Search

Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, "spectral sparsification" reduces the number of edges to near-linear in the number of nodes, while approximately preserving the cut and spectral structure of the graph. In this work we demonstrate a polynomial quantum speedup for spectral sparsification and many of its applications. In particular, we give a quantum algorithm that, given a weighted graph with $n$ nodes and $m$ edges, outputs a classical description of an $\epsilon$-spectral sparsifier in sublinear time $\tilde{O}(\sqrt{mn}/\epsilon)$. This contrasts with the optimal classical complexity $\tilde{O}(m)$. We also prove that our quantum algorithm is optimal up to polylog-factors. The algorithm builds on a string of existing results on sparsification, graph spanners, quantum algorithms for shortest paths, and efficient constructions for $k$-wise independent random strings. Our algorithm implies a quantum speedup for solving Laplacian systems and for approximating a range of cut problems such as min cut and sparsest cut., Comment: v2: several small improvements to the text. An extended abstract will appear in FOCS'20; v3: corrected a minor mistake in Appendix A; v4: final version as published in SICOMP

Graph theory allows us to gain better insight concerning changes in brain functional architecture associated with cognitive impairments in the early stages of multiple sclerosis (MS). In the present study, we employed a machine-learning system based on graph measures from functional networks constructed by cognitive task-related functional magnetic resonance imaging (fMRI) data. We used a predefined atlas to define the brain regions and Pearson’s correlation to describe the connectivity strength between the regions. Then, several graph metrics were extracted for each subject. After that, the most efficient subsets of features were selected through the Wilcoxon rank-sum test, and the linear support vector machine (SVM) classifier was employed to distinguish between MS and healthy subjects. The node degree, subgraph centrality, K-coreness, and PageRank centralities measured in the left fusiform, hippocampus, and parahippocampal gyri regions demonstrated an accuracy of 85% through the combination of all local measures. Two optimal global measures, modularity and small-worldness index, and individual betweenness centrality feature improved the identification of MS patients with a sensitivity of 81.25%. Our results indicated the potential of the proposed system to identify cognitive changes in early MS for diagnostic purposes.

In this paper, we investigate the maximum flow routing strategy with the service function chain (SFC) constraints in the space information networks (SINs), where a SFC consists of a specific ordered sequence of service functions, and the mission flow must go through these functions in a predefined order. The time-varying SIN is modeled by the time-expanded graph (TEG). We formulate the maximum flow routing strategy problem with the SFC constraints as a linear programming (LP) problem. Furthermore, for a large-scale SIN, as the complexity of solving the LP problem is still very high, we propose a novel low-complexity SFC-constrained graph theory based (SFC-GT) algorithm. Specifically, we formulate this problem as one special single commodity maximum flow problem, where this flow must satisfy the SFC constraints. We first define the SFC-constrained residual network and the SFC-constrained augmenting path. Afterwards, we iteratively search the SFC-constrained augmenting path and update the SFC-constrained residual network. Simulation results demonstrate our proposed SFC-GT algorithm can achieve near-optimal performance with much less complexity.

Background: Physiological and pathological brain aging plays a central role in brain networks modulation. The aim of the present paper was to assess the stability of a proposed method for the evalu...

Correspondence-based rotation search and point cloud registration are two fundamental problems in robotics and computer vision. However, the presence of outliers, sometimes even occupying the great majority of the putative correspondences, can make many existing algorithms either fail or have very high computational cost. In this paper, we present RANSIC (RANdom Sampling with Invariant Compatibility), a fast and highly robust method applicable to both problems based on a new paradigm combining random sampling with invariance and compatibility. Generally, RANSIC starts with randomly selecting small subsets from the correspondence set, then seeks potential inliers as graph vertices from the random subsets through the compatibility tests of invariants established in each problem, and eventually returns the eligible inliers when there exists at least one K-degree vertex (K is automatically updated depending on the problem) and the residual errors satisfy a certain termination condition at the same time. In multiple synthetic and real experiments, we demonstrate that RANSIC is fast for use, robust against over 95% outliers, and also able to recall approximately 100% inliers, outperforming other state-of-the-art solvers for both the rotation search and the point cloud registration problems.

Today, the electrification of flight is more popular than ever, creating a wide array of concept aircraft and associated power system topologies. In order to gain insights into benefits of these varying architectures, this article introduces the development of a framework for electric aircraft power system (EAPS) optimization. The proposed framework accepts inputs from a designer in the form of component parameters and desired flight mission characteristics. A collective graph representing many possible architectures is formed, from which subgraphs that describe power system topologies meeting the flight requirements are extracted and analyzed. Optimal EAPS architectures with respect to goals of minimizing mass while maximizing efficiency and reliability can be subsequently selected from these subgraphs. The framework is exemplified on a 500-kW rated aircraft using data collected from surveys of component parameters, such as power density and efficiency. The presented results show a comparative analysis of different EAPS types with respect to the competing performance metrics of mass, efficiency, and survivability.

With the digital revolution and the Web 2.0 era, web-based social networks such as Facebook and others have become popular mediums for users to do various activities. While social networks are becoming increasingly popular, concerns about trust and trust-related issues are also growing among users. There are many applications where trust plays a vital role in users’ decision-making, requiring trust evaluation. There are several trust evaluation approaches for online social networks in the literature. However, the existing approaches focus only on certain aspects and believe that direct trust between participants is known. Thus, there is a need for a comprehensive trust evaluation approach that infers indirect trust and strives to measure direct trust. This paper proposes an interaction-based and graph-based hybrid approach that attempts to measure direct trust and infer indirect trust among users. Our direct trust measure method utilizes the most important features and similarities between users to measure direct trust. The proposed indirect trust inference method uses the graph theory concept to infer indirect trust. We implement the friend-request identification and the Sybil attack detection applications using the proposed direct trust measure method. Both the applications are evaluated on synthetic and real-world datasets. The empirical results show that the friend-request identification application achieves a high accuracy of 96.17%, and the Sybil attack detection application obtains a high detection rate of 93.20%. The false rates of both applications are very low. The proposed indirect trust inference method is efficient, and it outperforms the existing approach.

The tolerance graph is a well-defined topic for a crisp graph theory. But, tolerance in a fuzzy graph is defined recently and many properties have been investigated. But, in a fuzzy graph, only one tolerance is considered for every vertex. But, in an m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining tolerance for mPFG is not easy and needs some new ideas. By considering m tolerances for every component out of m components of membership values of a vertex or edge, we defined m-polar fuzzy tolerance graph (mPFTG). Here, m-polar fuzzy convex set (mPFCS) as well as strongly mPFCS are also studied. Some different types of mPFTGs like m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also introduced. Some related terms like bounded mPFTG, m-polar fuzzy interval containment graph, m-polar fuzzy unit tolerance graph (mPF unit TG) are also defined. Here, m-polar fuzzy intersection graph along with tolerance core as well as tolerance support length are also discussed. Some interesting properties on m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also investigated. Lastly, a real-life application based on an assigned work done by a private company has been discussed to show its practicability in mPFTG.

The connections in a graph generate a structure that is independent of a coordinate system. This visual metaphor allows creating a more flexible representation of data than a two-dimensional scatterplot. In this work, we present STAD (Simplified Topological Abstraction of Data), a parameter-free dimensionality reduction method that projects high-dimensional data into a graph. STAD generates an abstract representation of high-dimensional data by giving each data point a location in a graph which preserves the approximate distances in the original high-dimensional space. The STAD graph is built upon the Minimum Spanning Tree (MST) to which new edges are added until the correlation between the distances from the graph and the original dataset is maximized. Additionally, STAD supports the inclusion of additional functions to focus the exploration and allow the analysis of data from new perspectives, emphasizing traits in data which otherwise would remain hidden. We demonstrate the effectiveness of our method by applying it to two real-world datasets: traffic density in Barcelona and temporal measurements of air quality in Castile and Leon in ´ Spain. The authors wish to thank Danai Kafetzaki for valuable feedback and proofreading. This work was supported in part by the IWT/SBO 150056 project ”ACquiring CrUcial Medical information Using LAnguage TEchnology” (ACCUMULATE), and by the Flanders AI Impulse Program (“Onderzoeksprogramma Artificiele Intelligentie (AI) ¨ Vlaanderen”).

Synthetic aperture radar (SAR) as a wideband radar system is subject to complicated interferences, such as radio frequency interference or other narrowband interferences (NBIs). In order to suppress the NBI, voluminous literature focused on its signal models and characteristics, such as the sinusoidal model and relatively constant frequencies. However, in practice, the interference environment is commonly complicated. It is hard to model the interferences accurately and mitigate them clearly in an easy way, especially for the time-varying interferences. In this article, a novel graph-based algorithm is proposed to mitigate the time-varying NBIs by using graph theory, which constructs the connections between different azimuth samples of NBIs. As a result, the locally time-varying interferences can be clustered in a nonlinear low-dimensional manifold and effectively removed by the proposed algorithm. In addition, the case of the globally time-varying interference is also analyzed in detail with strict derivations to demonstrate its low-rank property. Furthermore, the matrix factorization scheme is introduced to improve the efficiency of the proposed algorithm, and the closed-form solutions are derived for each iteration. The real SAR data with measured NBIs are provided to demonstrate the effectiveness and efficiency of the proposed algorithm.

Smart homes of the future will have to deal with multi-occupancy scenarios. Multi-occupancy systems entail a preliminary and critical feature: the capability of counting people. This can be fulfilled by means of simple binary sensors, cheaper and more privacy preserving than other sensors, such as cameras. However, it is currently unclear how many people can be counted in a smart home, given the set of available sensors. In this paper, we propose a graph-based technique that allows to map a smart home to an undirected graph G and discover the lower-bound of certainly countable people, also defined as certain count. We prove that every independent set of n vertices of an undirected graph G represents a minimum count of n people. We also prove that the maximum number of certainly countable people corresponds to the maximum independent sets of G, and that the maximal independent sets of G provide every combination of active sensors that ensure different minimum count. Last, we show how to use this technique to identify and optimise suboptimal deployment of sensors, so that the assumptions can be tightened and the theoretical lower-bound improved., Funding agency:Örebro University

An original graph-based model and algorithm for optimal industrial task scheduling are proposed in this article. The innovative algorithm designed, dubbed “Dijkstra optimal tasking” (DOT), is suitable for fully distributed task scheduling of autonomous industrial agents for optimal resource allocation, including energy use. The algorithm was designed starting from graph theory fundamentals, from the ground up, to guarantee a generic nature, making it applicable on a plethora of tasking problems and not case-specific. For any industrial setting in which mobile agents are responsible for accomplishing tasks across a site, the objective is to determine the optimal task schedule for each agent, which maximizes the speed of task achievement while minimizing the movement, thereby minimizing energy consumption cost. The DOT algorithm is presented in detail in this manuscript, starting from the conceptualization to the mathematical formulation based on graph theory, having a thorough computational implementation and a detailed algorithm benchmarking analysis. The choice of Dijkstra, as opposed to other shortest path methods (namely, A * Search and Bellman-Ford) in the proposed graph-based model and algorithm, was investigated and justified. An example of a real-world application based on a refinery site is modeled and simulated and the proposed algorithm's effectiveness and computational efficiency are duly evaluated. A dynamic obstacle course was incorporated to effectively demonstrate the proposed algorithm's applicability to real-world applications.

Tessellations of kekulenes and cycloarenes are of considerable interest as nanomolecular belts in trapping and transportation of heavy metal ions and chloride ions, as they possess optimal electronic features and pore sizes. A class of cycloarenes called kekulenes have been the focus of several experimental and theoretical studies from the stand point of aromaticity, superaromaticity, chirality, and novel electrical and magnetic properties. In the present study, we investigate the entropies and topological characterization of different tessellations of kekulenes through topological computations of superaromatic structures with pores. We introduce the self-powered vertex degree-based topological indices and then derive the graph entropy measures for three different tessellations (zigzag, armchair, and rectangular) via various molecular descriptors that we derive here. Several applications to computing the molecular properties are pointed out. We demonstrate the existence of isentropic and yet nonisomorphic tessellations of kekulenes for the first time. The two tessellations are predicted to be quite close in energy with comparable energy gaps. Graph theory-based PPP methods with parameters derived from higher levels of theory are proposed to be promising tools for the predictions of relative stabilities of kekulene tessellations. We show that the developed techniques can be applied in the general context of artificial intelligence for the machine generation of nuclear magnetic resonance and electron spin resonance spectroscopic patterns as well as in robust computations of thermochemistry of a large combinatorial libraries of tessellations of kekulenes through the generation of bond-equivalence classes.

Maximal clique enumeration (MCE) is a classic problem in graph theory to identify all complete subgraphs in a graph. In prior MCE work, the Bron-Kerbosch algorithm is one of the most popular solutions, and there are several improved algorithms proposed on CPU platforms. However, while few studies have focused on the related issue of parallel implementation, recently, there have been numerous explorations of the acceleration of general purpose applications using a graphics processing unit (GPU) to reduce the computing power consumption. In this article, we develop a GPU-based Bron-Kerbosch algorithm that efficiently solves the MCE problem in parallel by optimizing the process of subproblem decomposition and computing resource usage. To speed up the computations, we use coalesced memory accesses and warp reductions to increase bandwidth and reduce memory latency. Our experimental results show that the proposed algorithm can fully exploit the resources of GPU architectures, allowing for the vast acceleration of operations to solve the MCE problem.

Obstetric studies had long revealed that the human female mental state, although subjective, has a nonlinear relation to the gestation, which could eventually leads to eugenics characteristics. Due to the difference of regions, there are differences between the data, people want to analyze the correlation between the survey data of different regions. Traditional obstetric studies explore health information on understanding and predicting this psychological state. However, most traditional research is based on statistical methods that exploring the correlation between numbers. This type of method lacks an understanding of the natural semantics of obstetric data, so it is prone to problems such as deviation or missing data (such as missing geospatial information) in data analysis. To tackle this problem, we study the use of a generic graph representation on gynecology and obstetric surveys with geospatial features, and propose a bipartite approach, or Geo-SPS, to mine the semantic relationship between low quality health information data. Our solution highlights our unconventional adaptation of novel graph theory from computational physics into biomedical ontology, that carefully maps semantic objects into a bipartite graph. With this tool, Geo-SPS provides a unique approach to semantic similarity metrics. The method supports fast and understandable processing of mixed textual data under different geographic spaces in a graph convolutional neural network. We further evaluate and validate the feasibility of Geo-SPS using a case study on obstetric surveys and health information data from over 3000 pregnant women in three different places from China. Results show that Geo-SPS can effectively represent prenatal mental state from this mixed data set, with an accurate classification on birth defects.

HDBSCAN*, a state-of-the-art density-based hierarchical clustering method, produces a hierarchical organization of clusters in a dataset w.r.t. a parameter $mpts$ m p t s . While a small change in $mpts$ m p t s typically leads to a small change in the clustering structure, choosing a “good” $mpts$ m p t s value can be challenging: depending on the data distribution, a high or low $mpts$ m p t s value may be more appropriate, and certain clusters may reveal themselves at different values. To explore results for a range of $mpts$ m p t s values, one has to run HDBSCAN* for each value independently, which can be computationally impractical. In this paper, we propose an approach to efficiently compute all HDBSCAN* hierarchies for a range of $mpts$ m p t s values by building upon results from computational geometry to replace HDBSCAN*’s complete graph with a smaller equivalent graph. An experimental evaluation shows that our approach can obtain over one hundred hierarchies for the computational cost equivalent to running HDBSCAN* about twice, which corresponds to a speedup of more than 60 times, compared to running HDBSCAN* independently that many times. We also propose a series of visualizations that allow users to analyze a collection of hierarchies for a range of $mpts$ m p t s values, along with case studies that illustrate how these analyses are performed.

The lack of information on the path to tourist attractions makes tourists confused in choosing the shortest path. To overcome this, this study proposes an optimal route search system with the steepest ascent hill climbing method to find the most optimal route to tourist attractions. The search process for this tourist spot begins by looking for the latitude and longitude distance of each tourist spot along with the distance between tourist attractions using google maps, then the distance is entered into the steepest ascent hill climbing method with the initial stage of determining the number of combinations, where the combination results in the number of derivative trails. Then swap the initial path with the derivative path using graph theory. This process is repeated so that if the initial trajectory is smaller than the descended path, the effective route and route will be displayed on google maps. So based on the system testing conducted, the steepest ascent hill climbing method used as the main method of this research can be implemented in the search for the most effective or fastest route using the undirected graph method for the exchange process between tourist attractions

Graph‐based deep‐learning accelerators have been developed. They function as the Multiple Instructions Multiple Data machines to perform massive parallel operations. Blaize Graph Streaming Processor (GSP) proposes the novel architecture based on Streaming Graph model for deep learning applications. The streaming graph is widely applied to software development ranging from network traffic to database applications. The research focuses on streaming graph algorithms and different partitions to enhance the overall efficiency. The GSP achieves four‐level parallelism in architectural design: task parallelism, thread parallelism, data parallelism, and instruction parallelism. Graphcore develops Intelligence Processing Unit which adopts a similar approach as Blaize GSP that applies the graph theory to perform the finegrained operation with a massive parallel thread for deep learning applications. The operation of IPU is based on Bulk Synchronous Parallel model. It divides the operation into the local computation phase, communication phase, and barrier synchronization.

Many materials with remarkable properties are structured as percolating nanoscale networks (PNNs). The design of this rapidly expanding family of composites and nanoporous materials requires a unifying approach for their structural description. However, their complex aperiodic architectures are difficult to describe using traditional methods that are tailored for crystals. Another problem is the lack of computational tools that enable one to capture and enumerate the patterns of stochastically branching fibrils that are typical for these composites. Here, we describe a computational package, StructuralGT, to automatically produce a graph theoretical (GT) description of PNNs from various micrographs that addresses both challenges. Using nanoscale networks formed by aramid nanofibers as examples, we demonstrate rapid structural analysis of PNNs with 13 GT parameters. Unlike qualitative assessments of physical features employed previously, StructuralGT allows researchers to quantitatively describe the complex structural attributes of percolating networks enumerating the network's morphology, connectivity, and transfer patterns. The accurate conversion and analysis of micrographs was obtained for various levels of noise, contrast, focus, and magnification, while a graphical user interface provides accessibility. In perspective, the calculated GT parameters can be correlated to specific material properties of PNNs (e.g., ion transport, conductivity, stiffness) and utilized by machine learning tools for effectual materials design.

Accurately tracking the influential nodes in swarm is the key to improve the control or defense against the drone combat. But the identification of influential nodes is intractable due to hardly capturing the pattern information of the running drones based on the traditional Graph Theory. To tackle this issue, in this paper, we propose a novel framework to identify the influential nodes, which includes Latent Interaction Graph Extraction (LIGE), Degree Centrality based Influential Inference (DCII) and Formation Stability Coefficient based Re-ranking (FSCR). LIGE is employed to reconstruct the latent interaction graph from the dynamic trajectory data by exploiting the encoder in Neural Relational Inference. DCII invokes the traditional graph model and measures the significance of nodes. In the re-ranking module FSCR, we introduce a novel metric, the formation stability coefficient, to measure swarm formation stability and re-ranking the candidates. The experimental results on the Drone swarm datasets demonstrate that our framework can effectively identify the influential nodes of drone swarm. The extracting time in LIGE is relatively long, which makes it difficult to recognize the core node within the limit time. By optimizing the encoder structure, the extraction time can be reduced to at least twice the original.

Purpose The purpose of this study is to provide an alternative graph-based airspace model for more effective free-route flight planning. Design/methodology/approach Based on graph theory and available data sets describing airspace, as well as weather phenomena, a new FRA model is proposed. The model is applied for near to optimal flight route finding. The software tool developed during the study and complexity analysis proved the applicability and timed effectivity of the flight planning approach. Findings The sparse bidirectional graph with edges connecting only (geographically) closest neighbours can naturally model local airspace and weather phenomena. It can be naturally applied to effective near to optimal flight route planning. Research limitations/implications Practical results were acquired for one country airspace model. Practical implications More efficient and applicable flight planning methodology was introduced. Social implications Aircraft following the new routes will fly shorter trajectories, which positively influence on the natural environment, flight time and fuel consumption. Originality/value The airspace model proposed is based on standard mathematical backgrounds. However, it includes the original airspace and weather mapping idea, as well as it enables to shorten flight planning computations.

Objective Exercise interventions have emerged as a promising approach for managing symptoms associated with multiple sclerosis (MS). However, changes in brain function underlying exercise-related improvements in symptoms of MS have not been fully investigated, and in no instances have they been investigated using a graph theory approach. For the first time, the effects of an exercise intervention on functional brain network connectivity were examined using graph theory analyses of resting-state functional MRI (fMRI) data among individuals with relapsing-remitting MS (RRMS). Methods Resting-state fMRI data were obtained from 10 participants before and after 12 weeks of a speeded walking intervention. Functional connectivity data were preprocessed in Data Processing Assistant for Resting-State fMRI Advanced (DPARSF A version 4.2) and analyzed in GraphVar2.02 to compute global and local graph theory metrics. To examine differences in graph metrics before and after the intervention, one-sample permutation tests were performed. Results There were no significant pre to post exercise intervention changes in global metrics. Changes in local metrics (i.e. clustering coefficient, local efficiency, degree centrality and betweenness centrality) were mixed, with both increases and decreases observed. Conclusion Following a 12-week speeded walking exercise intervention, there were no significant increases or decreases in global graph metrics and results at the level of local metrics were equivocal in individuals with RRMS. Further research with experimental designs that include baseline and longitudinal follow-up, as well as larger sample sizes, is needed to understand the underlying mechanisms of symptom improvement following exercise in RRMS.

Graph theory is a branch of mathematics that allows for the characterization of complex networks, and has rapidly grown in popularity in network neuroscience in recent years. Researchers have begun to use graph theory to describe the brain networks of individuals with brain tumors to shed light on disrupted networks. This systematic review summarizes the current literature on graph theoretical analysis of magnetic resonance imaging data in the brain tumor population with particular attention paid to treatment effects and other clinical factors. Included papers were published through June 24th, 2020. Searches were conducted on Pubmed, PsycInfo, and Web of Science using the search terms (graph theory OR graph analysis) AND (brain tumor OR brain tumour OR brain neoplasm) AND (MRI OR EEG OR MEG). Studies were eligible for inclusion if they: evaluated participants with a primary brain tumor, used graph theoretical analyses on structural or functional MRI data, MEG, or EEG, were in English, and were an empirical research study. Seventeen papers met criteria for inclusion. Results suggest alterations in network properties are often found in people with brain tumors, although the directions of differences are inconsistent and few studies reported effect sizes. The most consistent finding suggests increased network segregation. Changes are most prominent with more intense treatment, in hub regions, and with factors such as faster tumor growth. The use of graph theory to study brain tumor patients is in its infancy, though some conclusions can be drawn. Future studies should focus on treatment factors, changes over time, and correlations with functional outcomes to better identify those in need of early intervention.

The orthogonal disjunctive normal forms (DNFs) of Boolean functions have wide applications in the logical design of discrete devices. The problem of DNF orthogonalization is to get for a given function such a DNF that any two its terms would be orthogonal, i. e. the conjunction of them would be equal identically to zero. An approach to solve the problem using the means of graph theory is suggested. The approach is proposed by representation of the function as perfect DNF. Obtaining all the intervals of the Boolean space where the given function has value 1 is supposed, and the intersection graph of those intervals is considered. Two methods to obtain a minimum orthogonal DNF are considered. One of them reduces the problem toward finding out the smallest dominating set in the graph by covering its vertices with their closed neighborhoods, the other - to obtain the maximum independent set by lexicographic enumeration. It is shown how the suggested approach can be extended on incompletely specified Boolean functions.

Similarity search finds application in database systems handling complex data such as images or videos, which are typically represented by high-dimensional features and require specific indexing structures. This paper tackles the problem of better utilizing GPUs for this task. While GPUs excel at data parallel tasks such as distance computation, prior approaches in this domain are bottlenecked by algorithms that expose less parallelism, such as $k$ k -min selection, or make poor use of the memory hierarchy. We propose a novel design for $k$ k -selection. We apply it in different similarity search scenarios, by optimizing brute-force, approximate and compressed-domain search based on product quantization. In all these setups, we outperform the state of the art by large margins. Our implementation operates at up to 55 percent of theoretical peak performance, enabling a nearest neighbor implementation that is 8.5 × faster than prior GPU state of the art. It enables the construction of a high accuracy $k$ k -NN graph on 95 million images from the Yfcc100M dataset in 35 minutes, and of a graph connecting 1 billion vectors in less than 12 hours on 4 Maxwell Titan X GPUs. We have open-sourced our approach for the sake of comparison and reproducibility.

In this article, we introduce HashGraph, a new scalable approach for building hash tables that uses concepts taken from sparse graph representations—hence, the name HashGraph. HashGraph introduces a new way to deal with hash-collisions that does not use “open-addressing” or “separate-chaining,” yet it has the benefits of both these approaches. HashGraph currently works for static inputs. Recent progress with dynamic graph data structures suggests that HashGraph might be extendable to dynamic inputs as well. We show that HashGraph can deal with a large number of hash values per entry without loss of performance. Last, we show a new querying algorithm for value lookups. We experimentally compare HashGraph to several state-of-the-art implementations and find that it outperforms them on average 2× when the inputs are unique and by as much as 40× when the input contains duplicates. The implementation of HashGraph in this article is for NVIDIA GPUs. HashGraph can build a hash table at a rate of 2.5 billion keys per second on a NVIDIA GV100 GPU and can query at nearly the same rate.

The first article about graph theory was written by Leonhard Euler the famous Swiss mathematician which was published in 1736. Primarily, the idea of graph was not important as point of mathematics because it mostly deals with recreational puzzles. But the recent improvement in mathematics specially, its application brought a strong revolution in graph theory. Therefore, this article is written under the title of (Role of Zero-divisor graph in power set ring). This study clarifies the role of the zero-fraction graph in the strength ring and the library research method was used for the collection of information from the past research. This study first introduces the zero-divisor graph set of alternatives in R ring. Then presents the Role of Zero-divisor graph in power set ring. Whereas the vertex is denoted with K1 and the elements of an optional ring which are not zero-divisors they are the vertices without edges of that ring in zero-divisor graph. Next, we will study when a graph is planar in power set ring. The research found out that if the element numbers of set X  is less than 4, the graph of zero-divisor graph ring of P X( ) is planar and if the element numbers of set X is greater than or equals to 4, the zero-divisor graph ring is not planar.

Epileptic EEG signal recognition is an important method for epilepsy detection. In essence, epileptic EEG signal recognition is a typical imbalanced classification task. However, traditional machine learning methods used for imbalanced epileptic EEG signal recognition face many challenges: (1) traditional machine learning methods often ignore the imbalance of epileptic EEG signals, which leads to misclassification of positive samples and may cause serious consequences and (2) the existing imbalanced classification methods ignore the interrelationship between samples, resulting in poor classification performance. To overcome these challenges, a graph-based extreme learning machine method (G-ELM) is proposed for imbalanced epileptic EEG signal recognition. The proposed method uses graph theory to construct a relationship graph of samples according to data distribution. Then, a model combining the relationship graph and ELM is constructed; it inherits the rapid learning and good generalization capabilities of ELM and improves the classification performance. Experiments on a real imbalanced epileptic EEG dataset demonstrated the effectiveness and applicability of the proposed method.

A parameter is a numerical or other measurable factor whose values characterize a system. Connectivity parameters have indispensable role in the analysis of connectivity of networks. Strength of a cycle in an unweighted graph is always one. But, in a fuzzy graph, strengths of cycles may vary even for a given pair of vertices. Cyclic reachability is a property that determines the overall connectedness of a network. This article introduces two connectivity parameters namely, cyclic connectivity index (CCI) and average CCI (ACCI) of fuzzy graphs, which can be used to represent the cyclic reachability. CCI of fuzzy graph theoretic structures, such as trees, blocks, $\theta$ -fuzzy graphs, and complete fuzzy graphs, are discussed. Vertices of a fuzzy graph are classified into three categories in terms of ACCI and their characterizations are obtained. Three algorithms are proposed. One of them is to help find CCI and ACCI of a given fuzzy graph. Another helps to identify the nature of vertices and the third to enhance the existing ACCI of a fuzzy graph. Also, future directions in the study of CCI and ACCI are proposed.

CNNs, RNNs, GCNs, and CapsNets have shown significant insights in representation learning and are widely used in various text mining tasks such as large-scale multi-label text classification. Most existing deep models for multi-label text classification consider either the non-consecutive and long-distance semantics or the sequential semantics. However, how to coherently take them into account is still far from studied. In addition, most existing methods treat output labels as independent medoids, ignoring the hierarchical relationships among them, which leads to a substantial loss of useful semantic information. In this paper, we propose a novel hierarchical taxonomy-aware and attentional graph capsule recurrent CNNs framework for large-scale multi-label text classification. Specifically, we first propose to model each document as a word order preserved graph-of-words and normalize it as a corresponding word matrix representation preserving both the non-consecutive, long-distance and local sequential semantics. Then the word matrix is input to the proposed attentional graph capsule recurrent CNNs for effectively learning the semantic features. To leverage the hierarchical relations among the class labels, we propose a hierarchical taxonomy embedding method to learn their representations, and define a novel weighted margin loss by incorporating the label representation similarity. Extensive evaluations on three datasets show that our model significantly improves the performance of large-scale multi-label text classification by comparing with state-of-the-art approaches.

This article focuses on the design of a hierarchical framework for locating faults in smart grids by resorting to only modal components of three-phase voltage measurements. The search space for identifying the faulty lines is first limited to the impacted regions by the fault, which is determined through an improved graph analytic-based algorithm by contributing the system topology and attribute affinities. The faulty lines within the faulty regions are then identified by employing a heuristic index extracted from the wavelet multiresolution analysis of corresponding modal components. The fault location on the faulty lines is finally estimated by the regression analysis of two novel graph regularization-based learning models. This fault location proposal has been evaluated over numerous simulated scenarios on the IEEE 39-bus system with the measurements subject to sampling rate, fault resistance, and noise issues. The attained results validate the efficiency of the proposed framework.

The aim of this note is to provide an interpretation of two families of quasi anti-tridiagonal matrices in terms of graph theory. Understanding this junction allows us to recover a plethora of rece...

This paper addresses the relative position coordinated control problem for spacecraft formation flying under an undirected communication graph, whilst considering mass uncertainties, external disturbances, and limited communication resources. A new event-triggered information transmission mechanism is first presented, where each spacecraft only requires accessing to the states of neighbors intermittently. Subsequently, a novel event-based coordinated control scheme is proposed by combining a smooth adaptive projection rule that confines the parameter estimations to well-defined bounded convex hypercubes. Under the proposed control framework, the information exchange among spacecraft occurs only when the specified event is triggered, thereby significantly reducing the communication load and saving the onboard resources. Furthermore, a positive lower bound on interevent time intervals is guaranteed to exclude Zeno behavior. By virtue of Lyapunov stability analysis and graph theory, it is proved that the relative position tracking errors can converge to small invariant sets around the origin, and that all closed-loop signals are bounded, even in the presence of mass uncertainties and external disturbances. Finally, numerical simulations are given to evaluate the effectiveness and highlight the advantages of the developed control algorithm.

Funding: Ajay Kumar is supported by CSIR-UGC JRF, New Delhi, India, through Ref No.: 19/06/2016(i)EU-V/Roll No: 417267. Lavanya Selvaganesh is financially supported by SERB, India, through Grant No.: MTR/2018/000254 under the scheme MATRICS. T. Tamizh Chelvam is supported by CSIR Emeritus Scientist Scheme of Council of Scientific and Industrial Research (No.21 (1123)/20/EMR-II), Government of India. Algebraic graph theory is the study of the interplay between algebraic structures (both abstract as well as linear structures) and graph theory. Many concepts of abstract algebra have facilitated through the construction of graphs which are used as tools in computer science. Conversely, graph theory has also helped to characterize certain algebraic properties of abstract algebraic structures. In this survey, we highlight the rich interplay between the two topics viz groups and power graphs from groups. In the last decade, extensive contribution has been made towards the investigation of power graphs. Our main motive is to provide a complete survey on the connectedness of power graphs and proper power graphs, the Laplacian and adjacency spectrum of power graph, isomorphism, and automorphism of power graphs, characterization of power graphs in terms of groups. Apart from the survey of results, this paper also contains some new material such as the contents of Section 2 (which describes the interesting case of the power graph of the Mathieu group M_{11}) and subsection 6.1 (where conditions are discussed for the reduced power graph to be not connected). We conclude this paper by presenting a set of open problems and conjectures on power graphs. Publisher PDF

We develop an empirical electrical-based framework to compare between centrality measures as to judge their ability to predict the vulnerability of smart grids and their elements under various attacks. The centrality measures considered are based on a weighted graph adjacency matrix representing the real power flows. The vulnerability is measured by the post-attack unsatisfied load (UL), which is determined through steady-state simulation using the MatPower v6.0. We introduce a generalized vulnerability curve as a plot of measures of electrical damage (e.g., the UL), versus physical damage. We consider various measures of physical damage such as the Fraction of Elements (FOE) removed and sums of centrality scores of elements removed. The area under the vulnerability curve (denoted as VPM) is shown to be a logical, reliable, and consistent indicator of the predictive power of a centrality measure. The VPM is simulated for several attacks including the Remove Most Central Elements First (RMCEF) attack. We show that degree centrality is the most predictive, when compared to eigenvector and betweenness centralities. Moreover, the degree-based RMCEF attack is the worst among the RMCEF and 5400 random attacks. The FOE-degree centrality VPM is the most predictive as well as the most computationally efficient.

In a general sense, a metacommunity can be considered as a network of communities, the coherence of which is based on characteristics that are shared by members of different communities, whatever forces were responsible (dispersal, migration, local adaptation, etc.). The purpose is to show that by basing the assessment of coherence on the degree of nestedness of one community within another with respect to the shared characteristics, coherence components can be identified within the network. To assess coherence, a measure of nestedness is developed, and its application to complex (variable) object differences (including multiple traits or characters) is investigated. A community network is then viewed as a graph in which the nodes represent the communities and the edges connecting nodes are weighted by the reverse of the degrees of nestedness between the corresponding communities. Given this framework, it is argued that a minimum requirement for a set of communities to be coherent is the existence of a spanning tree known from graph theory, i.e. a subgraph that connects all nodes through a cycle-free sequence of edges with positive weights. Of all spanning trees, minimum spanning trees (MST, or spanning trees with the minimum sum of edge weights) are most indicative of coherence. By expressing the degree of coherence as one minus the average weight of the edges of an MST, it is uniquely determined which communities form a coherent set at any given level of community distinctness. By this method, community networks can be broken down into coherence components that are separated at a specified distinctness level. This is illustrated in a worked example showing how to apply graph theoretical methods to distinguish coherence components at various threshold levels of object difference (resolution) and community distinctness. These results provide a basis for discussion of coherence gradients and coherence at various levels of distinctness in terms of MST-characteristics. As intuitively expected and analytically confirmed, coherence is a non-decreasing function of the object difference threshold, and the number of coherence components is a non-increasing function of both the object difference and the community distinctness thresholds.

INTRODUCTION: Knowledge graphs have proven to be promising systems of information storage and retrieval. Due to the recent explosion of heterogeneous multimodal data sources generated in the biomedical domain, and an industry shift toward a systems biology approach, knowledge graphs have emerged as attractive methods of data storage and hypothesis generation. AREAS COVERED: In this review, the author summarizes the applications of knowledge graphs in drug discovery. They evaluate their utility; differentiating between academic exercises in graph theory, and useful tools to derive novel insights, highlighting target identification and drug repurposing as two areas showing particular promise. They provide a case study on COVID-19, summarizing the research that used knowledge graphs to identify repurposable drug candidates. They describe the dangers of degree and literature bias, and discuss mitigation strategies. EXPERT OPINION: Whilst knowledge graphs and graph-based machine learning have certainly shown promise, they remain relatively immature technologies. Many popular link prediction algorithms fail to address strong biases in biomedical data, and only highlight biological associations, failing to model causal relationships in complex dynamic biological systems. These problems need to be addressed before knowledge graphs reach their true potential in drug discovery.

Under the Smart City Project, Guwahatians got facility of Water ATMs. In this research main aim is to find out the optimal locations in the city on the basis of internal factors of the location (like quantity and quality of water etc.) so that maximum number of citizens avail the benefits of water ATM. There are sets of Water ATMs that cannot be taken down together, because they have certain critical functions like -installation of new software, update of existing software, installation of required equipment, raw water supply problem, maintenance of pipelines, change the capacity of water tanks, electricity problem, plumbing or all routine maintenance etc. This is a typical scheduling application of graph coloring problem. It turned out that 3 colors were good enough to color the graph of 12 nodes. So they could install updates in 3 passes.

Objectives: In communication engineering, the assignment of channels or frequencies to different transmitters in a communication network without interference is an important problem. Finding the span for such an assignment is a challenging task. The objective of this study is to find the span of quadrilateral snake families. Method: The solution to the channel assignment problem can be found out by modeling the communication network as a graph, where the transmitters are represented by nodes and connectivity between transmitters are given by edges. The labeling technique in graph theory is very useful to solve this problem. Let G=(V;E) be a graph with vertex set V, edge set E. Let u;v 2V(G). The radio antipodal mean labeling of a graph G is a function f that assigns to each vertex u, a non-negative integer f (u) such that f (u) = f (v) if d(u;v) < diam(G) and d(u;v)+⌈f (u)+ f (v)2⌉ diam(G) , where d(u;v) represents the shortest distance between any pair of vertices u and v of G and diam(G) is the diameter of G. The radio antipodal mean number of f, is the maximum number assigned to any vertex of G and is denoted by ramn( f ). The radio antipodal mean number of G, denoted by ramn(G) is the minimum value of ramn( f ) taken over all antipodal mean labeling f of G. Findings: In this study, we have obtained the bounds of radio antipodal mean number of quadrilateral snake families. Novelty: The radio antipodal mean number of quadrilateral snake families was not studied so far. Hence, the establishment of the bounds for radio mean number of quadrilateral snake families will motivate many researchers to study the radio antipodal mean number of other communication networks. Keywords: Radio antipodal mean labeling; quadrilateral snake; alternate quadrilateral snake; double quadrilateral snake; double alternate quadrilateral snake

Link prediction is challenging, especially based on (scarce) historic data or in cold start scenarios. In this paper, we show how to apply answer set programming (ASP) for formalizing link prediction in feature-rich networks, that is – in particular – using domain knowledge for network (and graph) analysis. We show, that applying ASP for link prediction provides a powerful declarative approach, as exemplified using simple predictors, and demonstrate according explanation generation using ASP. We present the application of the proposed methodological approach for explicative link prediction and analysis with explanation generation using different datasets. Keywords . Explainable AI, social network analysis, link prediction, answer set programming, Prolog, domain knowledge

The heterogeneity of cells in a battery pack is inevitable but brings high risks of premature failure and even safety hazards. Accordingly, for safe and long-life operation, it is necessary to adjust the state of charge (SOC) of all in-pack cells to the same level. To address this problem, this article first proposes a battery SOC observer and analyzes its stability and convergence analysis using the Lyapunov direct method. Different to most available estimators is that the proposed method does not require the information of cell capacities. Then, after modeling the equalization system as a directed graph, the equalization problem is cast as a path searching problem. Finally, an A-star algorithm subject to balancing constraints is proposed to find the shortest path in this graph, corresponding to the most efficient SOC equalization. Experimental results show that the steady-state error of the proposed observer is less than $2\%$ . It also demonstrates that the A-star algorithm can decrease the balancing time and energy loss during the balancing process by 9.59% and 19.5%, respectively, relative to the mean-difference-average method.

Motivation Polypharmacy side effects should be carefully considered for new drug development. However, considering all the complex drug–drug interactions that cause polypharmacy side effects is challenging. Recently, graph neural network (GNN) models have handled these complex interactions successfully and shown great predictive performance. Nevertheless, the GNN models have difficulty providing intelligible factors of the prediction for biomedical and pharmaceutical domain experts. Method A novel approach, graph feature attention network (GFAN), is presented for interpretable prediction of polypharmacy side effects by emphasizing target genes differently. To artificially simulate polypharmacy situations, where two different drugs are taken together, we formulated a node classification problem by using the concept of line graph in graph theory. Results Experiments with benchmark datasets validated interpretability of the GFAN and demonstrated competitive performance with the graph attention network in a previous work. And the specific cases in the polypharmacy side-effect prediction experiments showed that the GFAN model is capable of very sensitively extracting the target genes for each side-effect prediction. Availability and implementation https://github.com/SunjooBang/Polypharmacy-side-effect-prediction.

BACKGROUND: Hospital re-engineering initiatives aiming to meet the requirement for patient-centered care often face significant barriers. Opportunities from the optimization of patient flow logistics are often overlooked due to the perception that patient transport related services are ancillary. OBJECTIVES: To reorganize patient pathways by optimizing inpatient assignment and outpatient unit relocation. METHODS: Our analysis was conducted in a campus-based hospital hosting 1694 inpatient beds. Patient flow data was used for algorithm-based optimization to minimize the sum of the distances due to visits to outpatient units and visits by consulting physicians. Inpatients were reordered and outpatient units were relocated to minimize transport need. Optimized schemes were analyzed using graph- and spectral graph theory. RESULTS: Both optimizations yielded an altered hospital layout in which the need for patient transfers decreased (over 30% and 23% in terms of total distance and transfer episodes, respectively). The optimized systems gave rise to buildings with greater specialization, higher importance in terms of contributing to the network architecture, greater synchronization and robustness. CONCLUSIONS: The top-down algorithm-based optimization scheme yielded a system in which the need for cross-building patient transfer decreased. We suggest that network analysis may be a useful tool for capacity planning.

Finding the most suitable co-author is one of the most important ways to conduct effective research in scientific fields. Data science has contributed to achieving this possibility significantly. The present study aims at designing a mathematical model of co-author recommender system in bioinformatics using graph mining techniques and big data applications. The present study employed an applied-developmental research method and a mixed-methods research design. The research population consisted of all scientific products in bioinformatics in the PubMed database. To achieve the research objectives, the most appropriate effective features in choosing a co-author were selected, prioritized, and weighted by experts. Then, they were weighted using graph mining techniques and big data applications. Finally, the mathematical co-author recommender system model in bioinformatics was presented. Data analysis instruments included Expert Choice, Excel, Spark, Scala and Python programming languages in a big data server. The research was conducted in four steps: (1) identifying and prioritizing the criteria effective in choosing a co-author using AHP; (2) determining the correlation degree of articles based on the criteria obtained from step 1 using algorithms and big data applications; (3) developing a mathematical co-author recommender system model; and (4) evaluating the developed mathematical model. Findings showed that the journal titles and citations criteria have the highest weight while the abstract has the lowest weight in the mathematical co-author recommender system model. The accuracy of the proposed model was 72.26. It was concluded that using content-based features and expert opinions have high potentials in recommending the most appropriate co-authors. It is expected that the proposed co-author recommender system model can provide appropriate recommendations for choosing co-authors on various fields in different contexts of scientific information. The most important innovation of this model is the use of a combination of expert opinions and systemic weights, which can accelerate the finding of co-authors and consequently saving time and achieving a greater quality of scientific products.

Application scientists often employ feature tracking algorithms to capture the temporal evolution of various features in their simulation data. However, as the complexity of the scientific features is increasing with the advanced simulation modeling techniques, quantification of reliability of the feature tracking algorithms is becoming important. One of the desired requirements for any robust feature tracking algorithm is to estimate its confidence during each tracking step so that the results obtained can be interpreted without any ambiguity. To address this, we develop a confidence-guided feature tracking algorithm that allows reliable tracking of user-selected features and presents the tracking dynamics using a graph-based visualization along with the spatial visualization of the tracked feature. The efficacy of the proposed method is demonstrated by applying it to two scientific datasets containing different types of time-varying features.

This article investigates set invariance and optimal set stabilization of Boolean control networks (BCNs) from a novel graph-theoretical perspective. First, we establish the relationship between the control invariant sets and the strongly connected components of the state transition graph (STG), and propose a new algorithm to compute the largest control invariant subset. Second, both set stabilizability and time-optimal set stabilization via state feedback are characterized by a breadth-first tree of the STG. Though the prior two problems have been attempted by existing algebraic methods, the primary advantage of our alternative graphical approach is the enhanced computational efficiency. Third, we consider for the first time, the optimal set stabilization problem with general cost criteria, not limited to time optimality. A state feedback controller is constructed for general optimal set stabilization using a shortest-path tree of the STG. Finally, it is straightforward to extend the proposed approach to handle various constraints as well as other types of logical networks by slightly modifying the STG. Two biological networks are used to test the performance of our approach. Results show that in accordance with time complexity analysis, our algorithms can dramatically reduce the running time for the first two problems compared with existing work, and effectively solve the general optimal set stabilization problem.

It is proved that the coordination sequence of the graph obtained from a crystal is of quasi-polynomial type, as had been postulated by Grosse-Kunstleve et al. [Acta Cryst. (1996), A52, 879–889] in their study of coordination sequences of zeolites., The coordination sequence of a graph measures how many vertices the graph has at each distance from a fixed vertex and is a generalization of the coordination number. Here it is proved that the coordination sequence of the graph obtained from a crystal is of quasi-polynomial type, as had been postulated by Grosse-Kunstleve et al. [Acta Cryst. (1996), A52, 879–889].

There is an incredible importance of topological indices in the field of graph theory. M-polynomial is a very effective way for finding the topological indices of a graph. In this article, some important topological indices such as Atom bond connectivity index, geometric-arithmetic index, K-Banhatti indices, Hyper K-Banhatti indices and Modified K-Banhatti indices of Jahangir graph has been calculated from its M-polynomial.

Purpose of research. We have discovered a wide range of problems that are important in practice and which can be reduced in polynomial time to discrete combinatorial optimization problems, many of which can be solved using graph theory. One of these tasks is finding the chromatic number of a graph and its corresponding coloring. Taking into account the fact that the combinatorial problem of finding the chromatic number of a graph belongs to the complexity class and does not allow obtaining an optimal solution in a rational time for problems of practically important dimension, the search for a suitable heuristic method that allows obtaining high-quality solutions with low costs required for computation is demanded and relevant. The aim of the study is to analyze the results of using the bee colony method in the task at hand. The tasks of this research are: description of algorithmic techniques in a formalized form, which make it possible to apply the bee colony method in the problem to be solved, making modifications to the bee colony method that increase the efficiency of the method, namely the quality of the resulting final colorings, as well as the determination of factors affecting the quality and the time spent in finding solutions. Methods. To conduct research in the selected area, computational experiments were organized based on the use of heuristic methods in the problem under consideration. Meta-optimization of the tuning parameters of the methods and determination of their convergence rate was carried out, as well as a comparison of the quality and time of obtaining solutions. Results. As a result of the study, the convergence rate of the method was found to be higher than that of the random walk method; the dependence of the quality of the resulting final colorings on the graph size N and density d was found. It was found that the chosen method is faster than the method of weighted random enumeration with the variation of vertices according to the minimum of admissible colors on »67% , which currently generates solutions with the lowest chromatic number, while losing quality to it on »7% . A higher rate of convergence was noticed when compared with the method of random walks, the principle of which is the same as that of foraging bees. Conclusion. It was found that the bee colony method finds colorings with the same average chromatic number in fewer iterations than the random walk method, i.e. it has a higher convergence rate, while remaining significantly fast relative to the method of random search with a variation of vertices to reduce the allowed colors.