Large Graphs Research Articles

Concatenated Nanopore DNA Codes.

In nanopore sequencers, single-stranded DNA molecules (or k-mers) enter a small opening in a membrane called a nanopore and modulate the ionic current through the pore, producing a channel output in the form of a noisy piecewise constant signal. An important problem in DNA-based data storage is finding a set of k-mers, i.e. a DNA code, that is robust against noisy sample duplication introduced by nanopore sequencers. Good DNA codes should contain as many k-mers as possible that produce distinguishable current signals (squiggles) as measured by the sequencer. The dissimilarity between squiggles can be estimated using a bound on their pairwise error probability, which is used as a metric for code design. Unfortunately, code construction using the union bound is limited to small k's due to the difficulty of finding maximum cliques in large graphs. In this paper, we construct large codes by concatenating codewords from a base code, thereby packing more information in a single strand while retaining the storage efficiency of the base code. To facilitate decoding, we include a circumfix in the base code to reduce the effect of the nanopore channel memory. We show that the decoding complexity scales as [Formula: see text], where m is the number of concatenated k-mers. Simulations show that the base code error rate is stable as m increases.

Efficient -Clique Counting on Large Graphs: The Power of Color-Based Sampling Approaches

Efficient -Clique Counting on Large Graphs: The Power of Color-Based Sampling Approaches

Graph-Based Spatial Segmentation of Areal Data

Smoothing is often used to improve the readability and interpretability of noisy areal data. However, there are many instances where the underlying quantity is discontinuous. For such cases, specific methods are needed to estimate the piecewise constant spatial process. A well-known approach in this setting is to perform segmentation of the signal using the adjacency graph, such as the graph-based fused lasso. However, this method does not scale well to large graphs. A new method is introduced for piecewise constant spatial estimation that (i) is faster to compute on large graphs and (ii) yields sparser models than the fused lasso (for the same amount of regularization), resulting in estimates that are easier to interpret. The method is illustrated on simulated data and applied to real data on overweight prevalence in the Netherlands. Healthy and unhealthy zones are identified, which cannot be explained by demographic or socio-economic characteristics alone. The method is found capable of identifying such zones and can assist policymakers with their health improving strategies.

BL: An Efficient Index for Reachability Queries on Large Graphs

BL: An Efficient Index for Reachability Queries on Large Graphs

Haar Wavelet Feature Compression for Quantized Graph Convolutional Networks.

Graph convolutional networks (GCNs) are widely used in a variety of applications and can be seen as an unstructured version of standard convolutional neural networks (CNNs). As in CNNs, the computational cost of GCNs for large input graphs (such as large point clouds or meshes) can be high and inhibit the use of these networks, especially in environments with low computational resources. To ease these costs, quantization can be applied to GCNs. However, aggressive quantization of the feature maps can lead to a significant degradation in performance. On a different note, the Haar wavelet transforms are known to be one of the most effective and efficient approaches to compress signals. Therefore, instead of applying aggressive quantization to feature maps, we propose to use Haar wavelet compression and light quantization to reduce the computations involved with the network. We demonstrate that this approach surpasses aggressive feature quantization by a significant margin, for a variety of problems ranging from node classification to point cloud classification and both part and semantic segmentation.

On Low-Rank Directed Acyclic Graphs and Causal Structure Learning.

Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high-dimensional settings when the graphs to be learned are not sparse. In this article, we propose to exploit a low-rank assumption regarding the (weighted) adjacency matrix of a DAG causal model to help address this problem. We utilize existing low-rank techniques to adapt causal structure learning methods to take advantage of this assumption and establish several useful results relating interpretable graphical conditions to the low-rank assumption. Specifically, we show that the maximum rank is highly related to hubs, suggesting that scale-free (SF) networks, which are frequently encountered in practice, tend to be low rank. Our experiments demonstrate the utility of the low-rank adaptations for a variety of data models, especially with relatively large and dense graphs. Moreover, with a validation procedure, the adaptations maintain a superior or comparable performance even when graphs are not restricted to be low rank.

Imbalanced Large Graph Learning Framework for FPGA Logic Elements Packing Prediction

Imbalanced Large Graph Learning Framework for FPGA Logic Elements Packing Prediction

Accurate and interpretable drug-drug interaction prediction enabled by knowledge subgraph learning

BackgroundDiscovering potential drug-drug interactions (DDIs) is a long-standing challenge in clinical treatments and drug developments. Recently, deep learning techniques have been developed for DDI prediction. However, they generally require a huge number of samples, while known DDIs are rare.MethodsIn this work, we present KnowDDI, a graph neural network-based method that addresses the above challenge. KnowDDI enhances drug representations by adaptively leveraging rich neighborhood information from large biomedical knowledge graphs. Then, it learns a knowledge subgraph for each drug-pair to interpret the predicted DDI, where each of the edges is associated with a connection strength indicating the importance of a known DDI or resembling strength between a drug-pair whose connection is unknown. Thus, the lack of DDIs is implicitly compensated by the enriched drug representations and propagated drug similarities.ResultsHere we show the evaluation results of KnowDDI on two benchmark DDI datasets. Results show that KnowDDI obtains the state-of-the-art prediction performance with better interpretability. We also find that KnowDDI suffers less than existing works given a sparser knowledge graph. This indicates that the propagated drug similarities play a more important role in compensating for the lack of DDIs when the drug representations are less enriched.ConclusionsKnowDDI nicely combines the efficiency of deep learning techniques and the rich prior knowledge in biomedical knowledge graphs. As an original open-source tool, KnowDDI can help detect possible interactions in a broad range of relevant interaction prediction tasks, such as protein-protein interactions, drug-target interactions and disease-gene interactions, eventually promoting the development of biomedicine and healthcare.

DeepFGRN: inference of gene regulatory network with regulation type based on directed graph embedding.

The inference of gene regulatory networks (GRNs) from gene expression profiles has been a key issue in systems biology, prompting many researchers to develop diverse computational methods. However, most of these methods do not reconstruct directed GRNs with regulatory types because of the lack of benchmark datasets or defects in the computational methods. Here, we collect benchmark datasets and propose a deep learning-based model, DeepFGRN, for reconstructing fine gene regulatory networks (FGRNs) with both regulation types and directions. In addition, the GRNs of real species are always large graphs with direction and high sparsity, which impede the advancement of GRN inference. Therefore, DeepFGRN builds a node bidirectional representation module to capture the directed graph embedding representation of the GRN. Specifically, the source and target generators are designed to learn the low-dimensional dense embedding of the source and target neighbors of a gene, respectively. An adversarial learning strategy is applied to iteratively learn the real neighbors of each gene. In addition, because the expression profiles of genes with regulatory associations are correlative, a correlation analysis module is designed. Specifically, this module not only fully extracts gene expression features, but also captures the correlation between regulators and target genes. Experimental results show that DeepFGRN has a competitive capability for both GRN and FGRN inference. Potential biomarkers and therapeutic drugs for breast cancer, liver cancer, lung cancer and coronavirus disease 2019 are identified based on the candidate FGRNs, providing a possible opportunity to advance our knowledge of disease treatments.

Sparse graphs with bounded induced cycle packing number have logarithmic treewidth

A graph is Ok-free if it does not contain k pairwise vertex-disjoint and non-adjacent cycles. We prove that “sparse” (here, not containing large complete bipartite graphs as subgraphs) Ok-free graphs have treewidth (even, feedback vertex set number) at most logarithmic in the number of vertices. This is optimal, as there is an infinite family of O2-free graphs without K2,3 as a subgraph and whose treewidth is (at least) logarithmic.Using our result, we show that Maximum Independent Set and 3-Coloring in Ok-free graphs can be solved in quasi-polynomial time. Other consequences include that most of the central NP-complete problems (such as Maximum Independent Set, Minimum Vertex Cover, Minimum Dominating Set, Minimum Coloring) can be solved in polynomial time in sparse Ok-free graphs, and that deciding the Ok-freeness of sparse graphs is polynomial time solvable.

Stronger and Transferable Node Injection Attacks

Despite the increasing popularity of graph neural networks (GNNs), the security risks associated with their deployment have not been well explored. Existing works follow the standard adversarial attacks to maximize cross-entropy loss within an L-infinity norm bound. We analyze the robustness of GNNs against node injection attacks (NIAs) in black-box settings by allowing new nodes to be injected and attacked. In this work, we propose to design stronger and transferable NIAs. First, we propose margin aware attack (MAA) that uses a maximum margin loss to generate NIAs. We then propose a novel margin and direction aware attack (MDA) that diversifies the initial directions of MAA attack by minimizing the cosine similarity of the injected nodes with respect to their respective random initialization in addition to the maximization of max-margin loss. This makes the NIAs stronger. We further observe that using L2 norm of gradients in the attack step leads to an enhanced diversity amongst the node features, thereby further enhancing the strength of the attack. We incorporate transferability in NIAs by perturbing the surrogate model before generating the attack. An analysis of eigen spectrum density of the hessian of the loss emphasizes that perturbing the weights of the surrogate model improves the transferability. Our experimental results demonstrate that the proposed resilient node injection attack (R-NIA) consistently outperform PGD by margins about 7-15% on both large and small graph datasets. R-NIA is significantly stronger and transferable than existing NIAs on graph robustness benchmarks.

CyberQ: Generating Questions and Answers for Cybersecurity Education Using Knowledge Graph-Augmented LLMs

Building a skilled cybersecurity workforce is paramount to building a safer digital world. However, the diverse skill set, constantly emerging vulnerabilities, and deployment of new cyber threats make learning cybersecurity challenging. Traditional education methods struggle to cope with cybersecurity's rapidly evolving landscape and keep students engaged and motivated. Different studies on students' behaviors show that an interactive mode of education by engaging through a question-answering system or dialoguing is one of the most effective learning methodologies. There is a strong need to create advanced AI-enabled education tools to promote interactive learning in cybersecurity. Unfortunately, there are no publicly available standard question-answer datasets to build such systems for students and novice learners to learn cybersecurity concepts, tools, and techniques. The education course material and online question banks are unstructured and need to be validated and updated by domain experts, which is tedious when done manually. In this paper, we propose CyberGen, a novel unification of large language models (LLMs) and knowledge graphs (KG) to generate the questions and answers for cybersecurity automatically. Augmenting the structured knowledge from knowledge graphs in prompts improves factual reasoning and reduces hallucinations in LLMs. We used the knowledge triples from cybersecurity knowledge graphs (AISecKG) to design prompts for ChatGPT and generate questions and answers using different prompting techniques. Our question-answer dataset, CyberQ, contains around 4k pairs of questions and answers. The domain expert manually evaluated the random samples for consistency and correctness. We train the generative model using the CyberQ dataset for question answering task.

Linear-Time Algorithms for Front-Door Adjustment in Causal Graphs

Causal effect estimation from observational data is a fundamental task in empirical sciences. It becomes particularly challenging when unobserved confounders are involved in a system. This paper focuses on front-door adjustment – a classic technique which, using observed mediators allows to identify causal effects even in the presence of unobserved confounding. While the statistical properties of the front-door estimation are quite well understood, its algorithmic aspects remained unexplored for a long time. In 2022, Jeong, Tian, and Bareinboim presented the first polynomial-time algorithm for finding sets satisfying the front-door criterion in a given directed acyclic graph (DAG), with an O(n³(n+m)) run time, where n denotes the number of variables and m the number of edges of the causal graph. In our work, we give the first linear-time, i.e., O(n+m), algorithm for this task, which thus reaches the asymptotically optimal time complexity. This result implies an O(n(n+m)) delay enumeration algorithm of all front-door adjustment sets, again improving previous work by a factor of n³. Moreover, we provide the first linear-time algorithm for finding a minimal front-door adjustment set. We offer implementations of our algorithms in multiple programming languages to facilitate practical usage and empirically validate their feasibility, even for large graphs.

Pass-Efficient Algorithms for Graph Spectral Clustering (Student Abstract)

Graph spectral clustering is a fundamental technique in data analysis, which utilizes eigenpairs of the Laplacian matrix to partition graph vertices into clusters. However, classical spectral clustering algorithms require eigendecomposition of the Laplacian matrix, which has cubic time complexity. In this work, we describe pass-efficient spectral clustering algorithms that leverage recent advances in randomized eigendecomposition and the structure of the graph vertex-edge matrix. Furthermore, we derive formulas for their efficient implementation. The resulting algorithms have a linear time complexity with respect to the number of vertices and edges and pass over the graph constant times, making them suitable for processing large graphs stored on slow memory. Experiments validate the accuracy and efficiency of the algorithms.

The Ring: Worst-case Optimal Joins in Graph Databases using (Almost) No Extra Space

We present an indexing scheme for triple-based graphs that supports join queries in worst-case optimal (wco) time within compact space. This scheme, called a ring , regards each triple as a cyclic string of length 3. Each rotation of the triples is lexicographically sorted and the values of the last attribute are stored as a column, so we obtain the order of the next column by stably re-sorting the triples by its attribute. We show that, by representing the columns with a compact data structure called a wavelet tree, this ordering enables forward and backward navigation between columns without needing pointers. These wavelet trees further support wco join algorithms and cardinality estimations for query planning. While traditional data structures such as B-Trees, tries, and so on, require 6 index orders to support all possible wco joins over triples, we can use one ring to index them all. This ring replaces the graph and uses only sublinear extra space, thus supporting wco joins in almost no space beyond storing the graph itself. Experiments querying a large graph (Wikidata) in memory show that the ring offers nearly the best overall query times while using only a small fraction of the space required by several state-of-the-art approaches. We then turn our attention to some theoretical results for indexing tables of arity d higher than 3 in such a way that supports wco joins. While a single ring of length d no longer suffices to cover all d ! orders, we need much fewer rings to index them all: O (2 d ) rings with a small constant. For example, we need 5 rings instead of 120 orders for d =5. We show that our rings become a particular case of what we dub order graphs , whose nodes are attribute orders and where stably sorting by some attribute leads us from an order to another, thereby inducing an edge labeled by the attribute. The index is then the set of columns associated with the edges, and a set of rings is just one possible graph shape. We show that other shapes, like for example a single ring instead of several ones of length d , can lead us to even smaller indexes, and that other more general shapes are also possible. For example, we handle d =5 attributes within space equivalent to 4 rings.

ASG-HOMGAT: a high-order multi-head graph attention network with adaptive small graph structure for rolling bearing fault diagnosis

Traditional Euclidean spatial data processing is difficult to capture the inherent relationships of unstructured data such as bearing vibration signals. Representing vibration signals in graphical form helps to preserve their topological structure and temporal information. Secondly, most existing graph convolutional network methods are based on large graph structured data, which incurs certain memory overhead when aggregating high-order neighborhood node information and ignores important information between samples in the global graph structure. To address these issues, this paper proposes a high-order multi-head graph attention network based on an adaptive small graph structure (ASG-HOMGAT) for fault diagnosis of rolling bearings. Firstly, the adaptive preprocessing layer is used to adaptively denoise and compress the one-dimensional time-domain vibration signal, generating small rule graph data with topological structure. Then, these small graph structured data samples are input into a higher-order graph neural network, which aggregates features from multiple higher-order neighborhoods to achieve richer feature representations and fully explore the intrinsic correlation between samples. Finally, these features are aggregated into a reinforced representation of graph nodes through a multi head attention mechanism, and a SoftMax classifier is used for fault classification. The experimental results show that the ASG-HOMGAT method has better performance compared to mainstream graph neural network diagnostic models. The code and model will be released at: https://github.com/ding-ss/ASG-HOMGAT.

Tensor Network Message Passing.

When studying interacting systems, computing their statistical properties is a fundamental problem in various fields such as physics, applied mathematics, and machine learning. However, this task can be quite challenging due to the exponential growth of the state space as the system size increases. Many standard methods have significant weaknesses. For instance, message-passing algorithms can be inaccurate and even fail to converge due to short loops, while tensor network methods can have exponential computational complexity in large graphs due to long loops. In this Letter, we propose a new method called "tensor network message passing." This approach allows us to compute local observables like marginal probabilities and correlations by combining the strengths of tensor networks in contracting small subgraphs with many short loops and the strengths of message-passing methods in globally sparse graphs, thus addressing the crucial weaknesses of both approaches. Our algorithm is exact for systems that are globally treelike and locally dense-connected when the dense local graphs have a limited tree width. We have conducted numerical experiments on synthetic and real-world graphs to compute magnetizations of Ising models and spin glasses, and have demonstrated the superiority of our approach over standard belief propagation and the recently proposed loopy message-passing algorithm. In addition, we discuss the potential applications of our method in inference problems in networks, combinatorial optimization problems, and decoding problems in quantum error correction.

Domination of triangulated discs and maximal outerplanar graphs

Given an infinite family of graphs, its domination ratio is the smallest real k such that for every large enough graph in the family, the ratio between its domination number and order is at most k. We give bounds for the domination ratios of various families of triangulated discs, disproving two conjectures of Tokunaga. For instance, we show that the domination ratio of triangulated discs of minimum degree 3 is at least 3/10. We also give a natural extension of a theorem on the domination number of maximal outerplane graphs, proven by Campos and Wakabayashi, and independently Tokunaga. Motivated by the Matheson-Tarjan Conjecture, we present observations on dominating triangulations via Jackson-Yu decomposition trees as well as an approach on how to efficiently dominate, given a triangulation, many large subtriangulations thereof. Throughout the paper, results are accompanied by computational experiments.

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.

DoppelGanger++: Towards Fast Dependency Graph Generation for Database Replay

A database replay system (DRS) captures workloads on a production system and then replays them in a test system to test various system changes, avoiding any risk before realizing them in production. The dependency graph generation in a DRS is crucial in preserving output determinism while maximizing concurrency. The state-of-the-art dependency graph generation algorithm deployed in a commercial DBMS uses a generate-and-prune strategy. It first generates a dependency graph by performing backward scans for each request in a workload. It then prunes all redundant edges using an expensive, transitive reduction algorithm. However, we notice that this generates a large dependency graph that contains many redundant edges and its worst-case time complexity is quadratic to the number of requests in a workload. In order to solve these challenging problems, we formally propose four classes of dependency graphs for DRSs. We then present a stateful single forward scan algorithm, SSFS, to generate any class of dependency graphs by performing a single scan over all requests while succinctly maintaining states. Here, states refer to information that is stored and maintained for efficient dependency graph generation. We also propose the parallel SSFS to utilize the computation power with multi-core CPUs while balancing the loads. We implemented our DRS in a leading commercial DBMS. Extensive experiments using the TPC-C, SD benchmarks, and a real-world customer workload show that our DRS significantly improves the dependency graph generation time by up to two orders of magnitude, compared to the state-of-the-art.