The problem of structural diversity search has been widely studied recently, which aims to find out the users with the highest structural diversity in social networks. The structural diversity of a user is depicted by the number of social contexts inside his/her contact neighborhood. Three structural diversity models based on cohesive subgraph models (e.g., k-sized component, k-core, and k-truss), have been proposed. Previous solutions only focus on CPU-based sequential solutions, suffering from several key steps of that cannot be highly parallelized. GPUs enjoy high-efficiency performance in parallel computing for solving many complex graph problems such as triangle counting, subgraph pattern matching, and graph decomposition. In this paper, we provide a unified framework to utilize multiple GPUs to accelerate the computation of structural diversity search under the mentioned three structural diversity models. We first propose a GPU-based lock-free method to efficiently extract ego-networks in CSR format in parallel. Second, we design detailed GPU-based solutions for computingk-sized component-based,k-core-based, and alsok-truss-based structural diversity scores by dynamically grouping GPU resources. To effectively optimize the workload balance among multiple GPUs, we propose a greedy work-packing scheme and a dynamic work-stealing strategy to fulfill usage. Extensive experiments on real-world datasets validate the superiority of our GPU-based structural diversity search solutions in terms of efficiency and effectiveness.

With the widespread adoption of mobile internet and GPS-enabled smartphones, spatial crowdsourcing has emerged as a prevalent computing paradigm. In this paradigm, the human-machine collaborative task assignment mode, which empowers workers to select tasks based on their preferences, has become a preferred approach for various applications such as ridesharing and takeaways. Generally, the platform continuously presents a set of top-$k$tasks to individual workers by taking into account factors like travel distance, and allows workers to select tasks from this set. This decision approach is beneficial to both platform and workers. However, it still faces significant challenges in large-scale dynamic results maintenance, which incurs considerable computational costs. In this paper, we propose a novel solution framework with an adaptive two-layer cache structure to efficiently address the problem of updating dynamic top-$k$results. Additionally, we propose two effective learning-based methods which greatly improve the efficiency of result maintenance. Furthermore, we present a novel approach to identify and process caches that trigger intensive updates within a tight time limit, greatly reducing the peak demand for updating caches. Finally, extensive experimental results on real datasets demonstrate that our proposed algorithms exhibit strong performance across various parameter configurations.

Graph analysis is fundamental in real-world applications. Traditional approaches rely on SPARQL-like languages or clicking-and-dragging interfaces to interact with graph data. However, these methods either require users to possess high programming skills or support only a limited range of graph analysis functionalities. To address the limitations, we propose a large language model (LLM)-based framework called Chat-Graph. With ChatGraph, users can interact with graphs through natural language, making it easier to use and more flexible than traditional approaches. The core of ChatGraph lies in generating chains of graph analysis APIs based on the understanding of the texts and graphs inputted in the user prompts. To achieve this, ChatGraph consists of three main modules: an API retrieval module that searches for relevant APIs, a graph-aware LLM module that enables the LLM to comprehend graphs, and an API chain-oriented finetuning module that guides the LLM in generating API chains. We have implemented ChatGraph and will showcase its usability and efficiency in four scenarios using real-world graphs.

Nearest neighbor search is a fundamental task in various domains, such as federated learning, data mining, information retrieval, and biomedicine. With the increasing need to utilize data from different organizations while respecting privacy regulations, private data federation has emerged as a promising solution. However, it is costly to directly apply existing approaches to federated k-nearest neighbor (kNN) search with difficult-to-compute distance functions, like graph or sequence similarity. To address this challenge, we propose FedKNN, a system that supports secure federated kNN search queries with a wide range of similarity measurements. Our system is equipped with a new Distribution-Aware kNN (DANN) algorithm to minimize unnecessary local computations while protecting data privacy. We further develop DANN*, a secure version of DANN that satisfies differential obliviousness. Extensive evaluations show that FedKNN outperforms state-of-the-art solutions, achieving up to 4.8× improvement on federated graph kNN search and up to 2.7× improvement on federated sequence kNN search. Additionally, our approach offers a trade-off between privacy and efficiency, providing strong privacy guarantees with minimal overhead.

Line Density Visualization (LDV) is an important operation of geospatial analysis, which has been extensively used in many application domains, e.g., urban planning, criminology, and transportation science. However, LDV is computationally demanding. Therefore, existing exact solutions are not scalable (or even not feasible) to support large-scale datasets and high resolution sizes for generating LDV. To handle the efficiency issues, we develop the first solution to approximately compute LDV with an ϵ -relative error guarantee, which consists of two main parts. First, we develop the new indexing structure, called length-aggregation-based grid structure (LARGE). Second, based on LARGE, we develop two types of fast bound functions, namely (1) square-shaped lower and upper bound functions and (2) arbitrary-shaped lower and upper bound functions, which can filter a large portion of unnecessary computations. By theoretically analyzing the tightness of our bound functions and experimentally comparing our solution with existing exact solutions on four large-scale datasets, we demonstrate that our solution can be scalable to generate high-resolution LDVs using large-scale datasets. In particular, our solution achieves up to 291.8x speedups over the state-of-the-art solutions.

The shuffle model of differential privacy provides promising privacy-utility balances in decentralized, privacy-preserving data analysis. However, the current analyses of privacy amplification via shuffling lack both tightness and generality. To address this issue, we propose the variation-ratio reduction as a comprehensive framework for privacy amplification in both single-message and multi-message shuffle protocols. It leverages two new parameterizations: the total variation bounds of local messages and the probability ratio bounds of blanket messages, to determine indistinguishability levels. Our theoretical results demonstrate that our framework provides tighter bounds, especially for local randomizers with extremal probability design, where our bounds are exactly tight. Additionally, variation-ratio reduction complements parallel composition in the shuffle model, yielding enhanced privacy accounting for popular sampling-based randomizers employed in statistical queries (e.g., range queries, marginal queries, and frequent itemset mining). Empirical findings demonstrate that our numerical amplification bounds surpass existing ones, conserving up to 30% of the budget for single-message protocols, 75% for multi-message ones, and a striking 75%-95% for parallel composition. Our bounds also result in a remarkably efficient Õ ( n ) algorithm that numerically amplifies privacy in less than 10 seconds for n = 10 8 users.

Approximate nearest neighbor (ANN) search is a fundamental search in multi-dimensional databases, which has numerous real-world applications, such as image retrieval, recommendation, entity resolution, and sequence matching. Proximity graph (PG) has been the state-of-the-art index for ANN search. However, the search on existing PGs either suffers from a high time complexity or has no performance guarantee on the search result. In this paper, we propose a novel τ-monotonic graph (τ- MG) to address the limitations. The novelty of τ-MG lies in a τ-monotonic property. Based on this property, we prove that if the distance between a query q and its nearest neighbor is less than a constant τ, the search on τ-MG guarantees to find the exact nearest neighbor of q and the time complexity of the search is smaller than all existing PG-based methods. For index construction efficiency, we propose an approximate variant of τ-MG, namely τ-monotonic neighborhood graph (τ- MNG), which only requires the neighborhood of each node to be τ-monotonic. We further propose an optimization to reduce the number of distance computations in search. Our extensive experiments show that our techniques outperform all existing methods on well-known real-world datasets.

This paper studies privacy preserving graph pattern query services in a cloud computing paradigm. In such a paradigm, data owner stores the large data graph to a powerful cloud hosted by a service provider (SP) and users send their queries to SP for query processing. However, as SP may not always be trusted, the sensitive information of users' queries, importantly, the query structures, should be protected. In this paper, we study how to outsource the localized graph pattern queries (LGPQs) on the SP side with privacy preservation. LGPQs include a rich set of semantics, such as subgraph homomorphism, subgraph isomorphism, and strong simulation, for which each matched graph pattern is located in a subgraph called ball that have a restriction on its size. To provide privacy preserving query service for LGPQs, this paper proposes the first framework, called Prilo, that enables users to privately obtain the query results. To further optimize Prilo, we propose Prilo* that comprises the first bloom filter for trees in the trust execution environment (TEE) on SP, a query-oblivious twiglet-based technique for pruning non-answers, and a secure retrieval scheme of balls that enables user to obtain query results early. We conduct detailed experiments on real world datasets to show that Prilo* is on average 4x faster than the baseline, and meanwhile, preserves query privacy.

The problem of k-nearest neighbor (k-NN) search is fundamental in graph databases, which has numerous real-world applications, such as bioinformatics, computer vision, and software engineering. Graph edit distance (GED) and maximum common subgraph (MCS)-based distance are the most widely used distance measures in k-NN search. However, computing the exact k-NNs of a query graph$Q$using these measures is prohibitively time-consuming, as a large number of graph distance computations is needed, and computing GED and MCS are both NP-hard. In this paper, we study the approximate k-nearest neighbor (k-ANN) search with the aim of trading efficiency with a slight decrease in accuracy. Greedy routing on the proximity graph (PG) index is a state-of-the-art method for k-ANN search. However, such routing algorithms are not designed for graph databases, and simple adoption is inefficient. The core reason is that the exhaustive neighbor exploration at each routing step incurs a large number of distance computations (NDC). In this paper, we propose a learning-based k-ANN search method to reduce NDC. First, we propose to prune unpromising neighbors from distance computations. We use a graph learning model to rank the neighbors at each routing step and explore only the top neighbors. For the accuracy of rank prediction, we propose a neighbor ranking model that works only in the neighborhood of Q. Second, we propose a learning-based method to select the initial node for the routing. The initial node selected has a high probability of being in the neighborhood of Q, such that the neighbor ranking model can be used. Third, we propose a compressed GNN-graph to accelerate the neighbor ranking model and the initial node selection model. We prove that learning efficiency is improved without degrading the accuracy. Our extensive experiments show that our method is about 3.6x to 18.6x faster than the state-of-the-art methods on real-world datasets.

Network K -function has been the de facto operation for analyzing point patterns in spatial networks, which is widely used in many communities, including geography, ecology, transportation science, social science, and criminology. To analyze a location dataset, domain experts need to generate a network K -function plot that involves computing multiple network K -functions. However, network K -function is a computationally expensive operation that is not feasible to support large-scale datasets, let alone to generate a network K -function plot. To handle this issue, we develop two efficient algorithms, namely count augmentation (CA) and neighbor sharing (NS), which can reduce the worst-case time complexity for computing network K -functions. In addition, we incorporate the advanced shortest path sharing (ASPS) approach into these two methods to further lower the worst-case time complexity for generating network K -function plots. Experiment results on four large-scale location datasets (up to 7.33 million data points) show that our methods can achieve up to 165.85x speedup compared with the state-of-the-art methods.

Abstract Graphs have been widely used to represent complex data in many applications, such as e-commerce, social networks, and bioinformatics. Efficient and effective analysis of graph data is important for graph-based applications. However, most graph analysis tasks are combinatorial optimization (CO) problems, which are NP-hard. Recent studies have focused a lot on the potential of using machine learning (ML) to solve graph-based CO problems. Most recent methods follow the two-stage framework. The first stage is graph representation learning, which embeds the graphs into low-dimension vectors. The second stage uses machine learning to solve the CO problems using the embeddings of the graphs learned in the first stage. The works for the first stage can be classified into two categories, graph embedding methods and end-to-end learning methods. For graph embedding methods, the learning of the the embeddings of the graphs has its own objective, which may not rely on the CO problems to be solved. The CO problems are solved by independent downstream tasks. For end-to-end learning methods, the learning of the embeddings of the graphs does not have its own objective and is an intermediate step of the learning procedure of solving the CO problems. The works for the second stage can also be classified into two categories, non-autoregressive methods and autoregressive methods. Non-autoregressive methods predict a solution for a CO problem in one shot. A non-autoregressive method predicts a matrix that denotes the probability of each node/edge being a part of a solution of the CO problem. The solution can be computed from the matrix using search heuristics such as beam search. Autoregressive methods iteratively extend a partial solution step by step. At each step, an autoregressive method predicts a node/edge conditioned to current partial solution, which is used to its extension. In this survey, we provide a thorough overview of recent studies of the graph learning-based CO methods. The survey ends with several remarks on future research directions.

In this paper, we consider probabilistic reachability queries on uncertain graphs. To make the results more informative, we adopt a crowdsourcing-based approach to clean the uncertain edges. One important problem is how to efficiently select a limited set of edges for cleaning that maximizes the quality improvement. We prove that the edge selection problem is #P-hard. In light of the hardness of the problem, we propose a series of edge selection algorithms, followed by a number of optimization techniques and pruning heuristics for minimizing the computation time. Our experimental results demonstrate that our proposed techniques outperform a random selection by up to 27 times in terms of the result quality improvement and the brute-force solution by up to 60 times in terms of the elapsed time.

Uncertain graph models are widely used in real-world applications such as knowledge graphs and social networks. To capture the uncertainty, each edge in an uncertain graph is associated with an existential probability that signifies the likelihood of the existence of the edge. One notable issue of querying uncertain graphs is that the results are sometimes uninformative because of the edge uncertainty. In this paper, we consider probabilistic reachability queries, which are one of the fundamental classes of graph queries. To make the results more informative, we adopt a crowdsourcing-based approach to clean the uncertain edges. However, considering the time and monetary cost of crowdsourcing, it is a problem to efficiently select a limited set of edges for cleaning that maximizes the quality improvement. We prove that the edge selection problem is #P-hard. In light of the hardness of the problem, we propose a series of edge selection algorithms, followed by a number of optimization techniques and pruning heuristics for reducing the computation time. Our experimental results demonstrate that our proposed techniques outperform a random selection by up to 27 times in terms of the result quality improvement and the brute-force solution by up to 60 times in terms of the elapsed time.

Graph coloring is a fundamental NP-hard problem in graph theory. It has a wide range of real applications, such as Operations Research, Communication Network, Computational Biology and Compiler Optimization. Notable efforts have been spent on designing its approximation algorithms. Halldrsson proposed the algorithm (denoted as SampleIS) with the current best known approximation ratio. However, its time complexity is O(|G|3), where |G| is the number of vertices of a graph G. It is clear that SampleIS is not practical for large graphs. In this paper, we propose a practical vertex-cut based coloring technique (VColor) for coloring large graphs. First, we partition G into k connected components (CCs) of a small size s by removing a vertex-cut component (VCC). For each CC, we apply our novel coloring algorithm, based on maximal independent set enumeration. The approximation ratio and the time complexity for coloring the k CCs are log s + 1 and O(ks23s/3), respectively, whereas those of SampleIS are ks(log log ks)2/ log3 ks and O(k3s3). For the VCC, we simply apply SampleIS. To combine the colorings of the CCs and the VCC, we propose a maximum matching based algorithm. Second, in the context of a database of graphs, users may color many graphs. We propose an optimization technique, inspired by multi-query optimization, for coloring a set of graphs. We design a VP hierarchy (VPH) to represent the common subgraphs as the common CCs. Third, we propose techniques for determining the optimal values of the parameters of VColor. Our extensive experimental evaluation on real-world graphs confirms the efficiency and/or effectiveness of our proposed techniques. In particular, VColor is more than 500 times faster than SampleIS, and the number of colors used are comparable on real graphs Yeast and LS.

Subgraph similarity search is used in graph databases to retrieve graphs whose subgraphs are similar to a given query graph. It has been proven successful in a wide range of applications including bioinformatics and chem-informatics, etc. Due to the cost of providing efficient similarity search services on ever-increasing graph data, database outsourcing is apparently an appealing solution to database owners. Unfortunately, query service providers may be untrusted or compromised by attacks. To our knowledge, no studies have been carried out on the authentication of the search. In this paper, we propose authentication techniques that follow the popular filtering-and-verification framework. We propose an authentication-friendly metric index called GMTree. Specifically, we transform the similarity search into a search in a graph metric space and derive small verification objects (VOs) to-be-transmitted to query clients. To further optimize GMTree, we propose a sampling-based pivot selection method and an authenticated version of MCS computation. Our comprehensive experiments verified the effectiveness and efficiency of our proposed techniques.

Views and their updates have long been a fundamental technology required in a wide range of applications. However, it has been known that updates through views is a classical intractable problem. In this paper, we propose a novel, data-oriented approach to this problem that provides a practical support for view updates. In particular, we propose a summarization of the source database of views, which serves as an update filter. The update filter aims to efficiently reject untranslatable view updates by estimating the side effects of the updates, thereby avoiding costly translation analysis. For applications where estimation errors are not preferred, our update filter can be tuned to be exact. In this paper, we present our approach with SPJ views, an important class of view definitions. We first revise the notion of estimation errors to quantify the filter's qualities. We then propose a novel join cardinality summary (JCard) derived from cardinality equivalence. An estimation algorithm is proposed. Finally, we present optimizations enabling the construction of an accurate JCard through heuristics and sampling. Our extensive experiments show that update filters are efficient and can be easily tuned to produce accurate estimations on TPC-H and DBLP.

Due to the recent advances in graph databases, a large number of ad-hoc indexes for a fundamental query, in particular, reachability query, have been proposed. The performances of these indexes on different graphs have known to be very different. Worst still, deriving an accurate cost model for selecting the optimal index of a graph database appears to be a daunting task. In this paper, we propose a hierarchical prediction framework, based on neural networks and a set of graph features and a knowledge base on past predictions, to determine the optimal index for a graph database. For ease of presentation, we propose our framework with three structurally distinguishable indexes. Our experiments show that our framework is accurate.

Recent applications including the Semantic Web, Web ontology and XML have sparked a renewed interest on graph-structured databases. Among others, twig queries have been a popular tool for retrieving subgraphs from graph-structured databases. To optimize twig queries, selectivity estimation has been a crucial and classical step. However, the majority of existing works on selectivity estimation focuses on relational and tree data. In this paper, we investigate selectivity estimation of twig queries on possibly cyclic graph data. To facilitate selectivity estimation on cyclic graphs, we propose a matrix representation of graphs derived from prime labeling - a scheme for reachability queries on directed acyclic graphs. With this representation, we exploit the consecutive ones property (C1P) of matrices. As a consequence, a node is mapped to a point in a two-dimensional space whereas a query is mapped to multiple points. We adopt histograms for scalable selectivity estimation. We perform an extensive experimental evaluation on the proposed technique and show that our technique controls the estimation error under 1.3% on XMARK and DBLP, which is more accurate than previous techniques. On TREEBANK, we produce RMSE and NRMSE 6.8 times smaller than previous techniques.