Edge Connectivity Research Articles

A Validation of the Phenomenon of Linearly Many Faults on Burnt Pancake Graphs with Its Applications

“Linearly many faults” is a phenomenon observed by Cheng and Lipták in which a specific structure emerges when a graph is disconnected and often occurs in various interconnection networks. This phenomenon means that if a certain number of vertices or edges are deleted from a graph, the remaining part either stays connected or breaks into one large component along with smaller components with just a few vertices. This phenomenon can be observed in many types of graphs and has important implications for network analysis and optimization. In this paper, we first validate the phenomenon of linearly many faults for surviving graph of a burnt pancake graph BPn when removing any edge subset with a size of approximately six times λ(BPn). For graph G, the ℓ-component edge connectivity denoted as λℓ(G) (resp., the ℓ-extra edge connectivity denoted as λ(ℓ)(G)) is the cardinality of a minimum edge subset S such that G−S is disconnected and has at least ℓ components (resp., each component of G−S has at least ℓ+1 vertices). Both λℓ(G) and eλ(ℓ)(G) are essential metrics for network reliability assessment. Specifically, from the property of “linearly many faults”, we may further prove that λ5(BPn)=λ(3)(BPn)+3=4n−3 for n⩾5; λ6(BPn)=λ(4)(BPn)+4=5n−4 and λ7(BPn)=λ(5)(BPn)+5=6n−5 for n⩾6.

Partitioning the effects of coffee-Urochloa intercropping on soil microbial properties at a centimeter-scale

Conservation farming and crop diversity increase soil health, organic matter content, and soil microbial activity. However, the design and implementation of sustainable practices often lack a detailed understanding of their impacts on microbial communities in soil. Here, we studied the effects of an Arabica coffee (Coffea arabica) – Brachiaria (Urochloa spp.) intercropping system on soil microbial properties by partitioning at the centimeter-scale the topsoil layers. In particular, we collected and analyzed four soil layers in a vertical stratification gradient of 0–2.5 cm (layer 1), 2.5–5.0 cm (layer 2), 5–10 cm (layer 3), and 10–15 cm (layer 4). Soil samples were subjected to chemical analysis, bacterial community profiling, and quantification of microbial enzymatic activity for β-glucosidase and acid-phosphatase, in addition to the quantification of N-fixation and P-solubilization gene abundances. We found that intercropping increased acid-phosphatase activity at layer 1, β-glucosidase activity at layers 2 and 3, and the amount of soil organic matter and total magnesium at layers 2 and 3. Intercropping increased the relative abundance of the N-fixation gene at layer 3 and bacterial diversity at layers 1 and 3. Overall, intercropping significantly changed the soil bacterial community structure and resulted in a more interconnected co-occurrence network (i.e., greater node connectivity, network density, and lower edges average path length). Taken together, this study provides evidence for the positive impact of intercropping in the soil at a centimeter-scale vertical stratification. It corroborates the notion that plant diversity stimulates microbial activity and species interactions in soil.

Large-scale robustness-oriented efficient edge addition through traversal tree-based weak edge identification

To build robust networks, a popular way is to add edges to existing networks, which can help defend against natural disasters or malicious attacks that randomly or intentionally break several key links at once. There is an urgent need to optimally add edges to improve robustness, e.g., measured by general metrics such as graph connectivity. However, although exhausting and connecting both sides of all small cuts is a sure way to achieve feasible solutions, since the number of possible edges to add is much more than the existing number of edges, even the problem instances in the small graphs are too complex to be solved efficiently, while applying heuristic algorithms to large-scale graphs can only achieve very inefficient results. Fortunately, we find an efficient way to represent all candidate cuts based on the mapping between trees and cuts, and find the near-optimal set of endpoints that cross both sides of all these cuts, and finally find the optimal number of edges reinforcing these cuts to improve edge connectivity. Experiments in representative Erdos–Renyi and scale-free graphs show that the proposed algorithm can achieve perfectly improved results as the optimal algorithm, and the computing speed can be at most 6 orders of magnitude faster than the optimal algorithm, at the expense of slightly increased edge count. The large graph results show the obvious advantage of the proposed algorithms in providing near-perfect results, while popular heuristic algorithms are almost useless in protecting these networks. The proposed algorithm can be further efficient by exploiting its ready-to-parallelize logics for further acceleration.

Automatic tracking and intelligent observation of tidal bore propagation velocity based on UAV and computer vision

The rapidly developed Unmanned Aerial Vehicles (UAV) and artificial intelligence technology has prompted the real-time and accurate observation measurements of tidal bore, the basis of which is tidal bore propagation velocity. In this article, we construct a tidal observation system framework based on UAV and computer vision in order to obtain the tidal bore propagating velocity datasets. Firstly, we focus on the identification of tidal headlines based on the Sobel edge detection, the improved Otsu image segmentation algorithm and the edge connection algorithm with an accuracy of 91%. And then, the detected tidal headlines could be used to control the flight parameters of UAV in order to stably track tidal bore on the specified route with the deviation range below 0.5, and finally to acquire the tidal bore propagation velocity datasets. Comparing with the propagation velocity of the tidal line measured on site, the error of the results is maintained within 0.1 m/s, which demonstrates the effectiveness of our proposed observation method.

Algorithms for computing Pythagorean fuzzy average edge connectivity of Pythagorean fuzzy graphs

Algorithms for computing Pythagorean fuzzy average edge connectivity of Pythagorean fuzzy graphs

Menger-Type Connectivity of Line Graphs of Generalized Hypercubes With Faulty Edges

Abstract A connected graph $G$ is called strongly Menger edge connected if $G$ has min{deg$_{G}(x)$, deg$_{G}(y)$} edge-disjoint paths between any two distinct vertices $x$ and $y$ in $G$. In this paper, we consider two types of the strongly Menger edge connectivity of the line graphs of generalized $n$-dimensional hypercubes with faulty edges, namely the $m$-edge-fault-tolerant and $m$-conditional edge-fault-tolerant strongly Menger edge connectivity. We show that the line graphs of all generalized $n$-dimensional hypercubes are $(2n-4)$-edge-fault-tolerant strongly Menger edge connected for $n\geq 3$ and $(4n-10)$-conditional edge-fault-tolerant strongly Menger edge connected for $n\geq 4$. The two bounds for the maximum numbers of faulty edges are best possible.

Planar-thick panels and 3D-printed gap fillers: A hybrid digital fabrication approach to curved surface approximations

Curved surfaces may be approximated using polygonal panels to simplify complex architectural designs, yet their constructions can be expensive due to single-use moulds producing unique panels. To reduce costs, strategies like planarizing and reducing the number of different panels have been suggested, which are increasingly achievable with advancing digital fabrication technologies. However, current subtractive and additive manufacturing techniques face challenges in producing complex 3D shapes and large volumes, respectively. Combining these two techniques has been attempted, mainly with small 3D-printed nodes, leaving the direct realization of curved surface approximations unexplored. This paper extends the thick-panel origami theory to introduce planar-thick panels and 3D-printed gap fillers for cost-effective constructions. It presents a computational workflow to transform meshes into non-intersecting panels while preserving edge connectivity and frame-like gap fillers with minimized volumes. Physical prototypes demonstrate significant cost savings compared to direct 3D printing. All prototypes are accurate within a 10 mm material thickness due to the guidance of the gap fillers. The finite element analysis shows that structural performance is greatly influenced by the material properties, especially of panels, due to their relatively larger volume. Numerical examples are also presented using the k-means clustering-optimization method to reduce the number of different panels.

Event Graph Guided Compositional Spatial-Temporal Reasoning for Video Question Answering.

Video question answering (VideoQA) is challenging since it requires the model to extract and combine multi-level visual concepts from local objects to global actions from complex events for compositional reasoning. Existing works represent the video with fixed-duration clip features that make the model struggle in capturing the crucial concepts in multiple granularities. To overcome this shortcoming, we propose to represent the video with an Event Graph in a hierarchical structure whose nodes correspond to visual concepts of different levels (object, relation, scene and action) and edges indicate their spatial-temporal relationships. We further propose a H ierarchical S patial- T emporal T ransformer (HSTT) which takes nodes from the graph as visual input to realize compositional reasoning guided by the event graph. To fully exploit the spatial-temporal context delivered from the graph structure, on the one hand, we encode the nodes in the order of their semantic hierarchy (depth) and occurrence time (breadth) with our improved graph search algorithm; On the other hand, we introduce edge-guided attention to combine the spatial-temporal context among nodes according to their edge connections. HSTT then performs QA by cross-modal interactions guaranteed by the hierarchical correspondence between the multi-level event graph and the cross-level question. Experiments on the recent challenging AGQA and STAR datasets show that the proposed method clearly outperforms the existing VideoQA models by a large margin, including those pre-trained with large-scale external data. Our code is available at https://github.com/ByZ0e/HSTT.

Контекстный анализ связности двухполюсных структур

The paper discusses an original approach to the analysis of network structures of various natures, which are represented in the form of graphs. It is assumed that the probability of connectivity of individual edges functionally depends on their physical characteristics (edge length) and tends to zero. The issue of increasing the connectivity probability of the entire graph is being addressed, which is defined as the probability of the existence of a sequential set of edges connecting the selected start and end vertices. A distinctive feature of the proposed method is the move away from the traditional reservation of obviously weak connection points towards a functional impact on individual connections of the structure, changing their physical characteristics. Based on the theory of systems functioning and the theory of dominants, contextual approach is being developed aimed at identifying the dominant connections of the graph, reflecting the functional and meaningful meaning of the connections between the vertices of the original modeled object. As a result, a set of dominants S is identified, consisting of edges whose parameters meet the given criteria. The selection criterion is the length of the edge included in the asymptotic relation, which characterizes the connectivity probability of the entire graph. It has been proven that changing the length of edges from a given set by ε > 0 increases the probability of connectedness of the original graph in the maximum case in h-ε or h-εβ times, where h → 0 and β is a parameter depending on the number of graph paths passing through this edge. Various methods have been proposed to increase the connectivity probability of the graph under consideration: from the point of view of the point effect, by reducing the length of a single edge from the set S; from the position of influencing the maximum set of edges from S, allowing to obtain the overall maximum effect. A comparative analysis of the proposed ways to increase the probability of graph connectivity has been carried out, and the appropriate conditions have been identified to achieve the maximum effect from the selected methods of influence.

Design and realization of Lora wireless communication and 5G based middle and long distance running system under the healthy development of innovative sports

Abstract In innovative sports, integrating new-generation technologies is revolutionizing how we approach and analyze athletic performance. Our research focuses on developing a sophisticated middle and long-distance running system that harnesses the power of modern communication tech, including LoRa connectivity and 5G edge computing. By applying the IMF method, we effectively minimize data noise, enhancing the fidelity of sports signal analysis. Our system’s prowess is evident in its low latency (2.97 ms at 100 nodes), high accuracy (rating of 6.8), and impeccable anti-collision capabilities during competitive events. In practical tests over 1000 meters, it dramatically reduced timing errors to a mere fraction of manual methods, demonstrating its precision and potential to transform physical training and education. This innovation stands as a beacon for the future of sports, driving the integration of technology and athletics.

Explicit Topology Optimization of Voronoi Foams.

Topology optimization can maximally leverage the high DOFs and mechanical potentiality of porous foams but faces challenges in adapting to free-form outer shapes, maintaining full connectivity between adjacent foam cells, and achieving high simulation accuracy. Utilizing the concept of Voronoi tessellation may help overcome the challenges owing to its distinguished properties on highly flexible topology, natural edge connectivity, and easy shape conforming. However, a variational optimization of the so-called Voronoi foams has not yet been fully explored. In addressing the issue, a concept of explicit topology optimization of open-cell Voronoi foams is proposed that can efficiently and reliably guide the foam's topology and geometry variations under critical physical and geometric requirements. Taking the site (or seed) positions and beam radii as the DOFs, we explore the differentiability of the open-cell Voronoi foams w.r.t. its seed locations, and propose a highly efficient local finite difference method to estimate the derivatives. During the gradient-based optimization, the foam topology can change freely, and some seeds may even be pushed out of shape, which greatly alleviates the challenges of prescribing a fixed underlying grid. The foam's mechanical property is also computed with a much-improved efficiency by an order of magnitude, in comparison with benchmark FEM, via a new material-aware numerical coarsening method on its highly heterogeneous density field counterpart. We show the improved performance of our Voronoi foam in comparison with classical topology optimization approaches and demonstrate its advantages in various settings.

Enhancing fault tolerance of balanced hypercube networks by the edge partition method

Interconnection networks are key component of parallel and distributed systems. As the network scale increases, the growing number of link failures becomes inevitable. Therefore, how to enhance the fault tolerance of the network has become a research issue in parallel and distributed systems. Recently, two new metrics based on edge partition in networks have been introduced, called matroidal connectivity and conditional matroidal connectivity. Existing research indicates that they significantly enhance the fault tolerance of alternating group networks and star networks compared to other indicators such as g-component edge connectivity and g-extra edge connectivity. In this work, we consider the matroidal connectivity and conditional matroidal connectivity of the n-dimensional balanced hypercube BHn, a class of networks with vertex transitivity and edge transitivity, and theoretically demonstrate their high fault tolerance in BHn. Furthermore, through numerical simulation, it is observed that the matroidal connectivity and conditional matroidal connectivity of BHn are greater than the g-component edge connectivity and g-extra edge connectivity of BHn, which implies that (conditional) matroidal connectivity can further improve BHn' fault tolerance.

On 1-Regular and 2- Regular Edge Connectivity in Some Graph Classes

Düzenli ayrıt bağlantılılık yeni bir koşullu bağlantılılık türü olup, bu kavram bağlantısız yapılan her parça grafın düzenli olması esasına dayanır. Bu çalışmada, hiperküp graflarında ve bir tam grafın yol, çevre ve bir tam grafla kartezyen çarpımından elde edilen graflarda 1-düzenli ve 2-düzenli ayrıt bağlantılılık incelenmiştir.

Strongly Menger Connectedness of a Class of Recursive Networks

Abstract According to Menger’s theorem, connectivity and edge connectivity are closely related to node-disjoint paths and edge-disjoint paths, respectively. Node- and edge-disjoint paths can keep the effective transmission of information and confidentiality. Therefore, node-disjoint paths and edge-disjoint paths are two important parameters to measure the reliability of a network. For a faulty node (resp. edge) set $S\subset V$ (resp. $S\subset E$), a connected graph $G=(V,E)$ is $S$-strongly Menger-node-connected (resp. Menger-edge-connected) if any two distinct nodes $x$ and $y$ in $G-S$ are connected by $\min \{\deg _{G-S}(x),\deg _{G-S}(y)\}$ internally node-disjoint (resp. edge-disjoint) paths in $G-S$, where $\deg _{G-S}(x)$ and $\deg _{G-S}(y)$ are the degrees of $x$ and $y$ in $G-S$, respectively. And most of the previous studies are based on networks that are triangle-free. In this paper, we consider the strongly Menger (edge) connectedness of a class of $r$-dimensional recursive networks RNCG $G_{r}$ with triangles. Moreover, we show that $G_{r}$ is $(rl-l-1)$-strongly Menger-node-connected. And then we show that $G_{r}$ is $[k+(r-1)l-2]$-strongly Menger-edge-connected of order 1 and $[2k+2(r-1)l-6]$-strongly Menger-edge-connected of order 2. Since the class of $r$-dimensional recursive networks RNCG $G_{r}$ includes not only data center networks DCell and generalized DCell but also interconnection network dragonfly, etc., all the results are appropriate for these networks.

Characterization of matroidal connectivity of regular networks

High performance computing system, which takes an interconnection network as its infrastructure topology, has been utilized in scientific computing, big data analysis as well as artificial intelligence. With the rapid growth of infrastructure topology (interconnection network) in high performance computing system, the probability of network element malfunction increases dramatically. Generally, the reliability of interconnection network is measured by the traditional (edge) connectivity, which is limited by the minimum degree of the network. In order to overcome the defect, the matroidal connectivity has been newly proposed to extend the edge connectivity. For the regular network G, let Bk(G)={B1,B2,…,Bk} be a fixed edge partition ordered sequence of G and χk=(x1,x2,…,xk) be a sequence of k integers. For any D⊆E(G), if |D∩Bi|≤xi(i∈[k]) and G−D is disconnected, then D is named matroidal cut set of G. The matroidal connectivity of G, denoted by λ(G,Bk(G)), is the minimum size of matroidal cut set of G. In this work, we characterize the matroidal connectivity of a class of n-dimensional regular networks Gn. To be more specific, we show that λ(Gn,Bn(Gn))=(k−l+1)f(l+j), where f(n) is a function about n, and l,k,n are positive integers (l≥1), j=n−k. As empirical analysis, we directly determine the matroidal connectivity of some well-known interconnection networks, such as hypercube Qn, star graph STn and alternating group graph AGn.

AUTOMATIC GENERATION OF ROUTING GRAPHS FOR INDOOR-OUTDOOR TRANSITIONAL SPACE TO SUPPORT SEAMLESS NAVIGATION

Abstract. With the fast development of urbanization, the complexity of built environments has dramatically increased, driving a need for assistance in seamless indoor-outdoor navigation. This requires integration of spatial information of indoor and outdoor environments from heterogeneous data sources. While outdoor road network data is largely available from many sources (such as OpenStreetMap), indoor spatial information is either inexistent or is inconsistently represented using several different standards. Among these standards, IndoorGML is a well-developed standard with the focus on indoor location-based services. This standard has already been accepted by Open Geospatial Consortium (OGC) and is now under active development. Although in IndoorGML some mechanisms have been defined to enable integration of indoor and outdoor networks, there is still a lack of concrete guidelines for determination of indoor-outdoor connections. It also lacks solid scientific foundations and efficient tools to extract the connecting nodes and edges that link indoor and outdoor spaces. To address this gap, in this study we focus on the connection of indoor and outdoor spaces and aim to provide a tool, which can automatically construct navigation graphs of the indoor-outdoor transitional space to support seamless integration of indoor-outdoor navigation. To this end, voxel-based modeling approaches are used to model the connecting space between indoor and outdoor environments. Based on Python, we develop the intended tool, which can generate voxel models from point clouds, identify navigable space by taking into account the characteristics of agents (such as pedestrians, wheelchairs, and vehicles), and automatically build navigation graphs linking IndoorGML networks with outdoor street networks. It is expected that the methodology and tools developed from this project will benefit the IndoorGML ecosystem and greatly advance the capability of IndoorGML in representing navigable space to support location-based services.

The Private Virtual Network Operator Model for Field Area Network

Uninterrupted grid edge connectivity is essential for distribution utilities driving towards a future where efficient, secure, and reliable field area network (FAN) operation is not just preferable but required. Communications and network connectivity have been rapidly evolving over the last several years and will continue to do so—including in the areas of spectrum options, carrier solutions, device manufacturers, core manufacturers, and network management options. Utilities have a greater choice of options to deploy, while needing to remain prudent in their investments. One of the options gaining traction in the United States is the private virtual network operator (PVNO) model.

Towards Neural Charged Particle Tracking in Digital Tracking Calorimeters with Reinforcement Learning.

We propose a novel technique for reconstructing charged particles in digital tracking calorimeters using reinforcement learning aiming to benefit from the rapid progress and success of neural network architectures without the dependency on simulated or manually-labeled data. Here we optimize by trial-and-error a behavior policy acting as an approximation to the full combinatorial optimization problem, maximizing the physical plausibility of sampled trajectories. In modern processing pipelines used in high energy physics and related applications, tracking plays an essential role allowing to identify and follow charged particle trajectories traversing particle detectors. Due to the high multiplicity of charged particles and their physical interactions, randomly deflecting the particles, the reconstruction is a challenging undertaking, requiring fast, accurate and robust algorithms. Our approach works on graph-structured data, capturing track hypotheses through edge connections between particles in the detector layers. We demonstrate in a comprehensive study on simulated data for a particle detector used for proton computed tomography, the high potential as well as the competitiveness of our approach compared to a heuristic search algorithm and a model trained on ground truth. Finally, we point out limitations of our approach, guiding towards a robust foundation for further development of reinforcement learning based tracking.

A Timber–Concrete–Composite Edge Connection for Two-Way Spanning Cross-Laminated Timber Slabs—Experimental Investigations and Analytical Approach

This paper introduces a method to create a moment-resisting edge connection between two cross-laminated timber (CLT) panels. With this connection, two-way spanning cross-laminated timber slabs can be realised, where the span exceeds the manufacturing and transport-related width of the individual CLT panels. Until now, mostly on-site gluing solutions have been suggested for such connections. In this study, a solution using a timber–concrete–composite (TCC) system is proposed. For this, self-tapping screws are inserted along the edge face of the CLT component, enabling the formation of a lap splice between two adjacent CLT elements. This lap splice is reinforced by additional rebars and filled with concrete. This means that only familiar, easy-to-handle materials are used on-site, and there is no need for adhesives, which can be difficult to apply. To evaluate the load-bearing capacity of the connection, it was subjected to a pure bending load in four-point bending tests, where load-bearing capacities of up to 70% of the characteristic load-bearing capacity of the solid CLT elements were achieved. An analytical approach for a simplified engineering calculation model is introduced to determine the load acting upon the screws. Based on the experimental results, it is shown that the analytical approach is able to adequately represent the load-bearing capacity of the connection. The analytically determined forces on the screws may then be used to carry out further verifications on this connection method.

Comparing network structures on three aspects: A permutation test.

Network approaches to psychometric constructs, in which constructs are modeled in terms of interactions between their constituent factors, have rapidly gained popularity in psychology. Applications of such network approaches to various psychological constructs have recently moved from a descriptive stance, in which the goal is to estimate the network structure that pertains to a construct, to a more comparative stance, in which the goal is to compare network structures across populations. However, the statistical tools to do so are lacking. In this article, we present the network comparison test (NCT), which uses resampling-based permutation testing to compare network structures from two independent, cross-sectional data sets on invariance of (a) network structure, (b) edge (connection) strength, and (c) global strength. Performance of NCT is evaluated in simulations that show NCT to perform well in various circumstances for all three tests: The Type I error rate is close to the nominal significance level, and power proves sufficiently high if sample size and difference between networks are substantial. We illustrate NCT by comparing depression symptom networks of males and females. Possible extensions of NCT are discussed. (PsycInfo Database Record (c) 2022 APA, all rights reserved).