Edges Of Graph Research Articles

Efficient Path Planning Algorithm Based on Laser SLAM and an Optimized Visibility Graph for Robots

Mobile robots’ efficient path planning has long been a challenging task due to the complexity and dynamism of environments. If an occupancy grid map is used in path planning, the number of grids is determined by grid resolution and the size of the actual environment. Excessively high resolution increases the number of traversed grid nodes and thus prolongs path planning time. To address this challenge, this paper proposes an efficient path planning algorithm based on laser SLAM and an optimized visibility graph for mobile robots, which achieves faster computation of the shortest path using the optimized visibility graph. Firstly, the laser SLAM algorithm is used to acquire the undistorted LiDAR point cloud data, which are converted into a visibility graph. Secondly, a bidirectional A* path search algorithm is combined with the Minimal Construct algorithm, enabling the robot to only compute heuristic paths to the target node during path planning in order to reduce search time. Thirdly, a filtering method based on edge length and the number of vertices of obstacles is proposed to reduce redundant vertices and edges in the visibility graph. Additionally, the bidirectional A* search method is implemented for pathfinding in the efficient path planning algorithm proposed in this paper to reduce unnecessary space searches. Finally, simulation and field tests are conducted to validate the algorithm and compare its performance with classic algorithms. The test results indicate that the method proposed in this paper exhibits superior performance in terms of path search time, navigation time, and distance compared to D* Lite, FAR, and FPS algorithms.

Performance paradox of dynamic matching models under greedy policies

We consider the stochastic matching model on a non-bipartite compatibility graph and analyze the impact of adding an edge to the expected number of items in the system. One may see adding an edge as increasing the flexibility of the system, for example, asking a family registering for social housing to list fewer requirements in order to be compatible with more housing units. Therefore, it may be natural to think that adding edges to the compatibility graph will lead to a decrease in the expected number of items in the system and the waiting time to be assigned. In our previous work, we proved this is not always true for the First Come First Matched discipline and provided sufficient conditions for the existence of the performance paradox: despite a new edge in the compatibility graph, the expected total number of items can increase. These sufficient conditions are related to the heavy-traffic assumptions in queueing systems. The intuition behind this is that the performance paradox occurs when the added edge in the compatibility graph disrupts the draining of a bottleneck. In this paper, we generalize this performance paradox result to a family of so-called greedy matching policies and explore the type of compatibility graphs where such a paradox occurs. Intuitively, a greedy matching policy never leaves compatible items unassigned, so the state space of the system consists of finite words of item classes that belong to an independent set of the compatibility graph. Some examples of greedy matching policies are First Come First Match, Match the Longest, Match the Shortest, Random, Priority. We prove several results about the existence of performance paradoxes for greedy disciplines for some family of graphs. More precisely, we prove several results about the lifting of the paradox from one graph to another one. For a certain family of graphs, we prove that there exists a paradox for the whole family of greedy policies. Most of these results are based on strong aggregation of Markov chains and graph theoretical properties.

Eliminating ontology contradictions based on the Myerson value

Ontologies play a pivotal role in knowledge representation across various artificial intelligence domains, serving as foundational frameworks for organizing data and concepts. However, the construction and evolution of ontologies frequently lead to logical contradictions that undermine their utility and accuracy. Typically, these contradictions are addressed using an Integer Linear Programming (ILP) model, which traditionally treats all formulas with equal importance, thereby neglecting the distinct impacts of individual formulas within minimal conflict sets. To advance this method, we integrate cooperative game theory to compute the Shapley value for each formula, reflecting its marginal contribution towards resolving logical contradictions. We further construct a graph-based representation of the ontology, enabling the extension of Shapley values to Myerson values. Subsequently, we introduce a Myerson-weighted ILP model that employs a lexicographic approach to eliminate logical contradictions in ontologies. The model ensures the minimum number of formula deletions, subsequently applying Myerson values to guide the prioritization of deletions. Our comparative analysis across 18 ontologies confirms that our approach not only preserves more graph edges than traditional ILP models but also quantifies formula contributions and establishes deletion priorities, presenting a novel approach to ILP-based contradiction resolution.

Property Graph Partition Algorithm Based on Improved Barnacle Mating Optimization

Abstract Distributed graph processing systems have been used more frequently in various fields, and graph partitioning is the basis of these systems. Graph partitioning algorithms generally aim to minimize the communication cost while the number of vertices or edges reach the load balance. But the vertices and/or edges of property graphs require some storage volume, so the traditional graph partition algorithms will lead to an unbalanced storage volume load. This paper proposes an edge-cut graph partitioning algorithm to generate partitions with equal size and storage volume as well as low cut-edge ratio. Initially, it partitions the graph into k partitions with equal size and storage volume. It then migrates vertices based on the improved Barnacles mating optimizer. The experiments on real-world graphs show that the proposed algorithm can achieve the partition size of volume balance, and the cut-edge ratio is also very low.

Comparing Graph Sample and Aggregation (SAGE) and Graph Attention Networks in the Prediction of Drug-Gene Associations of Extended-Spectrum Beta-Lactamases in Periodontal Infections and Resistance.

Gram-negative bacteria exhibit more antibiotic resistance than gram-positive bacteria due to their cell wall structure and composition differences. Porins, or protein channels in these bacteria, can allow small, hydrophilic antibiotics to diffuse, affecting their susceptibility. Mutations in porin protein genes can also impair antibiotic entry. Predicting drug-gene associations of extended-spectrum beta-lactamases (ESBLs) is crucial as they confer resistance to beta-lactam antibiotics, challenging the treatment of infections. This aids clinicians in selecting suitable treatments, optimizing drug usage, enhancing patient outcomes, and controlling antibiotic resistance in healthcare settings. Graph-based neural networks can predict drug-gene associations in periodontal infections and resistance. The aim of the study was to predict drug-gene associations of ESBLs in periodontal infections and resistance. The study focuses on analyzing drug-gene associations using probes and drugs. The data was converted into graph language, assigning nodes and edges for drugs and genes. Graph neural networks (GNNs) and similar algorithms were implemented using Google Colab and Python. Cytoscape and CytoHubba are open-source software platforms used for network analysis and visualization. GNNswere used for tasks like node classification, link prediction, and graph-level prediction. Three graph-based models were used: graph convolutional network (GCN), Graph SAGE, and graph attention network (GAT). Each model was trained for 200 epochs using the Adam optimizer with a learning rate of 0.01 and a weight decay of 5e-4. The drug-gene association network has 57 nodes, 79 edges, and a 2.730 characteristic path length. Its structure, organization, and connectivity are analyzed using the GCN and Graph SAGE, which show high accuracy, precision, recall, and an F1-score of 0.94. GAT's performance metrics are lower, with an accuracy of 0.68, precision of 0.47, recall of 0.68, and F1-score of 0.56, suggesting that it may not be as effective in capturing drug-gene relationships. Compared to ESBLs, both GCN and Graph SAGE demonstrate excellent performance with accuracy, precision, recall, and an F1-score of 0.94. These results indicate that GCN and Graph SAGE are highly effective in predicting drug-gene associations related to ESBLs. GCN and Graph SAGE outperform GAT in predicting drug-gene associations for ESBLs. Improvements include data augmentation, regularization, and cross-validation. Ethical considerations, fairness, and open-source implementations are crucial for future research in precision periodontal treatment.

Efficient Local Coherent Structure Learning via Self-Evolution Bipartite Graph.

Dimensionality reduction (DR) targets to learn low-dimensional representations for improving discriminability of data, which is essential for many downstream machine learning tasks, such as image classification, information clustering, etc. Non-Gaussian issue as a long-standing challenge brings many obstacles to the applications of DR methods that established on Gaussian assumption. The mainstream way to address above issue is to explore the local structure of data via graph learning technique, the methods based on which however suffer from a common weakness, that is, exploring locality through pairwise points causes the optimal graph and subspace are difficult to be found, degrades the performance of downstream tasks, and also increases the computation complexity. In this article, we first propose a novel self-evolution bipartite graph (SEBG) that uses anchor points as the landmark of subclasses, and learns anchor-based rather than pairwise relationships for improving the efficiency of locality exploration. In addition, we develop an efficient local coherent structure learning (ELCS) algorithm based on SEBG, which possesses the ability of updating the edges of graph in learned subspace automatically. Finally, we also provide a multivariable iterative optimization algorithm to solve proposed problem with strict theoretical proofs. Extensive experiments have verified the superiorities of the proposed method compared to related SOTA methods in terms of performance and efficiency on several real-world benchmarks and large-scale image datasets with deep features.

The Complexity of Finding and Enumerating Optimal Subgraphs to Represent Spatial Correlation

Understanding spatial correlation is vital in many fields including epidemiology and social science. Lee et al. (Stat Comput 31(4):51, 2021. https://doi.org/10.1007/s11222-021-10025-7) recently demonstrated that improved inference for areal unit count data can be achieved by carrying out modifications to a graph representing spatial correlations; specifically, they delete edges of the planar graph derived from border-sharing between geographic regions in order to maximise a specific objective function. In this paper, we address the computational complexity of the associated graph optimisation problem. We demonstrate that this optimisation problem is NP-hard; we further show intractability for two simpler variants of the problem. We follow these results with two parameterised algorithms that exactly solve the problem. The first is parameterised by both treewidth and maximum degree, while the second is parameterised by the maximum number of edges that can be removed and is also restricted to settings where the input graph has maximum degree three. Both of these algorithms solve not only the decision problem, but also enumerate all solutions with polynomial time precalculation, delay, and postcalculation time in respective restricted settings. For this problem, efficient enumeration allows the uncertainty in the spatial correlation to be utilised in the modelling. The first enumeration algorithm utilises dynamic programming on a tree decomposition of the input graph, and has polynomial time precalculation and linear delay if both the treewidth and maximum degree are bounded. The second algorithm is restricted to problem instances with maximum degree three, as may arise from triangulations of planar surfaces, but can output all solutions with FPT precalculation time and linear delay when the maximum number of edges that can be removed is taken as the parameter.

Resource efficient stabilization for local tasks despite unknown capacity links

Self-stabilizing protocols enable distributed systems to recover correct behavior starting from any arbitrary configuration. In particular, when processors communicate by message passing and the communication links are unbounded, fake messages may be placed in communication links by an adversary. When the number of such fake messages is unknown, self-stabilization may require huge resources:•generic solutions (a.k.a. data link protocols) require unbounded resources, which makes them unrealistic to deploy,•specific solutions (e.g., census or tree construction) require O(nlog⁡n) or O(Δlog⁡n) bits of memory per node, where n denotes the network size and Δ its maximum degree, which may prevent scalability.We investigate the possibility of resource-efficient self-stabilizing protocols in this context.Specifically, we present self-stabilizing protocols for (Δ+1)-coloring and maximal independent set construction in any n-node graph, under the asynchronous message-passing model. The problems of (Δ+1)-coloring and maximal independent set construction are widely regarded as benchmark problems for evaluating local algorithms. Our protocols offer many desirable features. They are deterministic, converge in O(kΔn2log⁡n) message exchanges, where k is the (unknown) initial number of (possibly corrupted) messages in a communication link. They use messages of O(log⁡log⁡n+log⁡Δ) bits with a memory of O(Δlog⁡Δ+log⁡log⁡n) bits at each node. The resource consumption of our protocols is thus almost oblivious to the number of nodes, enabling scalability. Moreover, a striking property of our protocols is that the nodes do not need to know the number, or any bound on the number of messages initially present in each communication link of the initial (potentially corrupted) network configuration. This permits our protocols to handle any future network with unknown message capacity communication links.A key building block of our coloring and maximal independent set schemes is an algorithm to obtain an acyclic orientation of graph edges, that is of independent interest, and can serve as a useful tool for solving other tasks in this challenging setting.

A note on the k-colored crossing ratio of dense geometric graphs

A geometric graph is a graph whose vertex set is a set of points in general position in the plane, and its edges are straight line segments joining these points. We show that for every integer k≥2, there exists a constant c>0 such that the following holds. The edges of every dense geometric graph, with sufficiently many vertices, can be colored with k colors, such that the number of pairs of edges of the same color that cross is at most (1/k−c) times the total number of pairs of edges that cross. The case when k=2 and G is a complete geometric graph, was proved by Aichholzer et al. (2019) [2].

FlowX: Towards Explainable Graph Neural Networks via Message Flows.

We investigate the explainability of graph neural networks (GNNs) as a step toward elucidating their working mechanisms. While most current methods focus on explaining graph nodes, edges, or features, we argue that, as the inherent functional mechanism of GNNs, message flows are more natural for performing explainability. To this end, we propose a novel method here, known as FlowX, to explain GNNs by identifying important message flows. To quantify the importance of flows, we propose to follow the philosophy of Shapley values from cooperative game theory. To tackle the complexity of computing all coalitions' marginal contributions, we propose a flow sampling scheme to compute Shapley value approximations as initial assessments of further training. We then propose an information-controlled learning algorithm to train flow scores toward diverse explanation targets: necessary or sufficient explanations. Experimental studies on both synthetic and real-world datasets demonstrate that our proposed FlowX and its variants lead to improved explainability of GNNs.

On Strong Regal and Strong Royal Colorings

Two colorings have been introduced recently where an unrestricted coloring c assigns nonempty subsets of [ k ] = { 1 , … , k } to the edges of a (connected) graph G and gives rise to a vertex-distinguishing vertex coloring by means of set operations. If each vertex color is obtained from the union of the incident edge colors, then c is referred to as a strong royal coloring. If each vertex color is obtained from the intersection of the incident edge colors, then c is referred to as a strong regal coloring. The minimum values of k for which a graph G has such colorings are referred to as the strong royal index of G and the strong regal index of G respectively. If the induced vertex coloring is neighbor distinguishing, then we refer to such edge colorings as royal and regal colorings. The royal chromatic number of a graph involves minimizing the number of vertex colors in an induced vertex coloring obtained from a royal coloring. In this paper, we provide new results related to these two coloring concepts and establish a connection between the corresponding chromatic parameters. In addition, we establish the royal chromatic number for paths and cycles.

Semi-time-dependent stabilization results for asynchronously switched systems: An extended persistent dwell time switching strategy involving admissible transition information

This study investigates the stabilization problem for a kind of continuous-time asynchronously switched systems via a set of edge- or mode-dependent state-feedback controllers. To this end, an innovative switching strategy of admissible chain-dependent (or admissible edge-dependent) persistent dwell time property is presented by injecting the admissible transition chain (or admissible transition edge) notion into the existing persistent dwell time concept. Based on the admissible transition edges in a directed graph reported in the literature, the corresponding admissible transition chains can be determined. The individual allocation of transition weights for each admissible transition chain makes the presented admissible chain-dependent persistent dwell time switching less conservative than the other presented admissible edge-dependent persistent dwell time and the already existing mode-dependent persistent dwell time switching. Further, different from the Lyapunov functions commonly used in previous asynchronous stabilization works, a new semi-time-dependent Lyapunov function in a unique form that fits the nature of the discussed systems is suggested to provide a broader family of allowable switching signals. By the introduced switching and Lyapunov function approaches, new stability and stabilization criteria are formulated, through which the expected edge- or mode-dependent state-feedback controllers are devised. At last, the validity and applicability of the obtained stabilization solutions are demonstrated by a numerical example and a practical thermal system.

Fixed Point Method for Nonlinear Fractional Differential Equations with Integral Boundary Conditions on Tetramethyl-Butane Graph

Until now, little investigation has been done to examine the existence and uniqueness of solutions for fractional differential equations on star graphs. In the published articles on the subject, the authors used a star graph with one junction node that has edges with the other nodes, although there are no edges between them. These graph structures do not cover more generic non-star graph structures; they are specific examples. The purpose of this study is to prove the existence and uniqueness of solutions to a new family of fractional boundary value problems on the tetramethylbutane graph that have more than one junction node after presenting a labeling mechanism for graph vertices. The chemical compound tetramethylbutane has a highly symmetrical structure, due to which it has a very high melting point and a short liquid range; in fact, it is the smallest saturated acyclic hydrocarbon that appears as a solid at a room temperature of 25 °C. With vertices designated by 0 or 1, we propose a fractional-order differential equation on each edge of tetramethylbutane graph. Employing the fixed-point theorems of Schaefer and Banach, we demonstrate the existence and uniqueness of solutions for the suggested fractional differential equation satisfying the integral boundary conditions. In addition, we examine the stability of the system. Lastly, we present examples that illustrate our findings.

Getting linear time in graphs of bounded neighborhood diversity

AbstractParameterized complexity, introduced to efficiently solve NP‐hard problems for small values of a fixed parameter, has been recently used as a tool to speed up algorithms for tractable problems. Following this line of research, we design algorithms parameterized by neighborhood diversity () for several graph theoretic problems in : Maximum ‐Matching, Triangle Counting and Listing, Girth, Global Minimum Vertex Cut, and Perfect Graphs Recognition. Such problems are known to admit algorithms parameterized by modular‐width () and consequently—as is a special case of —by . However, the proposed novel algorithms allow for improving the computational complexity from time —where and denote, respectively, the number of vertices and edges in the input graph—to time which is only additive in the size of the input. Then we consider some classical NP‐hard problems (Maximum independent set, Maximum clique, and Minimum dominating set) and show that for several classes of hereditary graphs, they admit linear time algorithms for sufficiently small—nonnecessarily constant—values of the neighborhood diversity parameter.

Multimodal Shot Prediction Based on Spatial-Temporal Interaction between Players in Soccer Videos

Sports data analysis has significantly advanced and become an indispensable technology for planning strategy and enhancing competitiveness. In soccer, shot prediction has been realized on the basis of historical match situations, and its results contribute to the evaluation of plays and team tactics. However, traditional event prediction methods required tracking data acquired with expensive instrumentation and event stream data annotated by experts, and the benefits were limited to only some professional athletes. To tackle this problem, we propose a novel shot prediction method using soccer videos. Our method constructs a graph considering player relationships with audio and visual features as graph nodes. Specifically, by introducing players’ importance into the graph edge based on their field positions and team information, our method enables the utilization of knowledge that reflects the detailed match situation. Next, we extract latent features considering spatial–temporal interactions from the graph and predict event occurrences with uncertainty based on the probabilistic deep learning method. In comparison with several baseline methods and ablation studies using professional soccer match data, our method was confirmed to be effective as it demonstrated the highest average precision of 0.948, surpassing other methods.

IMPROVING THE PROCESSES OF ENSURING THE AIRWORTHINESS OF AIRCRAFT BY CREATING A HIGH-SPEED HETEROGENEOUS INFORMATION SYSTEM

The problem of forming the appearance of a high-speed heterogeneous information system for monitoring airworthiness during the operation of aviation equipment is considered. A mixed-integer model has been formed for forming the optimal data transmission path for verifying the authenticity of airway components, where integer variables determine the set of external systems from where and where data is transmitted, a set of data warehouses and connections between them, and continuous variables – characteristics of data transfer rates by web services and bandwidth of data transmission channels. The criterion for choosing the optimal solution is proposed – the time of data transfer between external data source systems and external data consumer systems, taking into account data warehouses. An algorithm for optimizing the structure and parameters of a heterogeneous information system has been developed, which ensures the organization of information interaction between heterogeneous data sources/consumers in a minimum time. It is shown that the problem under consideration relates to difficult combinatorial optimization problems, that is, there is no polynomial algorithm for solving it in a reasonable time. However, taking into account the specifics of the task, in some cases, allows you to build calculation schemes that provide sufficient accuracy of the solution and an acceptable time. After conducting a brief analysis of possible solutions, including Dijkstra, Johnson, Floyd – Warshall, the authors implemented computational procedures based on the Bellman – Ford method, the main advantages of which are the possibility of obtaining an accurate solution, no restrictions when working with negative edges of the network graph, low value of the algorithm execution time. The results of calculations are presented and the possibility of reducing the data transfer time by 20,2 % is shown by choosing the optimal connections between data sources and consumers, taking into account the data formats of the sources used and the compatibility of web services providing their processing.

Empowered corrosion-resistant products through HCP crystal network: a topological assistance

Human computer interaction (HCI) aims to enhance product effectiveness and efficiency by empowering users. This research examines corrosion resistance in alloys, a concern due to technological advancements. Metals and alloys are susceptible to degradation, leading to functionality loss, structural collapse, and environmental contamination. Improving corrosion resistance is crucial for product efficiency. In this paper, HCI identifies requirements that emphasize taking an existing hexagonal closely packed (HCP) network, investigating the network for requirements in the form of vertices and edges, mapping different vertices and edges of the network graph with topological invariants, solving the network graph by invariants, and providing results for modeling and design of advanced networks and architectures. The HCI also ensures and investigates the optimization of results produced under the specifications. The study examines network graph results for irregularities, providing guidelines for engineers and manufacturers to create advanced alloy architectures with characteristics through mathematical and graphical methods.

A note on the 2-colored rectilinear crossing number of random point sets in the unit square

Let S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S$$\\end{document} be a set of four points chosen independently, uniformly at random from a square. Join every pair of points of S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S$$\\end{document} with a straight line segment. Color these edges red if they have positive slope and blue, otherwise. We show that the probability that S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S$$\\end{document} defines a pair of crossing edges of the same color is equal to 1/4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1/4$$\\end{document}. This is connected to a recent result of Aichholzer et al. [1] who showed that by 2-colouring the edges of a geometric graph and counting monochromatic crossings instead of crossings, the number of crossings can be more than halved. Our result shows that for the described random drawings, there is a coloring of the edges such that the number of monochromatic crossings is in expectation 12-750\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{1}{2}-\\frac{7}{50}$$\\end{document} of the total number of crossings.

Sticky Links: Encoding Quantitative Data of Graph Edges.

Visually encoding quantitative information associated with graph links is an important problem in graph visualization. A conventional approach is to vary the thickness of lines to encode the strength of connections in node-link diagrams. In this paper, we present Sticky Links, a novel visual encoding method that draws graph links with stickiness. Taking the metaphor of links with glues, sticky links represent connection strength using spiky shapes, ranging from two broken spikes for weak connections to connected lines for strong connections. We conducted a controlled user study to compare the efficiency and aesthetic appeal of stickiness with conventional thickness encoding. Our results show that stickiness enables more effective and expressive quantitative encoding while maintaining the perception of node connectivity. Participants also found sticky links to be more aesthetic and less visually cluttering than conventional thickness encoding. Overall, our findings suggest that sticky links offer a promising alternative to conventional methods for encoding quantitative information in graphs.

Graph-Based Modeling and Optimization of WPT Systems for EVs

A model of a system of wireless power transfer (WPT) pads is developed, where each WPT pad is modeled as a node and the coupling between pads is modeled as graph edges. This modeling approach is generalized to admit primary, secondary, and booster coils, where power can flow among the pads and a pad can fill multiple roles. An excitation in one pad induces voltage and current in all neighboring pads, causing each pad to act as both a booster coil and either a transmitter or a receiver. Power flow through the entire system can be modeled with the graph structure; the power flow can then be optimized by alternating the phases of the WPT excitations to maximize power transfer. An example is shown where exploiting the graph-based WPT system modeling increases total energy transfer by 25% compared to another method. This increase occurs without altering the geometry of the pads or the magnitude of the pad excitations.