Graph Compression Research Articles

Mathematical models based on decision hypergraphs for designing a storage cabinet

We study the problem of designing a cabinet made up of a set of shelves that contain compartments whose contents slide forward on opening. Considering a set of items candidate to be stored in the cabinet over a given time horizon, the problem is to design a set of shelves and a set of compartments on each shelf, and select the items to insert into the compartments. The objective is to maximize the sum of the profits of the selected items. We call our problem the Storage Cabinet Physical Design (SCPD) problem. The SCPD problem combines a two-staged two-dimensional knapsack problem for designing the shelves and compartments with a set of temporal knapsack problems for selecting and assigning items to compartments. We formalize the SCPD problem and formulate it as a maximum cost flow problem in a decision hypergraph with additional linear constraints. To reduce the size of this model, we break symmetries, generalize graph compression techniques and exploit dominance rules for precomputing subproblem solutions. We also present a set of valid inequalities to improve the linear relaxation of the model. We empirically show that solving the arc-flow model with our enhancements outperforms solving a compact mixed integer linear programming formulation of the SCPD problem.

Improving Graph Compression for Efficient Resource-Constrained Graph Analytics

Recent studies have shown the promise of directly processing compressed graphs. However, its benefits have been limited by high peak-memory usage and unbearably long compression time. In this paper, we introduce Laconic, a novel rule-based graph processing solution that overcomes the challenges of restricted memory and impractical compression time faced by existing approaches. Laconic, for the first time, ensures minimal memory overhead during compression and significantly reduces graph sizes, thus reducing peak memory demand during computations. By employing an efficient parallel compression algorithm, Laconic achieves a remarkable reduction in compression time. In our experiments, we compare Laconic with state-of-the-art solutions. The results demonstrate that Laconic outperforms other methods, reducing peak memory consumption by an average of 70% during compression and 66% during computation. Additionally, Laconic reduces rule compression time by an average of 93% compared to traditional rule-based compression, achieving a 2.47× higher compression ratio, and providing a 2.12× performance speedup.

Scene Graph Lossless Compression with Adaptive Prediction for Objects and Relations

The scene graph is a novel data structure describing objects and their pairwise relationship within image scenes. As the size of scene graphs in vision and multimedia applications increases, the need for lossless storage and transmission of such data becomes more critical. However, the compression of scene graphs is less studied because of the complicated data structures involved and complex distributions. Existing solutions usually involve general-purpose compressors or graph structure compression methods, which are weak at reducing the redundancy in scene graph data. This article introduces a novel lossless compression framework with adaptive predictors for the joint compression of objects and relations in scene graph data. The proposed framework comprises a unified prior extractor and specialized element predictors to adapt to different data elements. Furthermore, to exploit the context information within and between graph elements, Graph Context Convolution is proposed to support different graph context modeling schemes for different graph elements. Finally, an overarching framework incorporates the learned distribution model to predict numerical data under complicated conditional constraints. Experiments conducted on labeled or generated scene graphs demonstrate the effectiveness of the proposed framework for scene graph lossless compression.

GraphScale: Scalable Processing on FPGAs for HBM and Large Graphs

Recent advances in graph processing on FPGAs promise to alleviate performance bottlenecks with irregular memory access patterns. Such bottlenecks challenge performance for a growing number of important application areas like machine learning and data analytics. While FPGAs denote a promising solution through flexible memory hierarchies and massive parallelism, we argue that current graph processing accelerators either use the off-chip memory bandwidth inefficiently or do not scale well across memory channels. In this work, we propose GraphScale, a scalable graph processing framework for FPGAs. GraphScale combines multi-channel memory with asynchronous graph processing (i.e., for fast convergence on results) and a compressed graph representation (i.e., for efficient usage of memory bandwidth and reduced memory footprint). GraphScale solves common graph problems like breadth-first search, PageRank, and weakly connected components through modular user-defined functions, a novel two-dimensional partitioning scheme, and a high-performance two-level crossbar design. Additionally, we extend GraphScale to scale to modern high-bandwidth memory (HBM) and reduce partitioning overhead of large graphs with binary packing.

Distance-Preserving Graph Compression Techniques

We study the problem of distance-preserving graph compression for weighted paths and trees. The problem entails a weighted graph $G = (V, E)$ with non-negative weights and a subset of edges $E^{\prime} \subset E$, which needs to be removed from G (with their endpoints merged as a supernode). The goal is to redistribute the weights of the deleted edges in a way that minimizes the error. The error is defined as the sum of the absolute differences of the shortest path lengths between different pairs of nodes before and after contracting $E^{\prime}$. Based on this error function, we propose optimal approaches for merging any subset of edges in a path and a single edge in a tree. Previous works on graph compression techniques aimed at preserving different graph properties (such as the chromatic number) or solely focused on identifying the optimal set of edges to contract. However, our focus in this paper is on achieving optimal edge contraction (when the contracted edges are provided as input), specifically for weighted trees and paths.

Self-Attention Enhanced Auto-Encoder for Link Weight Prediction With Graph Compression

Self-Attention Enhanced Auto-Encoder for Link Weight Prediction With Graph Compression

Self-supervised Pre-training via Multi-view Graph Information Bottleneck for Molecular Property Prediction.

Molecular representation learning has remarkably accelerated the development of drug analysis and discovery. It implements machine learning methods to encode molecule embeddings for diverse downstream drug-related tasks. Due to the scarcity of labeled molecular data, self-supervised molecular pre-training is promising as it can handle large-scale unlabeled molecular data to prompt representation learning. Although many universal graph pre-training methods have been successfully introduced into molecular learning, there still exist some limitations. Many graph augmentation methods, such as atom deletion and bond perturbation, tend to destroy the intrinsic properties and connections of molecules. In addition, identifying subgraphs that are important to specific chemical properties is also challenging for molecular learning. To address these limitations, we propose the self-supervised Molecular Graph Information Bottleneck (MGIB) model for molecular pre-training. MGIB observes molecular graphs from the atom view and the motif view, deploys a learnable graph compression process to extract the core subgraphs, and extends the graph information bottleneck into the self-supervised molecular pre-training framework. Model analysis validates the contribution of the self-supervised graph information bottleneck and illustrates the interpretability of MGIB through the extracted subgraphs. Extensive experiments involving molecular property prediction, including 7 binary classification tasks and 6 regression tasks demonstrate the effectiveness and superiority of our proposed MGIB.

D-Lite: Navigation-Oriented Compression of 3D Scene Graphs for Multi-Robot Collaboration

D-Lite: Navigation-Oriented Compression of 3D Scene Graphs for Multi-Robot Collaboration

Context-Aware Auto-Encoded Graph Neural Model for Dynamic Question Generation using NLP

Question generation is an important task in natural language processing that involves generating questions from a given text. This paper proposes a novel approach for dynamic question generation using a context-aware auto-encoded graph neural model. Our approach involves constructing a graph representation of the input text, where each node in the graph corresponds to a word or phrase in the text, and the edges represent the relationships between them. We then use an auto-encoder model to learn a compressed representation of the graph that captures the most important information in the input text. Finally, we use the compressed graph representation to generate questions by dynamically selecting nodes and edges based on their relevance to the context of the input text. We evaluate our approach on four benchmark datasets (SQuAD, Natural Questions, TriviaQA, and QuAC) and demonstrate that it outperforms existing state-of-the-art methods for dynamic question generation. In the experimentation, to evaluate the result four performance metrics are used i.e. BLEU, ROUGE, F1-Score, and Accuracy. The result of the proposed approach yields an accuracy of 92% on the SQuAD dataset, 89% with QuAC, and 84% with TriviaQA. while on the natural questions dataset, the model gives 79% accuracy. Our results suggest that the use of graph neural networks and auto-encoder models can significantly improve the accuracy and effectiveness of question generation in NLP. Further research in this area can lead to even more sophisticated models that can generate questions that are even more contextually relevant and natural-sounding.

GCSTI: A Single-Cell Pseudotemporal Trajectory Inference Method Based on Graph Compression.

The single-cell pseudotemporal trajectory inference is an important way to explore the process of developmental changes within a cell. Due to the uneven rate of cell growth, changes in gene expression depend less on the time of data collection and more on a cell's "internal clock". To overcome the challenges of gene analysis, and replicate biological developmental processes, several strategies have been put forth. However, due to the size of single-cell datasets, locating relevant signposts usually necessitate clustering analysis or a sizable amount of priori information. To this end, we propose a novel single-cell pseudotemporal trajectory inference technique: GCSTI method, which is based on graph compression and doesn't rely on a priori knowledge or clustering procedures, can handle the trajectory inference problem for a large network in a stable and efficient manner. Additionally, we simultaneously improve the pseudotime defining method currently employed in this study in order to obtain more trustworthy and beneficial outcomes for trajectory inference. Finally, we validate the efficacy and stability of the GCSTI method using datasets from human skeletal muscle myogenic cells and four simulated datasets.

GCDroid: Android Malware Detection Based on Graph Compression With Reachability Relationship Extraction for IoT Devices

With the widespread popularity of Internet of Things (IoT) devices based on the Android system, the amount of Android malware targeting IoT devices continues to increase, causing great economic losses. Accordingly, efficient and accurate Android malware detection methods are particularly important. Recently, many Android malware detection and classification methods have been proposed, but most of them ignore the deep relationships among software. In this paper, we propose a graph compression algorithm with reachability relationship extraction (GCRR) and design an Android malware detection and classification method called GCDroid based on this algorithm. A theoretical analysis shows that GCRR can reasonably extract the reachability relationships among APKs and compress a large heterogeneous APK-API relationship graph into a homogeneous APKs graph. Experiments show that GCDroid based on GCRR greatly reduces the required time consumption while improving detection accuracy. Compared with the existing excellent static Android malware detection methods, GCDroid improves upon their detection accuracies by 1.53%-39.13% on different datasets and outperforms the benchmark methods in terms of Android malware classification. Furthermore, compared with those of the baseline methods that are similar to GCDroid, GCDroid’s time consumption for model training and other aspects is only one-tenth as high or even less.

A multi-objective genetic algorithm for compression of weighted graphs to simplify epidemic analysis

The development of computational intelligence based approaches for the compression of graphs is an under-explored area of research. Further, compression of weighted graphs is significantly more complicated than compression of unweighted graphs. In this paper a multi-objective approach using NSGA-II is applied to the problem of weighted graph compression. The approach is designed to find a balance between the level of compression and the distortion created by the compression. Distortion is measured using two fitness functions that each evaluate changes both in graph structure and in edge weights. The methodology is applied to three weighted contact networks with differing characteristics. It was found that the multi-objective approach is useful in identifying suitable compression ratios based upon defined levels of acceptable distortion, with a single-objective genetic algorithm then applied to focus on this target compression ratio to further reduce distortion.

CompressGraph: Efficient Parallel Graph Analytics with Rule-Based Compression

Modern graphs exert colossal time and space pressure on graph analytics applications. In 2022, Facebook social graph reaches 2.91 billion users with trillions of edges. Many compression algorithms have been developed to support direct processing on compressed graphs to address this challenge. However, previous graph compression algorithms do not focus on leveraging redundancy in repeated neighbor sequences, so they do not save the amount of computation for graph analytics. We develop CompressGraph, an efficient rule-based graph analytics engine that leverages data redundancy in graphs to achieve both performance boost and space reduction for common graph applications. CompressGraph has three advantages over previous works. First, the rule-based abstraction of CompressGraph supports the reuse of intermediate results during graph traversal, thus saving time. Second, CompressGraph has intense expressiveness to support a wide range of graph applications. Third, CompressGraph scales well under high parallelism because the context-free rules have few dependencies. Experiments show that CompressGraph provides significant performance and space benefits on both CPUs and GPUs. On evaluating six typical graph applications, CompressGraph can achieve 1.97× speedup on the CPU, while 3.95× speedup on the GPU, compared to the state-of-the-art CPU and GPU methods, respectively. Moreover, CompressGraph can save an average of 71.27% memory savings on CPU and 70.36 on GPU.

Boosted Arc Flow Formulation Using Graph Compression for the Two-Dimensional Strip Cutting Problem

Since the requirement for a material cutting process occurs in a wide variety of applied contemporary manufacturing, the cutting stock problem plays a critical role in optimizing the amount of raw material utilized in everyday production operations. In this paper, we address the two-dimension strip-cutting problem and implement the graph compression technique to improve the performance of the arc-flow formulation. The number of variables of the obtained mathematical model are substantially reduced. A comparative study on a large set of benchmark instances shows that our compressed model yields very good results for the non-unitary item demand case in contrast to the state-of-the-art mathematical models. Moreover, improved bounds are provided for 24 unsolved benchmark instances, among which 8 have been solved to optimality.

EGC2: Enhanced graph classification with easy graph compression

Graph classification is crucial in network analyses. Networks face potential security threats, such as adversarial attacks. Some defense methods may trade off the algorithm complexity for robustness, such as adversarial training, whereas others may trade off clean example performance, such as smoothing-based defense. Most suffer from high complexity or low transferability. To address this problem, we proposed EGC2, an enhanced graph classification model with easy graph compression. EGC2 captures the relationship between the features of different nodes by constructing feature graphs and improving the aggregation of the node-level representations. To achieve lower-complexity defense applied to graph classification models, EGC2 utilizes a centrality-based edge-importance index to compress the graphs, filtering out trivial structures and adversarial perturbations in the input graphs, thus improving the model's robustness. Experiments on ten benchmark datasets demonstrate that the proposed feature read-out and graph compression mechanisms enhance the robustness of multiple basic models, resulting in a state-of-the-art performance in terms of accuracy and robustness against various adversarial attacks.

IRun: Horizontal and Vertical Shape of a Region-Based Graph Compression.

Graph data are pervasive worldwide, e.g., social networks, citation networks, and web graphs. A real-world graph can be huge and requires heavy computational and storage resources for processing. Various graph compression techniques have been presented to accelerate the processing time and utilize memory efficiently. SOTA approaches decompose a graph into fixed-size submatrices and compress it by applying the existing graph compression algorithm. This approach is promising if the input graph is dense. Otherwise, an optimal graph compression ratio cannot be achieved. Graphs such as those used by social networks exhibit a power-law distribution. Thus, applying compression to the fixed-size block of a matrix could lead to the empty cell processing of that matrix. In this paper, we solve the problem of ordered matrix compression on a deep level, dividing the block into sub-blocks to achieve the best compression ratio. We observe that the ordered matrix compression ratio could be improved by adopting variable-shape regions, considering both horizontal- and vertical-shaped regions. In our empirical evaluation, the proposed approach achieved a 93.8% compression ratio on average, compared with existing SOTA graph compression techniques.

Quasi-Stable Coloring for Graph Compression

We propose quasi-stable coloring , an approximate version of stable coloring. Stable coloring, also called color refinement, is a well-studied technique in graph theory for classifying vertices, which can be used to build compact, lossless representations of graphs. However, its usefulness is limited due to its reliance on strict symmetries. Real data compresses very poorly using color refinement. We propose the first, to our knowledge, approximate color refinement scheme, which we call quasi-stable coloring. By using approximation, we alleviate the need for strict symmetry, and allow for a tradeoff between the degree of compression and the accuracy of the representation. We study three applications: Linear Programming, Max-Flow, and Betweenness Centrality, and provide theoretical evidence in each case that a quasi-stable coloring can lead to good approximations on the reduced graph. Next, we consider how to compute a maximal quasi-stable coloring: we prove that, in general, this problem is NP-hard, and propose a simple, yet effective algorithm based on heuristics. Finally, we evaluate experimentally the quasi-stable coloring technique on several real graphs and applications, comparing with prior approximation techniques.

UniCon: A unified star-operation to efficiently find connected components on a cluster of commodity hardware.

With a cluster of commodity hardware, how can we efficiently find all connected components of an enormous graph containing hundreds of billions of nodes and edges? The problem of finding connected components has been used in various applications such as pattern recognition, reachability indexing, graph compression, graph partitioning, and random walk. Several studies have been proposed to efficiently find connected components in various environments. Most existing single-machine and distributed-memory algorithms are limited in scalability as they have to load all data generated during the process into the main memory; they require expensive machines with vast memory capacities to handle large graphs. Several MapReduce algorithms try to handle large graphs by exploiting distributed storage but fail due to data explosion problems, which is a phenomenon that significantly increases the size of data as the computation proceeds. The latest MapReduce algorithms resolve the problem by proposing two distinguishing star-operations and executing them alternately, while the star-operations still cause massive network traffic as a star-operation is a distributed operation that connects each node to its smallest neighbor. In this paper, we unite the two star-operations into a single operation, namely UniStar, and propose UniCon, a new distributed algorithm for finding connected components in enormous graphs using UniStar. The partition-aware processing of UniStar effectively resolves the data explosion problems. We further optimize UniStar by filtering dispensable edges and exploiting a hybrid data structure. Experimental results with a cluster of 10 cheap machines each of which is equipped with Intel Xeon E3-1220 CPU (4-cores at 3.10GHz), 16GB RAM, and 2 SSDs of 1TB show that UniCon is up to 13 times faster than competitors on real-world graphs. UniCon succeeds in processing a tremendous graph with 129 billion edges, which is up to 4096 times larger than graphs competitors can process.

An Improved Arc Flow Model with Enhanced Bounds for Minimizing the Makespan in Identical Parallel Machine Scheduling

In this paper, an identical parallel machine problem was considered with the objective of minimizing the makespan. This problem is NP-hard in the strong sense. A mathematical formulation based on an improved arc flow model with enhanced bounds was proposed. A variable neighborhood search algorithm was proposed to obtain an upper bound. Three lower bounds from the literature were utilized in the improved arc flow model to improve the efficiency of the mathematical formulation. In addition, a graph compression technique was proposed to reduce the size of the graph. As a consequence, the improved arc flow model was compared with an arc flow model from the literature. The computational results on benchmark instances showed that the improved arc flow model outperformed the literature arc flow model at finding optimal solutions for 99.97% of the benchmark instances, with the overall percentage of the reduction in time reaching 87%.

Triangle Counting Accelerations: From Algorithm to In-Memory Computing Architecture

Triangles are the basic substructure of networks and triangle counting (TC) has been a fundamental graph computing problem in numerous fields such as social network analysis. Nevertheless, like other graph computing problems, due to the high memory-computation ratio and random memory access pattern, TC involves a large amount of data transfers thus suffers from the bandwidth bottleneck in the traditional Von-Neumann architecture. To overcome this challenge, in this paper, we propose to accelerate TC with the emerging processing-in-memory (PIM) architecture through an algorithm-architecture co-optimization manner. To enable the efficient in-memory implementations, we come up to reformulate TC with bitwise logic operations (such as AND), and develop customized graph compression and mapping techniques for efficient data flow management. With the emerging computational Spin-Transfer Torque Magnetic RAM (STT-MRAM) array, which is one of the most promising PIM enabling techniques, the device-to-architecture co-simulation results demonstrate that the proposed TC in-memory accelerator outperforms the state-of-the-art GPU and FPGA accelerations by 12.2x and 31.8x, respectively, and achieves a 34x energy efficiency improvement over the FPGA accelerator.