Real-world Large-scale Graphs Research Articles

PimPam: Efficient Graph Pattern Matching on Real Processing-in-Memory Hardware

Graph pattern matching is powerful and widely applicable to many application domains. Despite the recent algorithm advances, matching patterns in large-scale real-world graphs still faces the memory access bottleneck on conventional computing systems. Processing-in-memory (PIM) is an emerging hardware architecture paradigm that puts computing cores into memory devices to alleviate the memory wall issues. Real PIM hardware has recently become commercially accessible to the public. In this work, we leverage the real PIM hardware platform to build a graph pattern matching framework, PimPam, to benefit from its abundant computation and memory bandwidth resources. We propose four key optimizations in PimPam to improve its efficiency, including (1) load-aware task assignment to ensure load balance, (2) space-efficient and parallel data partitioning to prepare input data for PIM cores, (3) adaptive multi-threading collaboration to automatically select the best parallelization strategy during processing, and (4) dynamic bitmap structures that accelerate the key operations of set intersection. When evaluated on five patterns and six real-world graphs, PimPam outperforms the state-of-the-art CPU baseline system by 22.5x on average and up to 71.7x, demonstrating significant performance improvements.

Promoting fairness in link prediction with graph enhancement.

Link prediction is a crucial task in network analysis, but it has been shown to be prone to biased predictions, particularly when links are unfairly predicted between nodes from different sensitive groups. In this paper, we study the fair link prediction problem, which aims to ensure that the predicted link probability is independent of the sensitive attributes of the connected nodes. Existing methods typically incorporate debiasing techniques within graph embeddings to mitigate this issue. However, training on large real-world graphs is already challenging, and adding fairness constraints can further complicate the process. To overcome this challenge, we propose FairLink, a method that learns a fairness-enhanced graph to bypass the need for debiasing during the link predictor's training. FairLink maintains link prediction accuracy by ensuring that the enhanced graph follows a training trajectory similar to that of the original input graph. Meanwhile, it enhances fairness by minimizing the absolute difference in link probabilities between node pairs within the same sensitive group and those between node pairs from different sensitive groups. Our extensive experiments on multiple large-scale graphs demonstrate that FairLink not only promotes fairness but also often achieves link prediction accuracy comparable to baseline methods. Most importantly, the enhanced graph exhibits strong generalizability across different GNN architectures. FairLink is highly scalable, making it suitable for deployment in real-world large-scale graphs, where maintaining both fairness and accuracy is critical.

A Restart Local Search for Solving Diversified Top-k Weight Clique Search Problem

Diversified top-k weight clique (DTKWC) search problem is an important generalization of the diversified top-k clique (DTKC) search problem with practical applications. The diversified top-k weight clique search problem aims to search k maximal cliques that can cover the maximum weight in a vertex weighted graph. In this work, we propose a novel local search algorithm called TOPKWCLQ for the DTKWC search problem which mainly includes two strategies. First, a restart strategy is adopted, which repeated the construction and updating processes of the maximal weight clique set. Second, a scoring heuristic is designed by giving different priorities for maximal weight cliques in candidate set. Meanwhile, a constraint model of the DTKWC search problem is constructed such that the research concerns can be evaluated. Experimental results show that the proposed algorithm TOPKWCLQ outperforms than the comparison algorithm on large-scale real-world graphs.

Access pattern-based high-performance main memory system for graph processing on single machines

With the increasing complexity of graph structures, the current real-world large-scale graphs are being represented by a considerable amount of vertex and edge data. Furthermore, the analysis of a large number of computing nodes has become a very complicated job that requires a large amount of hardware resources. Moreover, in large-scale graph processing, the vertex and edge data show random and sequential memory access patterns at the same time, and this is a major bottleneck in graph processing. In this paper, we present a high-capacity main memory system with an intelligent pattern-aware prefetching engine to overcome the scalability problem and the memory inefficiency of single-machine graph processing. The proposed intelligent pattern-aware prefetching engine is designed to predict and handle sequential or regular patterns and random-access patterns simultaneously. Experimental results demonstrated that the proposed model exhibited performance improvements of 60% over conventional DRAM models, approximately 40% over the existing prefetch models, and about 12.5% over the latest prefetch models.

A new branch-and-bound algorithm for the maximum edge-weighted clique problem

Abstract We study the maximum edge-weighted clique problem, a problem related to the maximum (vertex-weighted) clique problem which asks for finding a complete subgraph (i.e., a clique) of maximum total weight on its edges. The problem appears in a wide range of applications, including bioinformatics, material science, computer vision, robotics, and many more. In this work, we propose a new combinatorial branch-and-bound algorithm for the problem which relies on a novel bounding procedure capable of pruning a very large amount of nodes of the branch-and-bound tree. Extensive computational experiments on random and structured graphs, encompassing standard benchmarks used in the literature as well as recently introduced real-world large-scale graphs, show that our new algorithm outperforms the state-of-the-art by several orders of magnitude on many instances.

Node Embedding with Adaptive Similarities for Scalable Learning over Graphs

Node embedding is the task of extracting informative and descriptive features over the nodes of a graph. The importance of node embedding for graph analytics as well as learning tasks, such as node classification, link prediction, and community detection, has led to a growing interest and a number of recent advances. Nonetheless, node embedding faces several major challenges. Practical embedding methods have to deal with real-world graphs that arise from different domains, with inherently diverse underlying processes as well as similarity structures and metrics. On the other hand, similar to principal component analysis in feature vector spaces, node embedding is an inherently unsupervised task. Lacking metadata for validation, practical schemes motivate standardization and limited use of tunable hyperparameters. Finally, node embedding methods must be scalable in order to cope with large-scale real-world graphs of networks with ever-increasing size. The present work puts forth an adaptive node embedding framework that adjusts the embedding process to a given underlying graph, in a fully unsupervised manner. This is achieved by leveraging the notion of a tunable node similarity matrix that assigns weights on multihop paths. The design of multihop similarities ensures that the resultant embeddings also inherit interpretable spectral properties. The proposed model is thoroughly investigated, interpreted, and numerically evaluated using stochastic block models. Moreover, an unsupervised algorithm is developed for training the model parameters effieciently. Extensive node classification, link prediction, and clustering experiments are carried out on many real-world graphs from various domains, along with comparisons with state-of-the-art scalable and unsupervised node embedding alternatives. The proposed method enjoys superior performance in many cases, while also yielding interpretable information on the underlying graph structure.

Prioritized Relationship Analysis in Heterogeneous Information Networks

An increasing number of applications are modeled and analyzed in network form, where nodes represent entities of interest and edges represent interactions or relationships between entities. Commonly, such relationship analysis tools assume homogeneity in both node type and edge type. Recent research has sought to redress the assumption of homogeneity and focused on mining heterogeneous information networks (HINs) where both nodes and edges can be of different types. Building on such efforts, in this work, we articulate a novel approach for mining relationships across entities in such networks while accounting for user preference over relationship type and interestingness metric. We formalize the problem as a top- k lightest paths problem, contextualized in a real-world communication network, and seek to find the k most interesting path instances matching the preferred relationship type. Our solution, PROphetic HEuristic Algorithm for Path Searching (PRO-HEAPS), leverages a combination of novel graph preprocessing techniques, well-designed heuristics and the venerable A* search algorithm. We run our algorithm on real-world large-scale graphs and show that our algorithm significantly outperforms a wide variety of baseline approaches with speedups as large as 100X. To widen the range of applications, we also extend PRO-HEAPS to (i) support relationship analysis between two groups of entities and (ii) allow pattern path in the query to contain logical statements with operators AND, OR, NOT, and wild-card “.”. We run experiments using this generalized version of PRO-HEAPS and demonstrate that the advantage of PRO-HEAPS becomes even more pronounced for these general cases. Furthermore, we conduct a comprehensive analysis to study how the performance of PRO-HEAPS varies with respect to various attributes of the input HIN. We finally conduct a case study to demonstrate valuable applications of our algorithm.

Finding A Small Vertex Cover in Massive Sparse Graphs: Construct, Local Search, and Preprocess

The problem of finding a minimum vertex cover (MinVC) in a graph is a well known NP-hard combinatorial optimization problem of great importance in theory and practice. Due to its NP-hardness, there has been much interest in developing heuristic algorithms for finding a small vertex cover in reasonable time. Previously, heuristic algorithms for MinVC have focused on solving graphs of relatively small size, and they are not suitable for solving massive graphs as they usually have high-complexity heuristics. This paper explores techniques for solving MinVC in very large scale real-world graphs, including a construction algorithm, a local search algorithm and a preprocessing algorithm. Both the construction and search algorithms are based on low-complexity heuristics, and we combine them to develop a heuristic algorithm for MinVC called FastVC. Experimental results on a broad range of real-world massive graphs show that, our algorithms are very fast and have better performance than previous heuristic algorithms for MinVC. We also develop a preprocessing algorithm to simplify graphs for MinVC algorithms. By applying the preprocessing algorithm to local search algorithms, we obtain two efficient MinVC solvers called NuMVC2+p and FastVC2+p, which show further improvement on the massive graphs.

GARUDA

Unraveling "interesting" subgraphs corresponding to disease/crime hotspots or characterizing habitation shift patterns is an important graph mining task. With the availability and growth of large-scale real-world graphs, mining for such subgraphs has become the need of the hour for graph miners as well as non-technical end-users. In this demo, we present GARUDA, a system capable of mining large-scale graphs for statistically significant subgraphs in a scalable manner, and provide: (1) a detailed description of the various features and user-friendly GUI of GARUDA; (2) a brief description of the system architecture; and (3) a demonstration scenario for the audience. The demonstration showcases one real graph mining task as well as its ability to scale to large real graphs, portraying speed-ups of upto 8--10 times over the state-of-the-art MSCS algorithm.

GraphTwist

Large-scale real-world graphs are known to have highly skewed vertex degree distribution and highly skewed edge weight distribution. Existing vertex-centric iterative graph computation models suffer from a number of serious problems: (1) poor performance of parallel execution due to inherent workload imbalance at vertex level; (2) inefficient CPU resource utilization due to short execution time for low-degree vertices compared to the cost of in-memory or on-disk vertex access; and (3) incapability of pruning insignificant vertices or edges to improve the computational performance. In this paper, we address the above technical challenges by designing and implementing a scalable, efficient, and provably correct two-tier graph parallel processing system, GraphTwist. At storage and access tier, GraphTwist maximizes parallel efficiency by employing three graph parallel abstractions for partitioning a big graph by slice, strip or dice based partitioning techniques. At computation tier, GraphTwist presents two utility-aware pruning strategies: slice pruning and cut pruning, to further improve the computational performance while preserving the computational utility defined by graph applications. Theoretic analysis is provided to quantitatively prove that iterative graph computations powered by utility-aware pruning techniques can achieve a very good approximation with bounds on the introduced error.

A Ranking Approach on Large-Scale Graph With Multidimensional Heterogeneous Information.

Graph-based ranking has been extensively studied and frequently applied in many applications, such as webpage ranking. It aims at mining potentially valuable information from the raw graph-structured data. Recently, with the proliferation of rich heterogeneous information (e.g., node/edge features and prior knowledge) available in many real-world graphs, how to effectively and efficiently leverage all information to improve the ranking performance becomes a new challenging problem. Previous methods only utilize part of such information and attempt to rank graph nodes according to link-based methods, of which the ranking performances are severely affected by several well-known issues, e.g., over-fitting or high computational complexity, especially when the scale of graph is very large. In this paper, we address the large-scale graph-based ranking problem and focus on how to effectively exploit rich heterogeneous information of the graph to improve the ranking performance. Specifically, we propose an innovative and effective semi-supervised PageRank (SSP) approach to parameterize the derived information within a unified semi-supervised learning framework (SSLF-GR), then simultaneously optimize the parameters and the ranking scores of graph nodes. Experiments on the real-world large-scale graphs demonstrate that our method significantly outperforms the algorithms that consider such graph information only partially.

On the hardness of optimization in power-law graphs

Our motivation for this work is the remarkable discovery that many large-scale real-world graphs ranging from Internet and World Wide Web to social and biological networks appear to exhibit a power-law distribution: the number of nodes y i of a given degree i is proportional to i − β where β > 0 is a constant that depends on the application domain. There is practical evidence that combinatorial optimization in power-law graphs is easier than in general graphs, prompting the basic theoretical question: Is combinatorial optimization in power-law graphs easy? Does the answer depend on the power-law exponent β ? Our main result is the proof that many classical NP-hard graph-theoretic optimization problems remain NP-hard on power-law graphs for certain values of β . In particular, we show that some classical problems, such as CLIQUE and COLORING, remain NP-hard for all β ≥ 1 . Moreover, we show that all the problems that satisfy the so-called “optimal substructure property” remain NP-hard for all β > 0 . This includes classical problems such as MINIMUM VERTEX COVER, MAXIMUM INDEPENDENT SET, and MINIMUM DOMINATING SET. Our proofs involve designing efficient algorithms for constructing graphs with prescribed degree sequences that are tractable with respect to various optimization problems.