Size Of Graph Research Articles

Augmented and Virtual Reality Based Segmentation Algorithm for Human Pose Detection in Wearable Cameras

Pose graph optimisation is a crucial method that helps reduce cumulative errors while estimating visual trajectories for wearable cameras. However, when the posture graph's size increases with each additional camera movement, the optimization's efficiency diminishes. In terms of ongoing sensitive applications, such as extended reality and computer-generated reality, direction assessment is a major test. This research proposes an incremental pose graph segmentation technique that accounts for camera orientation variations as a solution to this challenge. The computation only improves the cameras that have seen large direction changes by breaking the posture chart during these instances. As a result, pose graph optimisation is essentially slowed down and optimised more quickly. For every camera that hasn't been optimised using a pose graph, the algorithm employs the wearable cameras at the start and end of each camera's trajectory segment. The final camera in attendance is then determined by weighted average the various postures evaluated with these wearable cameras; this eliminates the need for lengthy nonlinear enhancement computations, reduces disturbance, and achieves excellent accuracy. Experiments on the EuRoC, TUM, and KITTI datasets demonstrate that pose graph optimisation scope is reduced while maintaining camera trajectories accuracy.

Monte Carlo safeguarding of key links through multiple random walks in large network

Safeguarding important links is a useful way to promote network vulnerability, especially in sparse networks where random link failures can disconnect the network. Sustaining network connectivity is the main goal of safeguarding and can be handled by selectively safeguarding links belonging to certain cuts of a network. However, due to the inherent high complexity of cut enumeration, existing algorithms can only handle small‐scale networks with limited nodes. It is important to find practical algorithms that are feasible for large‐scale graphs, as a significant portion of real‐world graphs under investigation are not as small as dozens of nodes. To address the problem, we propose to use a high‐precision approximate approach to accelerate the first step of the two‐step safeguard process and thus accelerate the whole process. A Monte Carlo algorithm is proposed to exploit efficient random paths for small cuts enumeration, which can help locate important edges with high probability in large‐scale sparse networks. These edges will then be utilized to find the approximated minimum cost edge set whose safeguarding can sustain the expected network connectivity. The algorithm is validated using various sizes of graphs of random/Barbasi–Albert scale‐free/Clustered scale‐free/unit disk/Watts–Strogatz small‐world and real‐world graphs. The experimental results show that the algorithm can perfectly sustain the network connectivity, and the acceleration ratio of more than 105 can be achieved with a little additional overhead. Specifically, in large graphs of one million nodes, approximated safeguard solutions survive at least 99.9% random link failures, and the solution time can be further reduced to dozens of seconds when the algorithm steps are easily implemented in full parallel.

Cardinality and Isomorphic Properties of Hajós Graphs and Hajós Fuzzy Graphs

Objectives: Fuzzy graphs allow uncertainty in the ideas characterizing vertices and edges to be included when modelling real-world scenarios into graph models. This study aims to introduce Hajós fuzzy graph, cardinality of Hajós graph and Hajós fuzzy graph and to explore many properties. Methods : Here, the Hajós construction is applied to two fuzzy graphs, and the Hajós fuzzy graph is defined by assigning membership values to all the edges and vertices of the newly formed fuzzy graph. Fuzzy graph conditions are verified for the assigned membership values. Examples are used to illustrate the concept. Findings: The Hajós fuzzy graph's size and order are established. Isomorphic property is discussed. The number of Hajós (fuzzy) graphs that exist for some combinations of two (fuzzy) graphs is calculated. Novelty: Based on Hajós construction, the Hajós fuzzy graph is defined. Based on the fact that different choices of vertices and edges produce different Hajós (fuzzy) graph, its cardinality is defined. The notion of cardinality is a novel concept in Hajos graph which helps to find the total number of Hajós (fuzzy) graphs. The cardinality of the Hajós (fuzzy) graph which arises from two (fuzzy) graphs that can be a cycle, path, regular graph, complete graph and complete bipartite graph are derived. Mathematics subject classification. (2010): 05C72, 05C76 Keywords: Hajós Graph, Hajós fuzzy graph, Order, Size, Isomorphism, Cardinality of Hajós fuzzy graph

Optimal error‐detection system for identifying codes

AbstractAssume that a graph models a detection system for a facility with a possible “intruder,” or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing detectors at a subset of vertices in to determine the location of an intruder if there is any. Many types of detection systems have been defined for different sensor capabilities; in particular, we focus on identifying codes, where each detector can determine whether there is an intruder within its closed neighborhood. In this research we explore a fault‐tolerant variant of identifying codes applicable to real‐world systems. Specifically, error‐detecting identifying codes permit a false‐negative transmission from any single detector. We investigate minimum‐sized error‐detecting identifying codes in several classes of graphs, including cubic graphs and infinite grids, and show that the problem of determining said minimum size in arbitrary graphs is NP‐complete.

Fault Diagnosis Method for Vacuum Contactor Based on Time-Frequency Graph Optimization Technique and ShuffleNetV2.

This paper presents a fault diagnosis method for a vacuum contactor using the generalized Stockwell transform (GST) of vibration signals. The objective is to solve the problem of low diagnostic performance efficiency caused by the inadequate feature extraction capability and the redundant pixels in the graph background. The proposed method is based on the time-frequency graph optimization technique and ShuffleNetV2 network. Firstly, vibration signals in different states are collected and converted into GST time-frequency graphs. Secondly, multi-resolution GST time-frequency graphs are generated to cover signal characteristics in all frequency bands by adjusting the GST Gaussian window width factor λ. The OTSU algorithm is then combined to crop the energy concentration area, and the size of these time-frequency graphs is optimized by 68.86%. Finally, considering the advantages of the channel split and channel shuffle methods, the ShuffleNetV2 network is adopted to improve the feature learning ability and identify fault categories. In this paper, the CKJ5-400/1140 vacuum contactor is taken as the test object. The fault recognition accuracy reaches 99.74%, and the single iteration time of model training is reduced by 19.42%.

Hierarchical Glocal Attention Pooling for Graph Classification

Graph pooling is an essential operation in Graph Neural Networks that reduces the size of an input graph while preserving its core structural properties. Existing pooling methods find a compressed representation considering the Global Topological Structures (e.g., cliques, stars, clusters) or Local information at node level (e.g., top-k informative nodes). However, an effective graph pooling method does not hierarchically integrate both Global and Local graph properties. To this end, we propose a dual-fold Hierarchical Global Local Attention Pooling (HGLA-Pool) layer that exploits the aforementioned graph properties, generating more robust graph representations. Exhaustive experiments on nine publicly available graph classification benchmarks under standard metrics show that HGLA-Pool significantly outperforms eleven state-of-the-art models on seven datasets while being on par for the remaining two.

AdaMotif: Graph Simplification via Adaptive Motif Design.

With the increase of graph size, it becomes difficult or even impossible to visualize graph structures clearly within the limited screen space. Consequently, it is crucial to design effective visual representations for large graphs. In this paper, we propose AdaMotif, a novel approach that can capture the essential structure patterns of large graphs and effectively reveal the overall structures via adaptive motif designs. Specifically, our approach involves partitioning a given large graph into multiple subgraphs, then clustering similar subgraphs and extracting similar structural information within each cluster. Subsequently, adaptive motifs representing each cluster are generated and utilized to replace the corresponding subgraphs, leading to a simplified visualization. Our approach aims to preserve as much information as possible from the subgraphs while simplifying the graph efficiently. Notably, our approach successfully visualizes crucial community information within a large graph. We conduct case studies and a user study using real-world graphs to validate the effectiveness of our proposed approach. The results demonstrate the capability of our approach in simplifying graphs while retaining important structural and community information.

Quantum-assisted rendezvous on graphs: explicit algorithms and quantum computer simulations

Abstract We study quantum advantage in one-step rendezvous games on simple graphs analytically, numerically, and using noisy intermediate-scale quantum (NISQ) processors. Our protocols realise the recently discovered (Mironowicz 2023 New J. Phys. 25 013023) optimal bounds for small cycle graphs and cubic graphs. In the case of cycle graphs, we generalise the protocols to arbitrary graph size. The NISQ processor experiments realise the expected quantum advantage with high accuracy for rendezvous on the complete graph K 3. In contrast, for the graph 2 K 4 , formed by two disconnected 4-vertex complete graphs, the performance of the NISQ hardware is sub-classical, consistent with the deeper circuit and known qubit decoherence and gate error rates.

New Ramsey Multiplicity Bounds and Search Heuristics

AbstractWe study two related problems concerning the number of homogeneous subsets of given size in graphs that go back to questions of Erdős. Most notably, we improve the upper bounds on the Ramsey multiplicity of $$K_4$$ K 4 and $$K_5$$ K 5 and settle the minimum number of independent sets of size 4 in graphs with clique number at most 4. Motivated by the elusiveness of the symmetric Ramsey multiplicity problem, we also introduce an off-diagonal variant and obtain tight results when counting monochromatic $$K_4$$ K 4 or $$K_5$$ K 5 in only one of the colors and triangles in the other. The extremal constructions for each problem turn out to be blow-ups of a graph of constant size and were found through search heuristics. They are complemented by lower bounds established using flag algebras, resulting in a fully computer-assisted approach. For some of our theorems we can also derive that the extremal construction is stable in a very strong sense. More broadly, these problems lead us to the study of the region of possible pairs of clique and independent set densities that can be realized as the limit of some sequence of graphs.

Improved time complexity for spintronic oscillator ising machines compared to a popular classical optimization algorithm for the Max-Cut problem.

Solving certain combinatorial optimization problems like Max-Cut becomes challenging once the graph size and edge connectivity increase beyond a threshold, with brute-force algorithms which solve such problems exactly on conventional digital computers having the bottleneck of exponential time complexity. Hence currently, such problems are instead solved approximately using algorithms like Goemans-Williamson (GW) algorithm, run on conventional computers with polynomial time complexity. Phase binarized oscillators (PBOs), also often known as oscillator Ising machines, have been proposed as an alternative to solve such problems. In this paper, restricting ourselves to the combinatorial optimization problem Max-Cut solved on three kinds of graphs (Mobius Ladder, random cubic, Erdös Rényi) up to 100 nodes, we empirically show that computation time/time to solution (TTS) for PBOs (captured through Kuramoto model) grows at a much lower rate (logarithmically:O(log(N)), with respect to graph sizeN) compared to GW algorithm, for which TTS increases as square of graph size (O(N2)). However, Kuramoto model being a physics-agnostic mathematical model, this time complexity/ TTS trend for PBOs is a general trend and is device-physics agnostic. So for more specific results, we choose spintronic oscillators, known for their high operating frequency (in GHz), and model them through Slavin's model which captures the physics of their coupled magnetization oscillation dynamics. We thereby empirically show that TTS of spintronic oscillators also grows logarithmically with graph size (O(log(N)), while their accuracy is comparable to that of GW. So spintronic oscillators have improved time complexity over GW algorithm. For large graphs, they are expected to compute Max-Cut values much faster than GW algorithm, as well as other oscillators operating at lower frequencies, while maintaining the same level of accuracy.

A Note on Wiener and Hyper-Wiener Indices of Abid-Waheed Graph

A Hosoya polynomial is a polynomial connected to a molecular graph, which is a graph representation of a chemical compound with atoms as vertices and chemical bonds as edges. A graph invariant is the Hosoya polynomial; it is a graph attribute that does not change under graph isomorphism. It provides information about the number of unique non-empty subgraphs in a given graph. A molecular graph's size and branching complexity are determined by a topological metric known as the Wiener index. The Wiener index of each pair of vertices in a molecular network is the sum of those distances. The topological index, one of the various classes of graph invariants, is a real number related to a connected graph's structure .The goal of this article is to compute the Hosoya polynomial of some class of Abid-Waheed graph. Further, this research focused on a C++ algorithm to calculate the wiener index of and . The Wiener index (W∗I) and Hyper-Wiener index (H∗W∗I) are calculated using Hosoya polynomial (H∗-polynomial) of some family of Abid-Waheed graphs and . Illustrations and applications are given to enhance the research work.

Data Pruning-enabled High Performance and Reliable Graph Neural Network Training on ReRAM-based Processing-in-Memory Accelerators

Graph Neural Networks (GNNs) have achieved remarkable accuracy in cognitive tasks such as predictive analytics on graph-structured data. Hence, they have become very popular in diverse real-world applications. However, GNN training with large real-world graph datasets in edge-computing scenarios is both memory- and compute-intensive. Traditional computing platforms such as CPUs and GPUs do not provide the energy efficiency and low latency required in edge intelligence applications due to their limited memory bandwidth. Resistive random-access memory (ReRAM)-based processing-in-memory (PIM) architectures have been proposed as suitable candidates for accelerating AI applications at the edge, including GNN training. However, ReRAM-based PIM architectures suffer from low reliability due to their limited endurance, and low performance when they are used for GNN training in real-world scenarios with large graphs. In this work, we propose a learning-for-data-pruning framework, which leverages a trained Binary Graph Classifier (BGC) to reduce the size of the input data graph by pruning subgraphs early in the training process to accelerate the GNN training process on ReRAM-based architectures. The proposed light-weight BGC model reduces the amount of redundant information in input graph(s) to speed up the overall training process, improves the reliability of the ReRAM-based PIM accelerator, and reduces the overall training cost. This enables fast, energy-efficient, and reliable GNN training on ReRAM-based architectures. Our experimental results demonstrate that using this learning for data pruning framework, we can accelerate GNN training and improve the reliability of ReRAM-based PIM architectures by up to 1.6×, and reduce the overall training cost by 100× compared to state-of-the-art data pruning techniques.

Research on inter-well connectivity of water-flooding reservoir: Temporal neural network based on graph structure

Inter-well connectivity plays a crucial role in the development and production of water-flooding reservoirs, involving fluid transfer and mutual influence between different wells, and playing an important role in optimizing oilfield development and production. The traditional study of inter-well connectivity is mainly based on static information, while ignoring the dynamic changes over time and the graph structure of the well network. To address this issue, this paper proposes a temporal neural network based on graph structure (GSTNN). It combines the advantages of traditional neural networks and graph structures, fully considering the temporal information of the well network. A series of well network temporal feature information is used to predict inter-well connectivity within the framework of traditional neural networks, and optimize the model based on the graph structure of the well network. Experiments with GSTNN in different basic models and different graph sizes show that the method proposed in this paper is consistent with the actual geological characteristics of oil reservoirs. Compared with traditional neural network methods, GSTNN achieves more accurate results and shows good performance in less time in production prediction and inter-well connectivity reflection.

ArcMatch: high-performance subgraph matching for labeled graphs by exploiting edge domains

Consider a large labeled graph (network), denoted the target. Subgraph matching is the problem of finding all instances of a small subgraph, denoted the query, in the target graph. Unlike the majority of existing methods that are restricted to graphs with labels solely on vertices, our proposed approach, named can effectively handle graphs with labels on both vertices and edges. ntroduces an efficient new vertex/edge domain data structure filtering procedure to speed up subgraph queries. The procedure, called path-based reduction, filters initial domains by scanning them for paths up to a specified length that appear in the query graph. Additionally, ncorporates existing techniques like variable ordering and parent selection, as well as adapting the core search process, to take advantage of the information within edge domains. Experiments in real scenarios such as protein–protein interaction graphs, co-authorship networks, and email networks, show that s faster than state-of-the-art systems varying the number of distinct vertex labels over the whole target graph and query sizes.

A Local Search Algorithm with Vertex Weighting Strategy and Two-Level Configuration Checking for the Minimum Connected Dominating Set Problem.

The minimum connected dominating set problem is a combinatorial optimization problem with a wide range of applications in many fields. We propose an efficient local search algorithm to solve this problem. In this work, first, we adopt a new initial solution construction method based on three simplification rules. This method can reduce the size of the original graph and thus obtain a high-quality initial solution. Second, we propose an approach based on a two-level configuration checking strategy and a tabu strategy to reduce the cycling problem. Third, we introduce a perturbation strategy and a vertex weighting strategy to help the algorithm be able to jump out of the local optimum effectively. Fourth, we combine the scoring functions Cscore and Mscore with the aforementioned strategies to propose effective methods for selecting vertices. These methods assist the algorithm in selecting vertices that are suitable for addition to or removal from the current candidate solution. Finally, we verify the performance advantages of the local search algorithm by comparing it with existing optimal heuristic algorithms on two sets of instances. The experimental results show that the algorithm exhibits better performance on two sets of classical instances.

Toward Graph Self-Supervised Learning With Contrastive Adjusted Zooming.

Graph representation learning (GRL) is critical for graph-structured data analysis. However, most of the existing graph neural networks (GNNs) heavily rely on labeling information, which is normally expensive to obtain in the real world. Although some existing works aim to effectively learn graph representations in an unsupervised manner, they suffer from certain limitations, such as the heavy reliance on monotone contrastiveness and limited scalability. To overcome the aforementioned problems, in light of the recent advancements in graph contrastive learning, we introduce a novel self-supervised GRL algorithm via graph contrastive adjusted zooming, namely, G-Zoom, to learn node representations by leveraging the proposed adjusted zooming scheme. Specifically, this mechanism enables G-Zoom to explore and extract self-supervision signals from a graph from multiple scales: micro (i.e., node level), meso (i.e., neighborhood level), and macro (i.e., subgraph level). First, we generate two augmented views of the input graph via two different graph augmentations. Then, we establish three different contrastiveness on the above three scales progressively, from node, neighboring, to subgraph level, where we maximize the agreement between graph representations across scales. While we can extract valuable clues from a given graph on the micro and macro perspectives, the neighboring-level contrastiveness offers G-Zoom the capability of a customizable option based on our adjusted zooming scheme to manually choose an optimal viewpoint that lies between the micro and macro perspectives to better understand the graph data. In addition, to make our model scalable to large graphs, we use a parallel graph diffusion approach to decouple model training from the graph size. We have conducted extensive experiments on real-world datasets, and the results demonstrate that our proposed model outperforms the state-of-the-art methods consistently.

Visually encoding orthogonal planar graph drawings as graph mazes: An eye tracking study

There are various styles to visually represent relational data in the form of node-link diagrams. In particular, for planar graphs we can find orthogonal node-link diagrams consisting of links bending only at ninety degrees a successful and prominent variant. One of the benefits of such drawings is the tracking of longer paths through a network with the eyes due to their limited number of link orientations, changes, and variations, but on the negative side the links can have arbitrary bending shapes. In this article we developed a novel way to visualize such orthogonal planar drawings by making use of mazes that look more natural to the human eye due to the street-like visual metaphor that many people are familiar with. Tracking paths is one of the major tasks in such graph visualizations, similar to orthogonal node-link diagrams, however, we argue that mazes are a more natural way to find paths. To get insights in the visual scanning behavior when reading graph mazes we conducted a comparative eye tracking study with 26 male versus female participants of different experience levels while also alternating between orthogonal node-link drawings and graph mazes as well as different graph size levels. The major result of this comparative study is that the participants can track paths in both representation styles, including a geodesic path tendency in their visual search behavior, but typically have a longer fixation duration at branching nodes and locations in the mazes that lead to opposite directions to the geodesic path tendency, maybe the viewers had to start a reorientation phase in their visual scanning behavior. We also found out that the size, that is the number of graph vertices has an impact on the visual scanning behavior for both orthogonal node-link diagrams as well as street-like maze representations, but for the mazes we found this impact to be less strong (in terms of the eye movement data metrics fixation durations and saccade lengths) compared to the node-link diagrams. To conclude the article, we discuss limitations and scalability issues of our approach. Moreover, we give an outlook and future work for possible extensions.

Accelerating Graph Analytics Using Attention-Based Data Prefetcher

Graph analytics shows promise for solving challenging problems on relational data. However, memory constraints arise from the large size of graphs and the high complexity of algorithms. Data prefetching is a crucial technique to hide memory access latency by predicting and fetching data into the memory cache beforehand. Traditional prefetchers struggle with fixed rules in adapting to complex memory access patterns in graph analytics. Machine learning (ML) algorithms, particularly long short-term memory (LSTM) models, excel in memory access prediction. However, they encounter challenges such as difficulty in learning interleaved access patterns and high storage costs when predicting in large memory address space. In addition, there remains a gap between designing a high-performance ML-based memory access predictor and developing an effective ML-based prefetcher for an existing memory system. In this work, we propose a novel Attention-based prefetching framework to accelerate graph analytics applications. To achieve high-performance memory access prediction, we propose A2P, a novel Attention-based memory Access Predictor for graph analytics. We use the multi-head self-attention mechanism to extract features from memory traces. We design a novel bitmap labeling method to collect future deltas within a spatial range, making interleaved patterns easier to learn. We introduce a novel super page concept, allowing the model to surpass physical page constraints. To integrate A2P into a memory system, we design a three-module prefetching framework composed of an existing memory hierarchy, a prefetch controller, and the predictor A2P. In addition, we propose a hybrid design to combine A2P and existing hardware prefetchers for higher prefetching performance. We evaluate A2P and the prefetching framework using the widely used GAP benchmark. Prediction experiments show that for the top three predictions, A2P outperforms the widely used state-of-the-art LSTM-based model by 23.1% w.r.t. Precision, 21.2% w.r.t. Recall, and 10.4% w.r.t. Coverage. Prefetching experiments show that A2P provides 18.4% IPC Improvement on average, outperforming state-of-the-art prefetchers BO by 17.2%, ISB by 15.0%, and Delta-LSTM by 10.9%. The hybrid prefetcher combining A2P and ISB achieves 21.7% IPC Improvement, outperforming the hybrid of BO and ISB by 16.3%.

Enhanced adaptive-convergence in Harris’ hawks optimization algorithm

This paper presents a novel enhanced adaptive-convergence in Harris’ hawks optimization algorithm (EAHHO). In EAHHO, considering that Harris’ hawks will adopt different perching strategies and chasing styles according to the value of the escaping energy parameter E, nonlinear adaptive-convergence factor a is designed and adjusted to enhance the convergence and robustness of the algorithm. Moreover, the convergence and stability of EAHHO are proved mathematically by using the Markov chain theory and Lyapunov stability theory respectively. Moreover, numerical simulation results of 14 HHOs with different nonlinear convergence factors on 23 benchmark functions show that the nonlinear convergence factor of EAHHO is applicable to challenging problems with unknown search spaces, and the comparisons with the selected well-established algorithms on 56 test functions demonstrate that EAHHO performs competitively and effectively. Finally, the experiment results show that EAHHO algorithm also has a good performance to solve the optimization problems with relatively high dimensions and graph size of Internet of Vehicles routing problem.

Accelerating Maximal Clique Enumeration via Graph Reduction

As a fundamental task in graph data management, maximal clique enumeration (MCE) has attracted extensive attention from both academic and industrial communities due to its wide range of applications. However, MCE is very challenging as the number of maximal cliques may grow exponentially with the number of vertices. The state-of-the-art methods adopt a recursive paradigm to enumerate maximal cliques exhaustively, suffering from a large amount of redundant computation. In this paper, we propose a novel reduction-based framework for MCE, namely RMCE, that aims to reduce the search space and minimize unnecessary computations. The proposed framework RMCE incorporates three kinds of powerful reduction techniques including global reduction, dynamic reduction, and maximality check reduction. Global and dynamic reduction techniques effectively reduce the size of the input graph and dynamically construct subgraphs during the recursive sub-tasks, respectively. The maximality check reduction minimizes the computation for ensuring maximality by utilizing neighborhood dominance between visited vertices. Extensive experiments on 18 real graphs demonstrate that the existing approaches achieve remarkable speedups powered by the proposed techniques.