Graph Partitioning Research Articles

HashGrid: An optimized architecture for accelerating graph computing on FPGAs

Large-scale graph processing poses challenges due to its size and irregular memory access patterns, causing performance degradation in common architectures, such as CPUs and GPUs. Recent research includes accelerating graph processing using Field Programmable Gate Arrays (FPGAs). FPGAs can provide very efficient acceleration thanks to reconfigurable on-chip resources. Although limited, these resources offer a larger design space than CPUs and GPUs.We propose an approach in which data are preprocessed in small chunks with an optimized graph partitioning technique for execution on FPGA accelerators. The chunks, located on the host, are streamed directly into a customized memory layer implemented in the FPGA, which is tightly coupled with the processing elements responsible for the graph algorithm execution. This improves application memory access latency, which is crucial in large-sale graph computing performance.This work presents a hardware design that, combined with graph partitioning, enables us to achieve high-performance and potentially scalable handling of large graphs (i.e., graphs with millions of vertices and billions of edges in current scenarios) while using popular graph algorithms. The proposed framework accelerates performance 56 times compared with CPU (multicore with 16 logical cores in our reference experiments), 2.5 times and 4 times faster compared to state-of-the-art FPGA and GPU solutions (FPGA has 15 compute units, and GPU reference has 128 streaming-multiprocessors in our experiments), respectively, when using the PageRank algorithm. For the Single-Source-Shortest-Past (SSSP) algorithm, we achieve speedups of up to 65x, 26x, and 18x compared to CPU, GPU, and FPGA works, respectively. Lastly, in the context of the Weakly Connected Component (WCC) algorithm, our framework achieves a speedup of up to 403 times compared to the CPU, 7.4x against the GPU, and it is faster than the FPGA alternatives up to 10.3x.

Solving continuous quadratic programming for the discrete balanced graph partitioning problem using simulated annealing algorithm hybridized local search and multi-start algorithms

In a discrete balanced graph partitioning problem (DBGPP), a simple undirected weighted graph in that both vertices and edges are weighted is given. The task is dividing vertices into two disjoint subsets such that the sum of the weights of cut edges is minimized and the sum of the weights of vertices in each subset must equal or be as close as possible to each other. Here in order to solve the DBGPP, we first transform the problem into continuous quadratic programming and then show that the new problem has a binary solution, which is the optimal solution for the DBGPP. We also give necessary and sufficient conditions of continuous quadratic programming to identify stationary and local optimal solutions. In addition, we propose a local search to find a binary solution of the continuous quadratic programming. An approximated solution of the DBGPP is obtained using a hybrid simulated annealing algorithm. In our proposed algorithm, the structure of the objective function in a continues problem is considered as the evaluator function. Due to the Dolan–Moré performance profiles and the non-parametric statistical one-sided Wilcoxon signed rank test, we demonstrate the efficiency of our proposed approach in comparison with other available methods.

GCphase: an SNP phasing method using a graph partition and error correction algorithm

BackgroundThe utilization of long reads for single nucleotide polymorphism (SNP) phasing has become popular, providing substantial support for research on human diseases and genetic studies in animals and plants. However, due to the complexity of the linkage relationships between SNP loci and sequencing errors in the reads, the recent methods still cannot yield satisfactory results.ResultsIn this study, we present a graph-based algorithm, GCphase, which utilizes the minimum cut algorithm to perform phasing. First, based on alignment between long reads and the reference genome, GCphase filters out ambiguous SNP sites and useless read information. Second, GCphase constructs a graph in which a vertex represents alleles of an SNP locus and each edge represents the presence of read support; moreover, GCphase adopts a graph minimum-cut algorithm to phase the SNPs. Next, GCpahse uses two error correction steps to refine the phasing results obtained from the previous step, effectively reducing the error rate. Finally, GCphase obtains the phase block. GCphase was compared to three other methods, WhatsHap, HapCUT2, and LongPhase, on the Nanopore and PacBio long-read datasets. The code is available from https://github.com/baimawjy/GCphase.ConclusionsExperimental results show that GCphase under different sequencing depths of different data has the least number of switch errors and the highest accuracy compared with other methods.

Kemeny Constant-Based Optimization of Network Clustering Using Graph Neural Networks.

The recent trend in using network and graph structures to represent a variety of different data types has renewed interest in the graph partitioning (GP) problem. This interest stems from the need for general methods that can both efficiently identify network communities and reduce the dimensionality of large graphs while satisfying various application-specific criteria. Traditional clustering algorithms often struggle to capture the complex relationships within graphs and generalize to arbitrary clustering criteria. The emergence of graph neural networks (GNNs) as a powerful framework for learning representations of graph data provides new approaches to solving the problem. Previous work has shown GNNs to be capable of proposing partitionings using a variety of criteria. However, these approaches have not yet been extended to Markov chains or kinetic networks. These arise frequently in the study of molecular systems and are of particular interest to the biomolecular modeling community. In this work, we propose several GNN-based architectures to tackle the GP problem for Markov Chains described as kinetic networks. This approach aims to maximize the Kemeny constant, which is a variational quantity and it represents the sum of time scales of the system. We propose using an encoder-decoder architecture and show how simple GraphSAGE-based GNNs with linear layers can outperform much larger and more expressive attention-based models in this context. As a proof of concept, we first demonstrate the method's ability to cluster randomly connected graphs. We also use a linear chain architecture corresponding to a 1D free energy profile as our kinetic network. Subsequently, we demonstrate the effectiveness of our method through experiments on a data set derived from molecular dynamics. We compare the performance of our method to other partitioning techniques, such as PCCA+. We explore the importance of feature and hyperparameter selection and propose a general strategy for large-scale parallel training of GNNs for discovering optimal graph partitionings.

SPGMVC: Multiview Clustering via Partitioning the Signed Prototype Graph.

Multiview clustering (MVC) has been widely studied in machine learning and data mining for its capability of improving clustering performance by fusing the information from multiview data. In the past decade, a large number of MVC methods have made impressive progress, but most of them suffer from computational burdens, especially in large-scale tasks. Binary MVC (BMVC) is proposed to address this issue by representing the large-scale high-dimensional dataset as a group of consensus and low-dimensional binary codes. However, current BMVC-based approaches generate the clustering by executing binary k -means on the obtained binary codes, which fail to capture the embedded geometric information, leading to poor clustering performance. In addition, parameter selection is another "mission impossible" in unsupervised learning tasks including MVC. To tackle these challenges, a framework of multiview clustering via partitioning the signed prototype graph (SPGMVC) is proposed in this work. The SPGMVC framework offers several contributions. First, SPGMVC is designed as a unified framework for MVC. It combines effective technologies, such as consensus binary coding, code compression (CC), signed prototype graph (SPG) partitioning, and prototype-based cluster assignment. Second, SPGMVC partitions the signed graph (SG) based on the relationships between positive and negative edges. By capturing the underlying structure of the data, this partitioning strategy improves clustering accuracy (ACC). CC techniques are applied to reduce the graph's scale, enabling further partitioning and enhancing computational efficiency. Third, SPGMVC employs an alternate minimizing strategy to efficiently handle the optimization problem. This strategy has nearly linear time and space complexity with respect to the data volume, making it suitable for large-scale tasks. Fourth, SPGMVC proposes an automatic parameter selection strategy, eliminating the need for extensive parameter exploration. Comprehensive experiments illustrate the superiority of our model. The implementation of SPGMVC is available at: https://github.com/gepingyang/PSGMVC.

A unified framework for the Expander Mixing Lemma for irregular graphs and its applications

A unified framework for the Expander Mixing Lemma for irregular graphs using adjacency eigenvalues is presented, as well as two new versions of it. While the existing Expander Mixing Lemmas for irregular graphs make use of the notion of volume (the sum of degrees within a vertex set), we instead propose to use the Perron eigenvector entries as vertex weights, which is a way to regularize the graph. This provides a new application of weight partitions of graphs. The new Expander Mixing Lemma versions are then applied to obtain several eigenvalue bounds for NP-hard parameters such as the zero forcing number, the vertex integrity and the routing number of a graph.

Property Graph Partition Algorithm Based on Improved Barnacle Mating Optimization

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

Discovery and generalization of tissue structures from spatial omics data

Tissues are organized into anatomical and functional units at different scales. New technologies for high-dimensional molecular profiling in situ have enabled the characterization of structure-function relationships in increasing molecular detail. However, it remains a challenge to consistently identify key functional units across experiments, tissues, and disease contexts, a task that demands extensive manual annotation. Here, we present spatial cellular graph partitioning (SCGP), a flexible method for the unsupervised annotation of tissue structures. We further present a reference-query extension pipeline, SCGP-Extension, that generalizes reference tissue structure labels to previously unseen samples, performing data integration and tissue structure discovery. Our experiments demonstrate reliable, robust partitioning of spatial data in a wide variety of contexts and best-in-class accuracy in identifying expertly annotated structures. Downstream analysis on SCGP-identified tissue structures reveals disease-relevant insights regarding diabetic kidney disease, skin disorder, and neoplastic diseases, underscoring its potential to drive biological insight and discovery from spatial datasets.

Distributed Optimization of Graph Convolutional Network Using Subgraph Variance.

In recent years, distributed graph convolutional networks (GCNs) training frameworks have achieved great success in learning the representation of graph-structured data with large sizes. However, existing distributed GCN training frameworks require enormous communication costs since a multitude of dependent graph data need to be transmitted from other processors. To address this issue, we propose a graph augmentation-based distributed GCN framework (GAD). In particular, GAD has two main components: GAD-Partition and GAD-Optimizer. We first propose an augmentation-based graph partition (GAD-Partition) that can divide the input graph into augmented subgraphs to reduce communication by selecting and storing as few significant vertices of other processors as possible. To further speed up distributed GCN training and improve the quality of the training result, we design a subgraph variance-based importance calculation formula and propose a novel weighted global consensus method, collectively referred to as GAD-Optimizer. This optimizer adaptively adjusts the importance of subgraphs to reduce the effect of extra variance introduced by GAD-Partition on distributed GCN training. Extensive experiments on four large-scale real-world datasets demonstrate that our framework significantly reduces the communication overhead ( ≈ 50% ), improves the convergence speed ( ≈ 2 × ) of distributed GCN training, and obtains a slight gain in accuracy ( ≈ 0.45% ) based on minimal redundancy compared to the state-of-the-art methods.

Attribute graph clustering via transformer and graph attention autoencoder

Graph clustering is a crucial technique for partitioning graph data. Recent research has concentrated on integrating topology and attribute information from attribute graphs to generate node embeddings, which are subsequently clustered using classical algorithms. However, these methods have some limitations, such as insufficient information inheritance in shallow networks or inadequate quality of reconstructed nodes, leading to suboptimal clustering performance. To tackle these challenges, we introduce two normalization techniques within the graph attention autoencoder framework, coupled with an MSE loss, to facilitate node embedding learning. Furthermore, we integrate Transformers into the self-optimization module to refine node embeddings and clustering outcomes. Our model can induce appropriate node embeddings for graph clustering in a shallow network. Our experimental results demonstrate that our proposed approach outperforms the state-of-the-art in graph clustering over multiple benchmark datasets. In particular, we achieved 76.3% accuracy on the Pubmed dataset, an improvement of at least 7% compared to other methods.

Appearance-posture fusion network for distracted driving behavior recognition

In recent years, detection techniques using computer vision and deep learning have shown promise in assessing driver distraction. This paper proposes a fusion network that combines a Spatial-Temporal Graph Convolutional Network (ST-GCN) and a hybrid convolutional network to integrate multimodal input data for recognizing distracted driver behavior. Specifically, to address the limitations of the ST-GCN method in modeling long-distance joint interaction features and inadequate temporal feature extraction, we design the Spatially Symmetric Configuration Partitioning Graph Convolutional Network (SSCP-GCN) to model relative motion information of symmetric relationships between limbs. Specifically, we utilize densely connected blocks for processing multi-scale temporal information between consecutive frames, thereby enhancing the reuse of bottom features. Furthermore, the expression of important temporal information is augmented by the introduction of the channel attention mechanism. To tackle the problem that the Mixed Convolution (MC) combining 3D convolution with 2D convolution cannot extract higher-order timing information and has limitations in modeling global dependency relationships, we compensate for its inability to capture higher-order temporal semantic information using the Time Shift Module (TSM) without consuming additional computational resources. Additionally, the 3D Multi-Head Self-Attention mechanism (3D MHSA) is employed to integrate global spatial–temporal information of high-level features, avoiding the issue of model complexity proliferation caused by the deep stacking design of Convolutional Neural Networks (CNN). Lastly, we introduce a multistream network framework that integrates driver posture and appearance features to harness complementary advantages, enabling us to combine multimodal input features to achieve better model performance. Experimental results indicate that the accuracy of the network designed in this paper reaches 95.6% and 94.3% on ASU dataset and NTU-RGB+D dataset, respectively. The small size of the model offers the possibility for practical application of the algorithm.

An Improved Graph Partitioning Algorithm Based Approach for Workflow Offloading in a Fog Environment

An Improved Graph Partitioning Algorithm Based Approach for Workflow Offloading in a Fog Environment

Stability from graph symmetrization arguments in generalized Turán problems

AbstractGiven graphs and , denotes the largest number of copies of in ‐free ‐vertex graphs. Let . We say that is F‐Turán‐stable if the following holds. For any there exists such that if an ‐vertex ‐free graph contains at least copies of , then the edit distance of and the ‐partite Turán graph is at most . We say that is weakly F‐Turán‐stable if the same holds with the Turán graph replaced by any complete ‐partite graph . It is known that such stability implies exact results in several cases. We show that complete multipartite graphs with chromatic number at most are weakly ‐Turán‐stable. Partly answering a question of Morrison, Nir, Norin, Rzażewski, and Wesolek positively, we show that for every graph , if is large enough, then is ‐Turán‐stable. Finally, we prove that if is bipartite, then it is weakly ‐Turán‐stable for large enough.

Inverse of the squared distance matrix of a complete multipartite graph

Let $G$ be a connected graph on $n$ vertices and $d_{ij}$ be the length of the shortest path between vertices $i$ and $j$ in $G$. We set $d_{ii}=0$ for every vertex $i$ in $G$. The squared distance matrix $\Delta(G)$ of $G$ is the $n\times n$ matrix with $(i,j)^{th}$ entry equal to $0$ if $i = j$ and equal to $d_{ij}^2$ if $i \neq j$. For a given complete $t$-partite graph $K_{n_1,n_2,\cdots,n_t}$ on $n=\sum_{i=1}^t n_i$ vertices, under some condition we find the inverse $\Delta(K_{n_1,n_2,\cdots,n_t})^{-1}$ as a rank-one perturbation of a symmetric Laplacian-like matrix $\mathcal{L}$ with $\text{rank} (\mathcal{L})=n-1$. We also investigate the inertia of $\mathcal{L}$.

Minimum motif-cut: a workload-aware RDF graph partitioning strategy

Minimum motif-cut: a workload-aware RDF graph partitioning strategy

Total coalitions in graphs

We define a total coalition in a graph G as a pair of disjoint subsets A 1,A 2 ⊆ A that satisfy the following conditions: (a) neither A 1 nor A 2 constitutes a total dominating set of G, and (b) A 1 ∪ A 2 constitutes a total dominating set of G. A total coalition partition of a graph G is a partition ϒ = {A 1,A 2, . ,Ak } of its vertex set such that no subset of ϒ acts as a total dominating set of G, but for every set Ai ∈ ϒ, there exists a set Aj ∈ ϒ such that Ai and Aj combine to form a total coalition. We define the total coalition number of G as the maximum cardinality of a total coalition partition of G, and we denote it by Ct (G). The purpose of this paper is to begin an investigation into the characteristics of total coalition in graphs.

Graph Theoretical Models for Enhancing Highway Connectivity and Safety in Vehicular Networks

Vehicular networks play a crucial role in modern transportation systems, significantly impacting connectivity and safety on highways. This paper explores the application of graph theoretical models to enhance both connectivity and safety in vehicular networks. Graph theory, a branch of discrete mathematics, provides a robust framework for modeling and analyzing complex networks, including those formed by vehicles on highways. Our study begins by defining the vehicular network as a graph where nodes represent vehicles, and edges denote communication links between them. We employ various graph theoretical concepts such as connectivity, centrality, and network flow to evaluate and improve the network's performance. Key metrics, including the degree of nodes, clustering coefficients, and shortest path lengths, are utilized to quantify network connectivity and identify critical nodes and edges that influence overall network efficiency. One of the primary objectives is to ensure uninterrupted connectivity in the presence of dynamic and often unpredictable vehicular movement. To this end, we analyze the network's resilience to node failures and propose strategies to enhance robustness using redundancy and alternative routing paths. By incorporating concepts like k-connectivity and network diameter, we develop models that maintain high levels of connectivity despite the removal or failure of multiple nodes or edges. Safety is addressed through the lens of network stability and reliability. We investigate the impact of vehicular density, speed, and communication range on the network's ability to sustain reliable communication channels. Techniques such as dynamic topology management and adaptive power control are proposed to mitigate the risks associated with network fragmentation and communication delays. Furthermore, we introduce optimization algorithms that leverage graph partitioning and community detection to improve the management of vehicular clusters, facilitating efficient data dissemination and reducing the likelihood of congestion-related incidents. The proposed models are validated through simulations that mimic real-world highway conditions, demonstrating significant improvements in both connectivity and safety metrics. In conclusion, the application of graph theoretical models offers a promising approach to enhancing highway connectivity and safety in vehicular networks

TC-Match: Fast Time-Constrained Continuous Subgraph Matching

Continuously monitoring structural patterns in streaming graphs is a critical task in many real-time graph-based applications. In this paper, we study the problem of time-constrained continuous subgraph matching (shorted as TCSM) over streaming graphs. Given a query graph Q with timing order constraint and a data graph stream G , TCSM aims to report all incremental matches of Q in G for each update of G , where a match should obey both structure constraint (i.e., isomorphism) and timing order constraint of Q. Although TCSM has a wide range of applications, such as cyber-attack detection and credit card fraud detection, we note that this problem has not been well addressed. The state-of-the-art bears the limitations of high index space cost and intermediate result maintenance cost. In this paper, we propose TC-Match, an effective approach to TCSM. First, we design a space and time cost-effective index CSS, which is essentially a k -partite graph structure where a node corresponds to an edge in G. By carefully creating links between nodes, we can encapsulate into CSS the partial embedding and timing order information between edges in G. We theoretically show that CSS has polynomial space and construction time complexities. Second, based on the property of CSS, we develop an efficient incremental matching algorithm with an effective node merging optimization. Extensive experiments show that TC-Match can achieve up to 3 orders of magnitude query performance improvement over the baseline methods, and meanwhile the memory consumption is reduced by 48.7%-86.7%.

Algorithm 1044: PyGenStability, a Multiscale Community Detection Framework with Generalized Markov Stability

We present PyGenStability, a general-use Python software package that provides a suite of analysis and visualization tools for unsupervised multiscale community detection in graphs. PyGenStability finds optimized partitions of a graph at different levels of resolution by maximizing the generalized Markov Stability quality function with the Louvain or Leiden algorithm. The package includes automatic detection of robust graph partitions and allows the flexibility to choose quality functions for weighted undirected, directed, and signed graphs and to include other user-defined quality functions.

An efficient approach for discovering Graph Entity Dependencies (GEDs)

Graph entity dependencies (GEDs) are novel graph constraints, unifying keys and functional dependencies, for property graphs. They have been found useful in many real-world data quality and data management tasks, including fact checking on social media networks and entity resolution. In this paper, we study the discovery problem of GEDs—finding a minimal cover of valid GEDs in a given graph data. We formalise the problem, and propose an effective and efficient approach to overcome major bottlenecks in GED discovery. In particular, we leverage existing graph partitioning algorithms to enable fast GED-scope discovery, and employ effective pruning strategies over the prohibitively large space of candidate dependencies. Furthermore, we define an interestingness measure for GEDs based on the minimum description length principle, to score and rank the mined cover set of GEDs. Finally, we demonstrate the scalability and effectiveness of our GED discovery approach through extensive experiments on real-world benchmark graph data sets; and present the usefulness of the discovered rules in different downstream data quality management applications.