horizon T. We provide a O(n2k+1T) algorithm to decide whether a given evolution sequence for an underlying graph with n vertices is k-cop-win via a reduction to a reachability game. In the online case, there is no knowledge of the evolution sequence, and the game might go on forever. Also, each generated instance is required to be connected. We provide a nearly tight characterization for sparse underlying graphs with at most a linear number of edges. We prove λ + 1 cops suffice to capture the robber in any underlying graph with n -- 1+ λ edges. Furthermore, we define a family of underlying graphs with n -- 1 + λ edges where λ -- 1 cops are necessary (and sufficient) for capture. [ABSTRACT FROM AUTHOR]

Given an initial set of planar nodes, the problem is to build a minimum spanning tree connecting the maximum possible number of nodes by not exceeding the maximum edge length. To obtain a set of edges, a Delaunay triangulation is performed over the initial set of nodes. Distances between every pair of the nodes in respective edges are calculated used as graph weights. The edges whose length exceeds the maximum edge length are removed. A minimum spanning tree is built over every disconnected graph. The minimum spanning trees covering a maximum of nodes are selected, among which the tree whose length is minimal is the solution. It is 1.17 % shorter on average for 10 to 80 nodes compared to a nonselected tree. [ABSTRACT FROM AUTHOR]

The challenge of anomaly detection is to obtain an accurate understanding of expected behaviour which is intensified when the data are distributed heterogeneously. Transmitting raw data to a central site incurs high communication overhead and raises privacy issues. The concept of Edge AI allows computation to be performed at the edge site allowing for quick decision making in mission critical scenarios such as self-driving cars. A model is learnt locally and its parameters are transmitted and aggregated. However, existing methods of aggregation do not account for variance and heterogeneous distribution of data. They also do not consider edge constraints such as limited computational, memory and communication capabilities of edge devices. In this work, a fully Bayesian approach is employed by means of a Bayesian Random Vector Functional Link AutoEncoder being incorporated with Expectation Propagation for distributed training. Our anomaly detection system operates without any transmission of raw data, is robust under inhomogeneous network densities and under uneven and biased data distributions. It allows for asynchronous updates to converge in a few iterations and is a relatively simple neural network addressing edge constraints without compromising on performance as compared to existing more complex models. [ABSTRACT FROM AUTHOR]

There is growing interest in applying distributed machine learning to edge computing, forming federated edge learning. Federated edge learning faces non-i.i.d. and heterogeneous data, and the communication between edge workers, possibly through distant locations and with unstable wireless networks, is more costly than their local computational overhead. In this work, we propose ${{\sf DONE}}$ DONE , a distributed approximate Newton-type algorithm with fast convergence rate for communication-efficient federated edge learning. First, with strongly convex and smooth loss functions, ${{\sf DONE}}$ DONE approximates the Newton direction in a distributed manner using the classical Richardson iteration on each edge worker. Second, we prove that ${{\sf DONE}}$ DONE has linear-quadratic convergence and analyze its communication complexities. Finally, the experimental results with non-i.i.d. and heterogeneous data show that ${{\sf DONE}}$ DONE attains a comparable performance to Newton's method. Notably, ${{\sf DONE}}$ DONE requires fewer communication iterations compared to distributed gradient descent and outperforms DANE, FEDL, and GIANT, state-of-the-art approaches, in the case of non-quadratic loss functions. [ABSTRACT FROM AUTHOR]

Deep neural networks (DNNs) have been showing significant success in various anomaly detection applications such as smart surveillance and industrial quality control. It is increasingly important to detect anomalies directly on edge devices, because of high responsiveness requirements and tight latency constraints. The accuracy of DNN-based solutions rely on large model capacity and thus long training and inference time, making them inapplicable on resource strenuous edge devices. It is hence imperative to scale DNN model sizes in correspondence to the run-time system requirements, i.e., meeting deadlines with minimal accuracy losses, which are highly dependent on the platforms and real-time system status. Existing scaling techniques either take long training time to pre-generate scaling options or disturb the unsteady training process of anomaly detection DNNs, lacking the adaptability to heterogeneous edge systems and incurring low inference accuracies. In this article, we present LightDNN to scale DNN models for anomaly detection applications at edge, featuring high detection accuracies with lightweight training and inference time. To this end, LightDNN quickly extracts and compresses blocks in a DNN, and provides large scaling space (e.g., 1 million options) by dynamically combining these compressed blocks online. At run-time, LightDNN predicts the DNN’s inference latency according to the monitored system status, and optimizes the combination of blocks to maximize its accuracy under deadline constraints. We implement and extensively evaluate LightDNN on both CPU and GPU edge platforms using 8 popular anomaly detection workloads. Comparative experiments with state-of-the-art methods show that our approach provides 145.8 to 0.56 trillion times more scaling options without increasing training and inference overheads, thus achieving as much as 15.05% increase in accuracy under the same deadlines. [ABSTRACT FROM AUTHOR]

With the integration of Artificial Intelligence (AI) and Internet of Things (IoT), the Federated Edge Learning (FEL), a promising computing framework is developing. However, there are still unsolved issues on communication efficiency and data security due to the huge models and unreliable transmission links. To address these issues, this paper proposes a novel federated edge learning system, called LightFed, where the edge nodes upload only vital partial local models, and successfully achieve lightweight communication and model aggregation. First, a novel model aggregation method Model Splitting and Splicing (MSS) and a Selective Parameter Transmission (SPT) scheme are proposed. By detecting the updating gradients of local parameters and filtering significant parameters, selective rotated transmission and efficient aggregation of local models are achieved. Second, a Training Filling Model (TFM) is proposed to infer the total data distribution of edge nodes, and train a filling model to mitigate the unbalanced training data without violating the data privacy of individual users. Moreover, a blockchain-powered confusion transmission mechanism is proposed for defending the attacks from external adversaries and protecting the model information. Finally, extensive experimental results demonstrate that our LightFed significantly outperforms the existing FEL systems in terms of communication efficiency and privacy security. [ABSTRACT FROM AUTHOR]

Due to its ability to learn the relationship among nodes from graph data, the graph convolution network (GCN) has received extensive attention. In the machine fault diagnosis field, it needs to construct input graphs reflecting features and relationships of the monitoring signals. Thus, the quality of the input graph affects the diagnostic performance. But it still has two limitations: 1) the constructed input graph usually has redundant edges, consuming excessive computational costs; 2) the constructed input graph cannot reflect the relationship between the noisy signals well. In order to overcome them, a dynamic graph-based feature learning with few edges considering noisy samples is proposed for rotating machinery fault diagnosis in this article. Noisy vibration signals are converted into one spectrum feature-based static graph, where redundant edges are simplified by the distance metric function. Edge connections of the input static graph are updated according to the relationship among high-level features extracted by the GCN. Based on this, dynamic input graphs are reconstructed as new graph representations for noisy samples. To verify the effectiveness of the proposed method, validation experiments were conducted on practical platforms, and results show that the dynamic input graph with few edges can effectively improve the diagnostic performance under different SNRs. [ABSTRACT FROM AUTHOR]