Sparse Graphs Research Articles

On finding short reconfiguration sequences between independent sets

Token Sliding Optimization asks whether there exists a sequence of at most ℓ steps that transforms independent set S into T, where at each step a token slides to an unoccupied neighboring vertex (while maintaining independence). In Token Jumping Optimization, we are instead allowed to jump from a vertex to any unoccupied vertex. Both problems are known to be FPT when parameterized by ℓ on nowhere dense graphs. In this work, we show that both problems are FPT for parameter k+ℓ+d on d-degenerate graphs as well as for parameter |M|+ℓ+Δ on graphs having a modulator M to maximum degree Δ. We complement these results by showing that for parameter ℓ both problems become hard already on 2-degenerate graphs. Finally, we show that using such families one can obtain a unified algorithm for the standard Token Jumping problem parameterized by k on degenerate and nowhere dense graphs.

Representation and Analysis of Kinship, Based on the Naming Pattern

In this study, we develop a graph-theoretic network model for genealogical data. It is based on the naming system used by the Galo tribe in the Indian state of Arunachal Pradesh. P-graphs are used to visually represent the genealogy. According to the analysis of the network on social network metrics, the genealogical network is a sparsely connected, scale-free network with an average path length of 11.615 and a graph density of 0.002. Only a small portion of its nodes have high centrality values. The network has three communities, twenty authority nodes, two hub nodes, and observed no relinking marriages.

CESA: Communication efficient secure aggregation scheme via sparse graph in federated learning

As a distributed learning paradigm, federated learning can be effectively applied to the decentralized system since it can resolve the “data island” problem. However, it is also vulnerable to serious privacy breaches. Although existing secure aggregation technique can address privacy concerns, they also incur significant additional computation and communication costs. To address these challenges, this paper offers a Communication Efficient Secure Aggregation scheme. Firstly, the central server uses the communication delay between terminals as the weight of the fully terminal-connected graph to transform it into a sparse connected graph based on the minimal spanning tree. Secondly, instead of relying on central server for key advertisement, the terminals advertise keys via a neighboring terminal forwarding approach based on sparsely graph. Thirdly, we propose using the central server for auxiliary advertising to address unexpected terminal dropout. Simultaneously, we theoretically demonstrate our scheme’s security and have lower computation and communication costs. Experiments show that CESA can reduce the running time by 28.2% without sacrificing security and model accuracy compared to conventional secure aggregation when there are 10 terminals in the system.

Typical alien invasive aquatic-plant species changed the stability rather than the diversity of plankton community in fresh water

Alien invasive aquatic-plant (AIA) species are severely threatening the aquatic ecosystems worldwide, especially biodiversity. Although plankton have been used to monitor and address biodiversity, some gaps remain in understanding of the relationships between plankton communities and AIA species. Here, the effects of two typical AIA species (Pistia stratiotes and Eichhornia crassipes) on plankton communities in freshwater with a native plant Vallisneria natans were investigated using a 50-d microcosm experiment. Results showed that AIA species significantly decreased water pH and dissolved oxygen while increased oxidation-reduction potential (p < 0.05). AIA species, especially P. stratiotes, significantly inhibited dry biomass accumulation in V. natans by an average rate of 39.0 %, decreased water pH by up to 14.62 %, and increased aboveground lengths and chlorophyll contents of V. natans by up to 36.2 % and 63.7 % (p < 0.05), respectively. These species further modified the growth strategy of V. natans from dry biomass accumulation to aboveground elongation. Although the AIA species did not alter plankton diversity (p > 0.05), but they changed their dominant species, functional communities (e.g., Groups D and TB), and co-occurrence networks. P. stratiotes decreased the average degree of the networks by 12.37–19.02 % and the graph density by 10.53–14.47 %, while E. crassipes decreased the modularity of the networks by 10.24 % compared with the control (without AIA species), respectively. Overall, AIA species inhibited the growth of V. natans and decreased the stability of plankton communities and their resistance to environmental disturbances. These findings enhance our understanding of how AIA species affect the growth of native plants and variations in plankton communities, thereby providing a theoretical basis for improving the ecological function and safety of freshwater.

On non-superperfection of edge intersection graphs of paths

The routing and spectrum assignment problem in modern flexgrid elastic optical networks asks for assigning to given demands a route in an optical network and a channel within an optical frequency spectrum so that the channels of two demands are disjoint whenever their routes share a link in the optical network. This problem can be modeled in two phases: firstly, a selection of paths in the network and, secondly, an interval coloring problem in the edge intersection graph of these paths. The interval chromatic number equals the smallest size of a spectrum such that a proper interval coloring is possible, the weighted clique number is a natural lower bound. Graphs where both parameters coincide for all possible non-negative integral weights are called superperfect. Therefore, the occurrence of non-superperfect edge intersection graphs of routing paths can provoke the need of larger spectral resources. In this work, we examine the question which minimal non-superperfect graphs can occur in the edge intersection graphs of routing paths in different underlying networks: when the network is a path, a tree, a cycle, or a sparse planar graph with small maximum degree. We show that for any possible network (even if it is restricted to a path) the resulting edge intersection graphs are not necessarily superperfect. We close with a discussion of possible consequences and of some lines of future research.

GKE-TUNet: Geometry-Knowledge Embedded TransUNet Model for Retinal Vessel Segmentation Considering Anatomical Topology.

Automated retinal vessel segmentation is crucial for computer-aided clinical diagnosis and retinopathy screening. However, deep learning faces challenges in extracting complex intertwined structures and subtle small vessels from densely vascularized regions. To address these issues, we propose a novel segmentation model, called Geometry-Knowledge Embedded TransUNet (GKE-TUNet), which incorporates explicit embedding of topological features of retinal vessel anatomy. In the proposed GKE-TUNet model, a skeleton extraction network is pre-trained to extract the anatomical topology of retinal vessels from refined segmentation labels. During vessel segmentation, the dense skeleton graph is sampled as a graph of key-points and connections and is incorporated into the skip connection layer of TransUNet. The graph vertices are used as node features and correspond to positions in the low-level feature maps. The graph attention network (GAT) is used as the graph convolution backbone network to capture the shape semantics of vessels and the interaction of key locations along the topological direction. Finally, the node features obtained by graph convolution are read out as a sparse feature map based on their corresponding spatial coordinates. To address the problem of sparse feature maps, we employ convolution operators to fuse sparse feature maps with low-level dense feature maps. This fusion is weighted and connected to deep feature maps. Experimental results on the DRIVE, CHASE-DB1, and STARE datasets demonstrate the competitiveness of our proposed method compared to existing ones.

Braess's Paradox Analog in Physical Networks of Optimal Exploration.

In stochastic exploration of geometrically embedded graphs, intuition suggests that providing a shortcut between a pair of nodes reduces the mean first passage time of the entire graph. Counterintuitively, we find a Braess's paradox analog. For regular diffusion, shortcuts can worsen the overall search efficiency of the network, although they bridge topologically distant nodes. We propose an optimization scheme under which each edge adapts its conductivity to minimize the graph's search time. The optimization reveals a relationship between the structure and diffusion exponent and a crossover from dense to sparse graphs as the exponent increases.

Dense circuit graphs and the planar Turán number of a cycle

AbstractThe planar Turán number of a graph is the maximum number of edges in an ‐vertex planar graph without as a subgraph. Let denote the cycle of length . The planar Turán number is known for . We show that dense planar graphs with a certain connectivity property (known as circuit graphs) contain large near triangulations, and we use this result to obtain consequences for planar Turán numbers. In particular, we prove that there is a constant so that for all and . When this bound is tight up to the constant and proves a conjecture of Cranston, Lidický, Liu, and Shantanam.

Rep-ViG-Apple: A CNN-GCN Hybrid Model for Apple Detection in Complex Orchard Environments

Accurately recognizing apples in complex environments is essential for automating apple picking operations, particularly under challenging natural conditions such as cloudy, snowy, foggy, and rainy weather, as well as low-light situations. To overcome the challenges of reduced apple target detection accuracy due to branch occlusion, apple overlap, and variations between near and far field scales, we propose the Rep-ViG-Apple algorithm, an advanced version of the YOLO model. The Rep-ViG-Apple algorithm features a sophisticated architecture designed to enhance apple detection performance in difficult conditions. To improve feature extraction for occluded and overlapped apple targets, we developed the inverted residual multi-scale structural reparameterized feature extraction block (RepIRD Block) within the backbone network. We also integrated the sparse graph attention mechanism (SVGA) to capture global feature information, concentrate attention on apples, and reduce interference from complex environmental features. Moreover, we designed a feature extraction network with a CNN-GCN architecture, termed Rep-Vision-GCN. This network combines the local multi-scale feature extraction capabilities of a convolutional neural network (CNN) with the global modeling strengths of a graph convolutional network (GCN), enhancing the extraction of apple features. The RepConvsBlock module, embedded in the neck network, forms the Rep-FPN-PAN feature fusion network, which improves the recognition of apple targets across various scales, both near and far. Furthermore, we implemented a channel pruning algorithm based on LAMP scores to balance computational efficiency with model accuracy. Experimental results demonstrate that the Rep-ViG-Apple algorithm achieves precision, recall, and average accuracy of 92.5%, 85.0%, and 93.3%, respectively, marking improvements of 1.5%, 1.5%, and 2.0% over YOLOv8n. Additionally, the Rep-ViG-Apple model benefits from a 22% reduction in size, enhancing its efficiency and suitability for deployment in resource-constrained environments while maintaining high accuracy.

Multichannel Adaptive Data Mixture Augmentation for Graph Neural Networks

Graph neural networks (GNNs) have demonstrated significant potential in analyzing complex graph-structured data. However, conventional GNNs encounter challenges in effectively incorporating global and local features. Therefore, this paper introduces a novel approach for GNN called multichannel adaptive data mixture augmentation (MAME-GNN). It enhances a GNN by adopting a multi-channel architecture and interactive learning to effectively capture and coordinate the interrelationships between local and global graph structures. Additionally, this paper introduces the polynomial–Gaussian mixture graph interpolation method to address the problem of single and sparse graph data, which generates diverse and nonlinear transformed samples, improving the model's generalization ability. The proposed MAME-GNN is validated through extensive experiments on publicly available datasets, showcasing its effectiveness. Compared to existing GNN models, the MAME-GNN exhibits superior performance, significantly enhancing the model's robustness and generalization ability.

Sparse graphs-based dynamic attention networks

In previous research, the prevailing assumption was that Graph Neural Networks (GNNs) precisely depicted the interconnections among nodes within the graph's architecture. Nonetheless, real-world graph datasets are often rife with noise, elements that can disseminate through the network and ultimately affect the outcome of the downstream tasks. Facing the complex fabric of real-world graphs and the myriad potential disturbances, we introduce the Sparse Graph Dynamic Attention Networks (SDGAT) in this research. SDGAT employs the L0 regularization technique to achieve a sparse representation of the graph structure, which eliminates noise and generates a more concise sparse graph. Building upon this foundation, the model integrates a dynamic attention mechanism, allowing it to selectively focus on key nodes and edges, filter out irrelevant data, and simultaneously facilitate effective feature aggregation with important neighbors. To evaluate the performance of SDGAT, we conducted experiments on three citation datasets and compared its performance against commonly employed models. The outcomes indicate that SDGAT excels in node classification tasks, notably on the Cora dataset, with an accuracy rate of 85.29%, marking a roughly 3% enhancement over the majority of baseline models. The experimental findings provide evidence that SDGAT delivers effective performance on all three citation datasets, underscoring the efficacy of the dynamic attention network built upon a sparse graph.

Sparse Graph Representation Learning Based on Reinforcement Learning for Personalized Mild Cognitive Impairment (MCI) Diagnosis.

Resting-state functional magnetic resonance imaging (rs-fMRI) has gained attention as a reliable technique for investigating the intrinsic function patterns of the brain. It facilitates the extraction of functional connectivity networks (FCNs) that capture synchronized activity patterns among regions of interest (ROIs). Analyzing FCNs enables the identification of distinctive connectivity patterns associated with mild cognitive impairment (MCI). For MCI diagnosis, various sparse representation techniques have been introduced, including statistical- and deep learning-based methods. However, these methods face limitations due to their reliance on supervised learning schemes, which restrict the exploration necessary for probing novel solutions. To overcome such limitation, prior work has incorporated reinforcement learning (RL) to dynamically select ROIs, but effective exploration remains challenging due to the vast search space during training. To tackle this issue, in this study, we propose an advanced RL-based framework that utilizes a divide-and-conquer approach to decompose the FCN construction task into smaller sub-problems in a subject-specific manner, enabling efficient exploration under each sub-problem condition. Additionally, we leverage the learned value function to determine the sparsity level of FCNs, considering individual characteristics of FCNs. We validate the effectiveness of our proposed framework by demonstrating its superior performance in MCI diagnosis on publicly available cohort datasets.

Global-local aware Heterogeneous Graph Contrastive Learning for multifaceted association prediction in miRNA-gene-disease networks.

Unraveling the intricate network of associations among microRNAs (miRNAs), genes, and diseases is pivotal for deciphering molecular mechanisms, refining disease diagnosis, and crafting targeted therapies. Computational strategies, leveraging link prediction within biological graphs, present a cost-efficient alternative to high-cost empirical assays. However, while plenty of methods excel at predicting specific associations, such as miRNA-disease associations (MDAs), miRNA-target interactions (MTIs), and disease-gene associations (DGAs), a holistic approach harnessing diverse data sources for multifaceted association prediction remains largely unexplored. The limited availability of high-quality data, as vitro experiments to comprehensively confirm associations are often expensive and time-consuming, results in a sparse and noisy heterogeneous graph, hindering an accurate prediction of these complex associations. To address this challenge, we propose a novel framework called Global-local aware Heterogeneous Graph Contrastive Learning (GlaHGCL). GlaHGCL combines global and local contrastive learning to improve node embeddings in the heterogeneous graph. In particular, global contrastive learning enhances the robustness of node embeddings against noise by aligning global representations of the original graph and its augmented counterpart. Local contrastive learning enforces representation consistency between functionally similar or connected nodes across diverse data sources, effectively leveraging data heterogeneity and mitigating the issue of data scarcity. The refined node representations are applied to downstream tasks, such as MDA, MTI, and DGA prediction. Experiments show GlaHGCL outperforming state-of-the-art methods, and case studies further demonstrate its ability to accurately uncover new associations among miRNAs, genes, and diseases. We have made the datasets and source code publicly available at https://github.com/Sue-syx/GlaHGCL.

Dynamic compact data structure for temporal reachability with unsorted contact insertions

Abstract Temporal graphs represent interactions between entities over time. Deciding whether entities can reach each other through temporal paths is useful for various applications such as in communication networks and epidemiology. Previous works have studied the scenario in which addition of new interactions can happen at any point in time. A known strategy maintains, incrementally, a Timed Transitive Closure using a dynamic data structure composed of $O(n^{2})$ binary search trees containing non-nested time intervals. However, space usage for storing these trees grows rapidly as more interactions are inserted. In this paper, we introduce a compact data structure that represents each tree as two dynamic bit-vectors. Furthermore, we present two variants of this data structure: one representing bits in dynamic bit-vectors explicitly and the other representing only the active bits by encoding their consecutive distances. In our experiments, we observed that our data structure improves space usage while having similar time performance for incremental updates when comparing with the previous strategy. The first variant of our data structure gives the best space improvement when constructing Time Transitive Closures for temporally dense temporal graphs, and the second variant uses less space for temporally sparse temporal graphs.

Turing Bifurcation in the Swift–Hohenberg Equation on Deterministic and Random Graphs

The Swift–Hohenberg equation (SHE) is a partial differential equation that explains how patterns emerge from a spatially homogeneous state. It has been widely used in the theory of pattern formation. Following a recent study by Bramburger and Holzer (SIAM J Math Anal 55(3):2150–2185, 2023), we consider discrete SHE on deterministic and random graphs. The two families of the discrete models share the same continuum limit in the form of a nonlocal SHE on a circle. The analysis of the continuous system, parallel to the analysis of the classical SHE, shows bifurcations of spatially periodic solutions at critical values of the control parameters. However, the proximity of the discrete models to the continuum limit does not guarantee that the same bifurcations take place in the discrete setting in general, because some of the symmetries of the continuous model do not survive discretization. We use the center manifold reduction and normal forms to obtain precise information about the number and stability of solutions bifurcating from the homogeneous state in the discrete models on deterministic and sparse random graphs. Moreover, we present detailed numerical results for the discrete SHE on the nearest-neighbor and small-world graphs.

An Unsupervised Long- and Short-Term Sparse Graph Neural Network for Multisensor Anomaly Detection

An Unsupervised Long- and Short-Term Sparse Graph Neural Network for Multisensor Anomaly Detection

Enhanced Remote Sensing Image Compression Method Using Large Network with Sparse Extracting Strategy

Deep neural networks based on hyper-encoders play a critical role in estimating prior distributions in remote sensing image compression issues. However, most of the existing encoding methods suffer from a problem on the hyper-encoding side, namely the mismatch of extraction ability with the encoder. This ability bias results in likelihood features that fail to extract sufficient information from latent representations. To solve this problem, the feature extraction capabilities of the hyper-encoder are enhanced to better estimate the Gaussian likelihood of the latent representation in end-to-end network optimization. Specifically, residual blocks and a parameter estimation module are incorporated to balance the performance of the encoder and the hyper-encoder. Furthermore, it is observed that the well-trained compression model tends to generate a fixed pattern of latent representations. Therefore, we incorporate a nonlocal cross-channel graph (NCG) on the backside of the encoder. Specifically, it aggregates features between similar latent representations in a graphical manner to further enhance the side information extraction capability of the hyper-encoder. Considering the computational cost, a sparse graph strategy is further developed to dynamically select the most relevant latent representations for aggregation operations, which greatly reduces the computational effort. The proposed algorithm is named nonlocal cross-channel efficient graph (NCEG). A long-dependent residual network is selected as the backbone, and a sparse attention module is inserted into the encoder/decoder side to enhance the perceptual field of the network. The experimental results on two evaluation datasets demonstrate that the proposed method achieves satisfactory results compared to other learning-based methods.

RuMER-RL: A hybrid framework for sparse knowledge graph explainable reasoning

Knowledge Graph (KG) reasoning is a crucial technology for ensuring the accuracy and utility of KGs. However, robust and explainable reasoning on sparse KGs is challenging due to the lack of information and truncated paths. To address this issue, we introduce RuMER-RL, a hybrid reasoning framework comprising three modules: Rule Mining (RM), Embedding Representation (ER), and Reinforcement Learning (RL). The ER and RM modules collaborate to enhance the embedding models and rule quality, generating additional triples to mitigate the sparsity of the KG. The RL module models multi-hop KG reasoning as a Markov Decision Process (MDP), employing dynamic anticipation, action space expansion, and curiosity-driven strategies to enrich the reasoning process and mitigate sparsity. Additionally, we reshape the reward function by incorporating embedding representation, rule matching, and curiosity rewards to guide the training and optimization of the policy network. Extensive experiments on six sparse KG datasets demonstrate that RuMER-RL outperforms state-of-the-art models in terms of link prediction accuracy and interpretability.

Graph features based classification of bronchial and pleural rub sound signals: the potential of complex network unwrapped.

The study presents a novel technique for lung auscultation based on graph theory, emphasizing the potential of graph parameters in distinguishing lung sounds and supporting earlier detection of various respiratory pathologies. The frequency spread and the component magnitudes are revealed from the analysis of eighty-five bronchial (BS) and pleural rub (PS) lung sounds employing the power spectral density (PSD) plot and wavelet scalogram. The low-frequency spread, and persistence of the high-intensity frequency components are visible in BS sounds emanating from the uniform cross-sectional area of the trachea. The frictional rub between the pleurae causes a higher frequency spread of low-intensity intermittent frequency components in PS signals. From the complex networks of BS and PS, the extracted graph features are - graph density ([Formula: see text], transitivity ([Formula: see text], degree centrality ([Formula: see text]), betweenness centrality ([Formula: see text], eigenvector centrality ([Formula: see text]), and graph entropy (En). The high values of [Formula: see text] and [Formula: see text] show a strong correlation between distinct segments of the BS signal originating from a consistent cross-sectional tracheal diameter and, hence, the generation of high-intense low-spread frequency components. An intermittent low-intense and a relatively greater frequency spread in PS signal appear as high [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] values. With these complex network parameters as input attributes, the supervised machine learning techniques- discriminant analyses, support vector machines, k-nearest neighbors, and neural network pattern recognition (PRNN)- classify the signals with more than 90% accuracy, with PRNN having 25 neurons in the hidden layer achieving the highest (98.82%).

Symmetric spatiotemporal learning network with sparse meter graph for short-term energy-consumption prediction in manufacturing systems

Short-term energy-consumption prediction is the basis of anomaly detection, real-time scheduling, and energy-saving control in manufacturing systems. Most existing methods focus on single-node energy-consumption prediction and suffer from difficult parameter collection and modelling. Although several methods have been presented for multinode energy-consumption prediction, their prediction performance needs to be improved owing to a lack of appropriate knowledge guidance and learning networks for complex spatiotemporal relationships. This study presents a symmetric spatiotemporal learning network (SSTLN) with a sparse meter graph (SMG) (SSTLN-SMG) that aims to predict multiple nodes based on energy-consumption time series and general process knowledge. The SMG expresses process knowledge by abstracting production nodes, material flows, and energy usage, and provides initial guidance for the SSTLN to extract spatial features. SSTLN, a symmetrical stack of graph convolutional networks (GCN) and gated linear units (GLU), is devised to achieve a trade-off not only between spatial and temporal feature extraction but also between detail capture and noise suppression. Extensive experiments were performed using datasets from an aluminium profile plant. The experimental results demonstrate that the proposed method allows multinode energy-consumption prediction with less prediction error than state-of-the-art methods, methods with deformed meter graphs, and methods with deformed learning networks.