Edges Of Graph Research Articles

Distribution of similar configurations in subsets of [formula omitted

Let Fq be a finite field of order q and E be a set in Fqd. The distance set of E is defined by Δ(E):={‖x−y‖:x,y∈E}, where ‖α‖=α12+…+αd2. Iosevich, Koh and Parshall (2018) proved that if d≥2 is even and |E|≥9qd/2, thenFq=Δ(E)Δ(E)={ab:a∈Δ(E),b∈Δ(E)∖{0}}. In other words, for each r∈Fq⁎ there exist (x,y)∈E2 and (x′,y′)∈E2 such that ‖x−y‖≠0 and ‖x′−y′‖=r‖x−y‖.Geometrically, this means that if the size of E is large, then for any given r∈Fq⁎ we can find a pair of edges in the complete graph K|E| with vertex set E such that one of them is dilated by r∈Fq⁎ with respect to the other. A natural question arises whether it is possible to generalize this result to arbitrary subgraphs of K|E| with vertex set E and this is the goal of this paper.In this paper, we solve this problem for k-paths (k≥2), simplexes and 4-cycles. We are using a mix of tools from different areas such as enumerative combinatorics, group actions and Turán type theorems.

Skeleton-based action recognition with local dynamic spatial–temporal aggregation

Skeleton-based action recognition has attracted more and more attention due to its advantage in avoiding environmental noise including light transformations and viewpoint changing. Most current approaches consist of interleaving spatial-only modules and temporal-only modules, where messages are first spatially aggregated between human joints and then temporally delivered. Although efficient, such factorized design hinders direct information flow among joints in adjacent frames, thus failing to (1) effectively convey information in a larger neighborhood and (2) be inferior to capture short-term motion to distinguish similar action pairs. To handle these limitations, we propose spatial–temporal graph attention network (STGAT) to dynamically model local cross-spacetime information. Keeping the temporal-only modules unchanged, it inflates the spatial-only modules to perform spatial–temporal modeling from the local spatial–temporal neighborhood without a second transmission cost. Especially, different from previous spatial–temporal modeling methods, graph edges are adaptively computed to dynamically aggregate beneficial information to capture short-term movements, getting rid of predefined fixed connectivity. This ensures STGAT could dynamically attend to important joints in a local spatial–temporal neighborhood to capture critical short-term movements. While STGAT is theoretically effective in introducing local spatial–temporal information by comprising a large spatial–temporal neighborhood, we find its effectiveness is impeded by the inherent redundancy in local features. We propose three simple modules to reduce local feature redundancy to calibrate the feature modeling schema and further release the potential of STGAT, which (1) narrow the scope of self-attention operators, (2) dynamically weight joints along the temporal dimension, and (3) separate subtle motion from static features, respectively. As a result, STGAT achieves state-of-the-art performance on three large-scale datasets: NTU RGB＋D 60, NTU RGB＋D 120, and Kinetics Skeleton 400. Thanks to special care on local cross-spacetime information, STGAT generalizes better upon classifying hard similar actions than previous methods. Visualizations demonstrate that STGAT could intelligently attend to critical joints when dealing with different actions. Code is available at https://github.com/hulianyuyy/STGAT.

A multi-modal garden dataset and hybrid 3D dense reconstruction framework based on panoramic stereo images for a trimming robot

Recovering an outdoor environment’s surface mesh is vital for an agricultural robot during task planning and remote visualization. Image-based dense 3D reconstruction is sensitive to large movements between adjacent frames and the quality of the estimated depth maps. Our proposed solution for these problems is based on a newly-designed panoramic stereo camera along with a hybrid novel software framework that consists of three fusion modules: disparity fusion, pose fusion, and volumetric fusion. The panoramic stereo camera with a pentagon shape consists of 5 stereo vision camera pairs to stream synchronized panoramic stereo images for the following three fusion modules. In the disparity fusion module, rectified stereo images produce the initial disparity maps using multiple stereo vision algorithms. Then, these initial disparity maps, along with the intensity images, are input into a disparity fusion network to produce refined disparity maps. Next, the refined disparity maps are converted into full-view (360°) point clouds or single-view (72°) point clouds for the pose fusion module. The pose fusion module adopts a two-stage global-coarse-to-local-fine strategy. In the first stage, each pair of full-view point clouds is registered by a global point cloud matching algorithm to estimate the transformation for a global pose graph’s edge, which effectively implements loop closure. In the second stage, a local point cloud matching algorithm is used to match single-view point clouds in different nodes. Next, we locally refine the poses of all corresponding edges in the global pose graph using three proposed rules, thus constructing a refined pose graph. The refined pose graph is optimized to produce a global pose trajectory for volumetric fusion. In the volumetric fusion module, the global poses of all the nodes are used to integrate the single-view point clouds into the volume to produce the mesh of the whole garden. The proposed framework and its three fusion modules are tested on a real outdoor garden dataset to show the superiority of the performance. The whole pipeline takes about 4 min on a desktop computer to process the real garden dataset, which is available at: https://github.com/Canpu999/Trimbot-Wageningen-SLAM-Dataset.

Spectral Feature Augmentation for Graph Contrastive Learning and Beyond

Although augmentations (e.g., perturbation of graph edges, image crops) boost the efficiency of Contrastive Learning (CL), feature level augmentation is another plausible, complementary yet not well researched strategy. Thus, we present a novel spectral feature argumentation for contrastive learning on graphs (and images). To this end, for each data view, we estimate a low-rank approximation per feature map and subtract that approximation from the map to obtain its complement. This is achieved by the proposed herein incomplete power iteration, a non-standard power iteration regime which enjoys two valuable byproducts (under mere one or two iterations): (i) it partially balances spectrum of the feature map, and (ii) it injects the noise into rebalanced singular values of the feature map (spectral augmentation). For two views, we align these rebalanced feature maps as such an improved alignment step can focus more on less dominant singular values of matrices of both views, whereas the spectral augmentation does not affect the spectral angle alignment (singular vectors are not perturbed). We derive the analytical form for: (i) the incomplete power iteration to capture its spectrum-balancing effect, and (ii) the variance of singular values augmented implicitly by the noise. We also show that the spectral augmentation improves the generalization bound. Experiments on graph/image datasets show that our spectral feature augmentation outperforms baselines, and is complementary with other augmentation strategies and compatible with various contrastive losses.

Anytime bottom-up rule learning for large-scale knowledge graph completion

Knowledge graph completion is the task of predicting correct facts that can be expressed by the vocabulary of a given knowledge graph, which are not explicitly stated in that graph. Broadly, there are two main approaches for solving the knowledge graph completion problem. Sub-symbolic approaches embed the nodes and/or edges of a given graph into a low-dimensional vector space and use a scoring function to determine the plausibility of a given fact. Symbolic approaches learn a model that remains within the primary representation of the given knowledge graph. Rule-based approaches are well-known examples. One such approach is AnyBURL. It works by sampling random paths, which are generalized into Horn rules. Previously published results show that the prediction quality of AnyBURL is close to current state of the art with the additional benefit of offering an explanation for a predicted fact. In this paper, we propose several improvements and extensions of AnyBURL. In particular, we focus on AnyBURL’s capability to be successfully applied to large and very large datasets. Overall, we propose four separate extensions: (i) We add to each rule a set of pairwise inequality constraints which enforces that different variables cannot be grounded by the same entities, which results into more appropriate confidence estimations. (ii) We introduce reinforcement learning to guide path sampling in order to use available computational resources more efficiently. (iii) We propose an efficient sampling strategy to approximate the confidence of a rule instead of computing its exact value. (iv) We develop a new multithreaded AnyBURL, which incorporates all previously mentioned modifications. In an experimental study, we show that our approach outperforms both symbolic and sub-symbolic approaches in large-scale knowledge graph completion. It has a higher prediction quality and requires significantly less time and computational resources.

A large-scale data security detection method based on continuous time graph embedding framework

Graph representation learning has made significant strides in various fields, including sociology and biology, in recent years. However, the majority of research has focused on static graphs, neglecting the temporality and continuity of edges in dynamic graphs. Furthermore, dynamic data are vulnerable to various security threats, such as data privacy breaches and confidentiality attacks. To tackle this issue, the present paper proposes a data security detection method based on a continuous-time graph embedding framework (CTDGE). The framework models temporal dependencies and embeds data using a graph representation learning method. A machine learning algorithm is then employed to classify and predict the embedded data to detect if it is secure or not. Experimental results show that this method performs well in data security detection, surpassing several dynamic graph embedding methods by 5% in terms of AUC metrics. Furthermore, the proposed framework outperforms other dynamic baseline methods in the node classification task of large-scale graphs containing 4321477 temporal information edges, resulting in a 10% improvement in the F1 score metric. The framework is also robust and scalable for application in various data security domains. This work is important for promoting the use of continuous-time graph embedding framework in the field of data security.

Road Network Representation Learning: A Dual Graph-based Approach

Road network is a critical infrastructure powering many applications including transportation, mobility and logistics in real life. To leverage the input of a road network across these different applications, it is necessary to learn the representations of the roads in the form of vectors, which is named road network representation learning (RNRL). While several models have been proposed for RNRL, they capture the pairwise relationships/connections among roads only (i.e., as a simple graph), and fail to capture among roads the high-order relationships (e.g., those roads that jointly form a local region usually have similar features such as speed limit) and long-range relationships (e.g., some roads that are far apart may have similar semantics such as being roads in residential areas). Motivated by this, we propose to construct a hypergraph , where each hyperedge corresponds to a set of multiple roads forming a region. The constructed hypergraph would naturally capture the high-order relationships among roads with hyperedges. We then allow information propagation via both the edges in the simple graph and the hyperedges in the hypergraph in a graph neural network context. In addition, we introduce different pretext tasks based on both the simple graph (i.e., graph reconstruction) and the hypergraph (including hypergraph reconstruction and hyperedge classification) for optimizing the representations of roads. The graph reconstruction and hypergraph reconstruction tasks are conventional ones and can capture structural information. The hyperedge classification task can capture long-range relationships between pairs of roads that belong to hyperedges with the same label. We call the resulting model HyperRoad . We further extend HyperRoad to problem settings when additional inputs of road attributes and/or trajectories that are generated on the roads are available. We conduct extensive experiments on two real datasets, for five downstream tasks, and under four problem settings, which demonstrate that our model achieves impressive improvements compared with existing baselines across datasets, tasks, problem settings, and performance metrics. CCS Concepts: • Information systems → Data mining ; • Urban computing ; • Spatial-temporal systems ;

Global and Local Differentially Private Release of Count-Weighted Graphs

Many complex natural and technological systems are commonly modeled as count-weighted graphs, where nodes represent entities, edges model relationships between them, and edge weights define some counting statistics associated with each relationship. As graph data usually contain sensitive information about entities, preserving privacy when releasing this type of data becomes an important issue. In this context, differential privacy (DP) has become the de facto standard for data release under strong privacy guarantees. When dealing with DP for weighted graphs, most state-of-the-art works assume that the graph topology is known. However, in several real-world applications, the privacy of the graph topology also needs to be ensured. In this paper, we aim to bridge the gap between DP and count-weighted graph data release, considering both graph structure and edge weights as private information. We first adapt the weighted graph DP definition to take into account the privacy of the graph structure. We then develop two novel approaches to privately releasing count-weighted graphs under the notions of global and local DP. We also leverage the post-processing property of DP to improve the accuracy of the proposed techniques considering graph domain constraints. Experiments using real-world graph data demonstrate the superiority of our approaches in terms of utility over existing techniques, enabling subsequent computation of a variety of statistics on the released graph with high utility, in some cases comparable to the non-private results.

Unsupervised video anomaly detection in UAVs: a new approach based on learning and inference

In this paper, an innovative approach to detecting anomalous occurrences in video data without supervision is introduced, leveraging contextual data derived from visual characteristics and effectively addressing the semantic discrepancy that exists between visual information and the interpretation of atypical incidents. Our work incorporates Unmanned Aerial Vehicles (UAVs) to capture video data from a different perspective and to provide a unique set of visual features. Specifically, we put forward a technique for discerning context through scene comprehension, which entails the construction of a spatio-temporal contextual graph to represent various aspects of visual information. These aspects encompass the manifestation of objects, their interrelations within the spatio-temporal domain, and the categorization of the scenes captured by UAVs. To encode context information, we utilize Transformer with message passing for updating the graph's nodes and edges. Furthermore, we have designed a graph-oriented deep Variational Autoencoder (VAE) approach for unsupervised categorization of scenes, enabling the extraction of the spatio-temporal context graph across diverse settings. In conclusion, by utilizing contextual data, we ascertain anomaly scores at the frame-level to identify atypical occurrences. We assessed the efficacy of the suggested approach by employing it on a trio of intricate data collections, specifically, the UCF-Crime, Avenue, and ShanghaiTech datasets, which provided substantial evidence of the method's successful performance.

Attack Graphs & Subset Sabotage Games

We consider an extended version of sabotage games played over Attack Graphs. Such games are two-player zero-sum reachability games between an Attacker and a Defender. This latter player can erase particular subsets of edges of the Attack Graph. To reason about such games we introduce a variant of Sabotage Modal Logic (that we call Subset Sabotage Modal Logic) in which one modality quantifies over non-empty subset of edges. We show that we can characterize the existence of winning Attacker strategies by formulas of Subset Sabotage Modal Logic.

Cross-view graph contrastive learning with hypergraph

Graph contrastive learning (GCL) provides a new perspective to alleviate the reliance on labeled data for graph representation learning. Recent efforts on GCL leverage various graph augmentation strategies, i.e., node dropping and edge masking, to create augmented views of the original graph, and then contrast the representations in these augmented views to learn expressive graph embeddings. Nevertheless, the contrasting is still conducted between small variations of the original graph, where limited information can be extracted. In this work, for the first time, we propose to use hypergraph to establish a new view for graph contrastive learning. Specifically, for each graph, we construct its corresponding hypergraph, and then contrast the graph representations learned in the hypergraph view and the original graph view, by which the high-order information of a graph can be captured to produce graph representations of higher quality. Furthermore, to bridge the potential gap between the graph and hypergraph representations, we utilize the diffusion model to exchange the information contained in these two views, enabling better graph contrastive learning. We evaluate our proposal with a collection of experiments, and the empirical results validate that the proposed model can improve node and graph classification performance.

Partitioning edges of a planar graph into linear forests and a matching

AbstractWe show that the edges of any planar graph of maximum degree at most 9 can be partitioned into four linear forests and a matching. Combined with known results, this implies that the edges of any planar graph of odd maximum degree can be partitioned into linear forests and one matching. This strengthens well‐known results stating that graphs in this class have chromatic index and linear arboricity at most .

Recursive State Machine Guided Graph Folding for Context-Free Language Reachability

Context-free language reachability (CFL-reachability) is a fundamental framework for program analysis. A large variety of static analyses can be formulated as CFL-reachability problems, which determines whether specific source-sink pairs in an edge-labeled graph are connected by a reachable path, i.e., a path whose edge labels form a string accepted by the given CFL. Computing CFL-reachability is expensive. The fastest algorithm exhibits a slightly subcubic time complexity with respect to the input graph size. Improving the scalability of CFL-reachability is of practical interest, but reducing the time complexity is inherently difficult. In this paper, we focus on improving the scalability of CFL-reachability from a more practical perspective---reducing the input graph size. Our idea arises from the existence of trivial edges, i.e., edges that do not affect any reachable path in CFL-reachability. We observe that two nodes joined by trivial edges can be folded---by merging the two nodes with all the edges joining them removed---without affecting the CFL-reachability result. By studying the characteristic of the recursive state machines (RSMs), an alternative form of CFLs, we propose an approach to identify foldable node pairs without the need to verify the underlying reachable paths (which is equivalent to solving the CFL-reachability problem). In particular, given a CFL-reachability problem instance with an input graph G and an RSM, based on the correspondence between paths in G and state transitions in RSM, we propose a graph folding principle, which can determine whether two adjacent nodes are foldable by examining only their incoming and outgoing edges. On top of the graph folding principle, we propose an efficient graph folding algorithm GF. The time complexity of GF is linear with respect to the number of nodes in the input graph. Our evaluations on two clients (alias analysis and value-flow analysis) show that GF significantly accelerates RSM/CFL-reachability by reducing the input graph size. On average, for value-flow analysis, GF reduces 60.96% of nodes and 42.67% of edges of the input graphs, obtaining a speedup of 4.65× and a memory usage reduction of 57.35%. For alias analysis, GF reduces 38.93% of nodes and 35.61% of edges of the input graphs, obtaining a speedup of 3.21× and a memory usage reduction of 65.19%.

An Edge Irregular Reflexive k−labeling of Comb Graphs with Additional 2 Pendants

Let G be a connected, simple, and undirrected graph, where V (G) is the vertex set and E(G) is the edge set. Let k be a natural numbers. For graph G we define a total k−labeling ρ such that the vertices of graph G are labeled with {0, 2, 4, . . . , 2kv} and the edges of graph G are labeled with {1, 2, 3, . . . , ke}, where k = max{2kv, ke}. Total k−labeling ρ called an edge irregular reflexive k− labeling if every two distinct edge of graph G have distinct edge weights, where the edge weight is defined as the sum of the label of that edge and the label of the vertices that are incident to this edge. The minimum k such that G has an edge irregular reflexive k−labeling called the reflexive edge strength of G. In this paper we determine the reflexive edge strength of some comb graphs.

An Edge Irregular Reflexive k−labeling of Comb Graphs with Additional 2 Pendants

Let G be a connected, simple, and undirrected graph, where V (G) is the vertex set and E(G) is the edge set. Let k be a natural numbers. For graph G we define a total k−labeling ρ such that the vertices of graph G are labeled with {0, 2, 4, . . . , 2kv} and the edges of graph G are labeled with {1, 2, 3, . . . , ke}, where k = max{2kv, ke}. Total k−labeling ρ called an edge irregular reflexive k− labeling if every two distinct edge of graph G have distinct edge weights, where the edge weight is defined as the sum of the label of that edge and the label of the vertices that are incident to this edge. The minimum k such that G has an edge irregular reflexive k−labeling called the reflexive edge strength of G. In this paper we determine the reflexive edge strength of some comb graphs.

Contrastive Multi-view Composite Graph Convolutional Networks Based on Contribution Learning for Autism Spectrum Disorder Classification.

The resting-state functional magnetic resonance imaging (rs-fMRI) faithfully reflects the brain activities and thus provides a promising tool for autism spectrum disorder (ASD) classification. Up to now, graph convolutional networks (GCNs) have been successfully applied in rs-fMRI based ASD classification. However, most of these methods were developed based on functional connectivities (FCs) that only reflect low-level correlation between brain regions, without integrating both high-level discriminative knowledge and phenotypic information into classification. Besides, they suffered from the overfitting problem caused by insufficient training samples. To this end, we propose a novel contrastive multi-view composite GCN (CMV-CGCN) for ASD classification using both FCs and HOFCs. Specifically, a pair of graphs are constructed based on the FC and HOFC features of the subjects, respectively, and they share the phenotypic information in the graph edges. A novel contrastive multi-view learning method is proposed based on the consistent representation of both views. A contribution learning mechanism is further incorporated, encouraging the FC and HOFC features of different subjects to have various contribution in the contrastive multi-view learning. The proposed CMV-CGCN is evaluated on 613 subjects (including 286 ASD patients and 327 NCs) from the Autism Brain Imaging Data Exchange (ABIDE). We demonstrate the performance of the method for ASD classification, which yields an accuracy of 75.20% and an area under the curve (AUC) of 0.7338. Experimental results show that our proposed method outperforms state-of-the-art methods on the ABIDE database.

Social-Aware Graph-Based Collaborative Caching in Edge-User Networks

The soaring data traffic brings tremendous pressure on core networks. Collaborative caching among edge servers and user devices has been regarded as a promising technology for releasing backhaul pressure and reducing content download delay in the next-generation communication network. However, given the capacity constraint of edge servers and caching devices, a challenge is how to exploit these storage resources efficiently. In this paper, we introduce a three-tier collaborative caching architecture for edge-user networks and propose a social-aware graph-based collaborative caching (SGCC) strategy to minimize content download delay. Specifically, the small base station tier and user equipment tier are modeled as a one-tier directed graph. Moreover, we model the physical attributes and social attributes as the weight of the directed edges in the physical link graph and social graph, respectively. Then, we construct a social-aware graph by merging the two-tier topology of the physical link graph and social graph to simplify the caching decision. Further, we design SGCC to cache the most popular content according to the weighted content popularity. Simulation results demonstrate that the proposed SGCC can effectively reduce the average download delay and has a 26.8% lower average download delay, compared with the uniform popular caching baseline.

Multivariate Time Series Clustering based on Graph Convolutional Network

Multivariable time series (MTS) clustering is an important topic in time series data mining. The major challenge of MTS clustering is to capture the temporal correlations and the dependencies between multiple variables. In this paper, we propose a novel MTS clustering approach based on graph convolutional network (GCN), which is a powerful feature extractor for graph structure data. We regard each variable in MTS as a node in the graph and construct edges through the correlation between variables. Furthermore, GCN and deep learning back-ropagation technology are used to continuously learn the relationship between multiple variables. Combining the learned variables with the characteristics of the time dimensions, the comprehensive features can be fused to form effective representation for MTS clustering task. We carry out extensive experimental analysis on four open time series data sets and six benchmark algorithms, which shows the superiority of the proposed method.

IFDS-based Context Debloating for Object-Sensitive Pointer Analysis

Object-sensitive pointer analysis, which separates the calling contexts of a method by its receiver objects, is known to achieve highly useful precision for object-oriented languages such as Java. Despite recent advances, all object-sensitive pointer analysis algorithms still suffer from the scalability problem due to the combinatorial explosion of contexts in large programs. In this article, we introduce a new approach, Conch , that can be applied to debloat contexts for all object-sensitive pointer analysis algorithms, thereby improving significantly their efficiency while incurring a negligible loss of precision. Our key insight is to approximate a recently proposed set of two necessary conditions for an object in a program to be context-sensitive, i.e., context-dependent (whose precise verification is undecidable) with a set of three linearly verifiable conditions in terms of the number of edges in the pointer assignment graph (PAG) representation of the program. These three linearly verifiable conditions, which turn out to be almost always necessary in practice, are synthesized from three key observations regarding context-dependability for the objects created and used in real-world object-oriented programs. To develop a practical implementation for Conch , we introduce an IFDS-based algorithm for reasoning about object reachability in the PAG of a program, which runs linearly in terms of the number of edges in the PAG. By debloating contexts for three representative object-sensitive pointer analysis algorithms, which are applied to a set of representative Java programs, Conch can speed up these three baseline algorithms substantially at only a negligible loss of precision (less than 0.1%) with respect to several commonly used precision metrics. In addition, Conch also improves their scalability by enabling them to analyze substantially more programs to completion than before (under a time budget of 12 hours). Conch has been open-sourced (http://www.cse.unsw.edu.au/~corg/tools/conch), opening up new opportunities for other researchers and practitioners to further improve this research. To demonstrate this, we introduce one extension of Conch to accelerate further the three baselines without losing any precision, providing further insights on extending Conch to make precision-efficiency tradeoffs in future research.

Spectrum of the wave equation with Dirac damping on a non-compact star graph

We consider the wave equation on non-compact star graphs, subject to a distributional damping defined through a Robin-type vertex condition with complex coupling. It is shown that the non-self-adjoint generator of the evolution problem admits an abrupt change in its spectral properties for a special coupling related to the number of graph edges. As an application, we show that the evolution problem is highly unstable for the critical couplings. The relationship with the Dirac equation in non-relativistic quantum mechanics is also mentioned.