Number Of Nodes In Graph Research Articles

SCGG: A deep structure-conditioned graph generative model.

Deep learning-based graph generation approaches have remarkable capacities for graph data modeling, allowing them to solve a wide range of real-world problems. Making these methods able to consider different conditions during the generation procedure even increases their effectiveness by empowering them to generate new graph samples that meet the desired criteria. This paper presents a conditional deep graph generation method called SCGG that considers a particular type of structural conditions. Specifically, our proposed SCGG model takes an initial subgraph and autoregressively generates new nodes and their corresponding edges on top of the given conditioning substructure. The architecture of SCGG consists of a graph representation learning network and an autoregressive generative model, which is trained end-to-end. More precisely, the graph representation learning network is designed to compute continuous representations for each node in a graph, which are not only affected by the features of adjacent nodes, but also by the ones of farther nodes. This network is primarily responsible for providing the generation procedure with the structural condition, while the autoregressive generative model mainly maintains the generation history. Using this model, we can address graph completion, a rampant and inherently difficult problem of recovering missing nodes and their associated edges of partially observed graphs. The computational complexity of the SCGG method is shown to be linear in the number of graph nodes. Experimental results on both synthetic and real-world datasets demonstrate the superiority of our method compared with state-of-the-art baselines.

OPTIMIZATION OF SWARM ROBOTICS ALGORITHMS

Context. Among the variety of tasks solved by robotics, one can single out a number of those for the solution of which small dimensions of work are desirable and sometimes necessary. To solve such problems, micro-robots with small dimensions are needed, the mass of which allows them to move freely in tight passages, in difficult weather conditions, and remain unnoticed. At the same time, the small dimensions of the microrobot also impose some indirect restrictions; therefore, it is better to use groups of microrobots for the solution of these problems. The efficiency of using groups of microrobots depends on the chosen control strategy and stochastic search algorithms for optimizing the control of a group (swarm) of microrobots.
 Objective. The purpose of this work is to consider a group of swarm algorithms (methods) belonging to the class of metaheuristics. The group of these algorithms includes, in particular, the ant colony algorithm, the possibilities of which were investigated to solve the traveling salesman problem, which often arises when developing an algorithm for the behavior of a group of microrobots.
 Method. At the first stage of the study, the main groups of parameters were identified that determine the flow and characterize the state at any time of the ant colony algorithm: input, control, disturbance parameters, output parameters. After identifying the main groups of parameters, an algorithm was developed, the advantage of which lies in scalability, as well as guaranteed convergence, which makes it possible to obtain an optimal solution regardless of the dimension of the graph. At the second stage, an algorithm was developed, the code of which was implemented in the Matlab language. Computer experiments were carried out to determine the influence of input, control, output, and disturbance parameters on the convergence of the algorithm. Attention was paid to the main groups of indicators that determine the direction of the method and characterize the state of the swarm of microrobots at a given time. In the computational experiment, the number of ants placed in the nodes of the network, the amount of pheromone, the number of graph nodes were varied, the number of iterations to find the shortest path, and the execution time of the method were determined. The final test of modeling and performance of the method was carried out.
 Results. Research has been carried out on the application of the ant algorithm for solving the traveling salesman problem for test graphs with a random arrangement of vertices; for a constant number of vertices and a change in the number of ants, for a constant number of vertices at different values of the coefficient Q; to solve the traveling salesman problem for a constant number of vertices at different values of the pheromone evaporation coefficient p; for a different number of graph vertices. The results showed that ant methods find good traveling salesman routes much faster than clear-cut combinatorial optimization methods. The dependence of the search time and the found optimal route on the values of control parameters are established using the example of test networks for a different number of graph vertices and iterations.
 Conclusions. The studies were carried out to make it possible to give recommendations on the application of the ant colony algorithm to control a group (swarm) of microrobots.

Understanding the Implication of Non-Volatile Memory for Large-Scale Graph Neural Network Training

Graph neural networks (GNNs) can extract features by learning both the representation of each objects (i.e., graph nodes) as well as the relationship across different objects (i.e., the edges that connect nodes), achieving state-of-the-art performance on a wide range of graph-based tasks. Despite its strengths, utilizing these algorithms in a production environment faces several key challenges as the number of graph nodes and edges amount to several billions to hundreds of billions scale, requiring substantial storage space for training. Unfortunately, existing ML frameworks based on the in-memory processing model significantly hamper the productivity of algorithm developers as it mandates the overall working set to fit within DRAM capacity constraints. In this work, we first study state-of-the-art, large-scale GNN training algorithms. We then conduct a detailed characterization on utilizing capacity-optimized non-volatile memory solutions for storing memory-hungry GNN data, exploring the feasibility of SSDs for large-scale GNN training.

Fully Retroactive Minimum Spanning Tree Problem

Abstract This article describes an algorithm that solves a fully dynamic variant of the minimum spanning tree (MST) problem. The fully retroactive MST allows adding an edge to time $t$, or to obtain the current MST at time $t$. By using the square root technique and a data structure link-cut tree, it was possible to obtain an algorithm that runs each query in $O(\sqrt{m} \lg{|V(G)|})$ amortized, in which $|V(G)|$ is the number of nodes in graph $G$ and $m$ is the size of the timeline. We use a different approach to solve the MST problem instead of the standard algorithms, such as Prim or Kruskal, and this allows using the square root technique to improve the final complexity of the algorithm. Our empirical analysis shows that the proposed algorithm runs faster than re-executing the standard algorithms, and this difference only increases when the number of nodes in these graphs is larger.

Development of the positive engagement continuously variable transmission design with the application of graph theory

Various designs of CVTs were explored from two points of view: analysis of the design itself and analysis of the methods and techniques, used in the process of creation of the CVT. To solve the problem of finding new designs of mechanisms, the graph transformation method was developed. It includes the following heuristic techniques: a decrease in the number of graph nodes at simplification of a design or to remove non-essential elements; a change in location of graph edges and comparison of a new location of edges and necessary changes in a design; a search for all possible options for location of the parts that correspond to the same graph; introduction to the graph of the nodes, corresponding to the property, for implementation of which a part (a node) can be added to a design or, vice versa, can be removed from a design, and the property it implemented will be implemented by other parts. The original design of the CVT, in which load is transmitted by gear engagement without using friction disks and flexible sections, was developed. A continuously variable of transition ratio is ensured by a gear wheel with a variable pitch. The gear wheel consists of three gear sectors, two of which are involved in meshing. The third unloaded sector performs a turn with angular velocity that is higher than velocity of rotation of the output shaft until it takes a position before coming into engagement. The CVT does not have such drawback as fluctuations of transmission ratio. Based on the analysis of the bond-graphs, efficiency was determined, which depending on velocity of the output shaft is in the range of 95…97 %. The disadvantage of the developed design is an insufficiently wide gear ratio range R=1.5…1.6, which is limited by transverse contact ratio e α

An Efficient Method for Attributed Graph Clustering

Graph is a universal model to describe real world complex systems,and large graph datasets are common in many application domains.Graph clustering techniques are critical for understanding,analyzing as well as visualizing large graphs.However,with the proliferation of rich attribute information available for objects in real-world graphs,how to leverage structure and attribute information for clustering attributed graphs becomes a new challenge.Most of the existing methods either take traditional clustering approaches by converting structure and attribute information into distance,or just consider one of the two aspects.In this paper,we propose a novel attributed graph clustering method GA-AGC,based on genetic algorithm and Minimum Description Length(MDL).By analyzing the problem of attributed graph clustering,we convert it to the category of Minimum Description Length.The genetic algorithm solution adopts an extended label propagation method as its initialization procedure,and combines a local mutation operator with decreasing description length.The algorithm proposed requires no specified number of clusters,and its running time scales linearly with total number of graph nodes and edges.Extensive experiments on real-life datasets prove the effectiveness and efficiency of our proposed method.

A Bayesian framework for dense depth estimation based on spatial–temporal correlation

Depth video is vital to the representation of the dynamic 3-D video, which is the fundamental for the rapidly growing 3-D video applications. The issues of accuracy and temporal consistency are the main concerns of the researches on depth videos. In previous works, the stereo matching methods with global optimization can generate accurate and dense depth videos. However, the global optimization is computationally intensive, and the temporal consistency is obtained with difficulty in the optimization procedure. In this paper, a Bayesian framework is proposed to generate accurate and temporal consistent dense depth videos in an efficient way. Firstly, the spatial and temporal correlations in 3-D videos from different viewpoints are used to generate the candidates for depth, and these correlations are further measured by extracted features. These features are adopted to estimate the risk of initial depth in our Bayesian framework. Then, a two-stage decision method is designed to select candidates of depth value in the initial depth map with the minimum risk probability. Finally, depth videos are refined by improved graph cuts algorithm with global optimization. An improved graph construction method is designed and applied on graph cuts algorithm to reduce the number of nodes in graph and thus the complexity of global optimization. The experimental results demonstrate that the proposed algorithm can achieve accurate depth videos with higher efficiency up to 68.14% than traditional methods.

Hyperbolic Wheel: A Novel Hyperbolic Space Graph Viewer for Hierarchical Information Content

Tree and graph structures have been widely used to present hierarchical and linked data. Hyperbolic trees are special types of graphs composed of nodes (points or vertices) and edges (connecting lines), which are visualized on a non-Euclidean space. In traditional Euclidean space graph visualization, distances between nodes are measured by straight lines. Displays of large graphs in Euclidean spaces may not utilize efficiently the available space and may impose limitations on the number of graph nodes. The special hyperbolic space rendering of tree-graphs enables adaptive and efficient use of the available space and facilitates the display of large hierarchical structures. In this paper we report on a newly developed advanced hyperbolic graph viewer, Hyperbolic Wheel, which enables the navigation, traversal, discovery and interactive manipulation of information stored in large hierarchical structures. Examples of such structures include personnel records, disc directory structures, ontological constructs, web-pages and other nested partitions. The Hyperbolic Wheel framework provides an intuitive and dynamic graphical interface to explore and retrieve information about individual nodes (data objects) and their relationships (data associations). The Hyperbolic Wheel is freely available online for educational and research purposes.

Smart delivery: a cooperative multi-agent framework for optimised delivery service

Agent technology offers a large number of unique features which makes it a potential choice for implementing real world applications. Owing to their tremendous capabilities, it is regarded as a promising paradigm for future distributed computing. In this paper, we have proposed smart delivery: a cooperative multi-agent framework for optimised delivery service to transfer packets from source to destinations in randomly varying environment in the most efficient way with the help of mobile agents. We are considering packet moving problem in 2D environment consisting of packets and destinations. The task of each mobile agent is to move the packet from the source to the destination. Simulated environment is dynamically generated with varying graph size (i.e., number of nodes in graph), packet ratio and number of destinations. Packets and destinations are randomly placed in the graph and the graph is divided into societies to encourage an efficient and manageable environment for the agents to work in parallel and share expertise within and outside the society. The proposed framework uses decentralised approach and based on layered agent architecture and once initialised manages all the activities autonomously with the help of mobile agents.

An adaptive neural networks model for isomorphism discernment of large-scale kinematic structure

Graphs isomorphism discernment is one of the most important and difficult issues in graphs theory based structures design. To solve the problem, a Hopfield Neural Networks (HNN) model is presented. The solution of HNN is design as a permutation matrix of two graphs, and some operators are improved to prevent premature convergence. The convergence properties of HNN model and the improved HNN model are studied by analysing the search process. The computation times of the HNN model will not be affected greatly by enhancing the number of nodes in graph and the algorithm is efficient for large-scale graphs isomorphism problem.

Frozen development in graph coloring

We define the ‘frozen development’ of coloring random graphs. We identify two nodes in a graph as frozen if they are of the same color in all legal colorings and define the collapsed graph as the one in which all frozen pairs are merged. This is analogous to studies of the development of a backbone or spine in SAT (the Satisfiability problem). We first describe in detail the algorithmic techniques used to study frozen development. We present strong empirical evidence that freezing in 3-coloring is sudden. A single edge typically causes the size of the graph to collapse in size by 28%. We also use the frozen development to calculate unbiased estimates of probability of colorability in random graphs. This applies even where this probability is infinitesimal such as 10 −300 , although our estimates might be subject to very high variance. We investigate the links between frozen development and the solution cost of graph coloring. In SAT, a discontinuity in the order parameter has been correlated with the hardness of SAT instances, and our data for coloring are suggestive of an asymptotic discontinuity. The uncolorability threshold is known to give rise to hard test instances for graph-coloring. We present empirical evidence that the cost of coloring threshold graphs grows exponentially, when using either a specialist coloring program, or encoding into SAT, or even when using the best of both techniques. Hard instances seem to appear over an increasing range of graph connectivity as graph size increases. We give theoretical and empirical evidence to show that the size of the smallest uncolorable subgraphs of threshold graphs becomes large as the number of nodes in graphs increases. Finally, we discuss some of the issues involved in applying our work to the statistical mechanics analysis of coloring.

Combinatorial Solution to the Partitioning of General Graphs

This paper reviews a dynamic programming procedure for the partitioning of connected graphs with integer-weighted nodes and positive valued edges. The upper bound on the number of feasible partitions generated using this technique is shown to grow factorially in the number of graph nodes. The use of graph properties is then introduced to reduce the number of feasible partitions generated in the determination of the optimal partition. Depending upon the structure of the graph, the use of these properties can cause a significant reduction in the computation time and storage space required to partition the graph.