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Recent advancements in large language model (LLM)-powered agents have shown that collective intelligence can significantly outperform individual capabilities, largely attributed to the meticulously designed inter-agent communication topologies. Though impressive in performance, existing multi-agent pipelines inherently introduce substantial token overhead, as well as increased economic costs, which pose challenges for their large-scale deployments. In response to this challenge, we propose an economical, simple, and robust multi-agent communication framework, termed $\texttt{AgentPrune}$, which can seamlessly integrate into mainstream multi-agent systems and prunes redundant or even malicious communication messages. Technically, $\texttt{AgentPrune}$ is the first to identify and formally define the \textit{communication redundancy} issue present in current LLM-based multi-agent pipelines, and efficiently performs one-shot pruning on the spatial-temporal message-passing graph, yielding a token-economic and high-performing communication topology. Extensive experiments across six benchmarks demonstrate that $\texttt{AgentPrune}$ \textbf{(I)} achieves comparable results as state-of-the-art topologies at merely $\$5.6$ cost compared to their $\$43.7$, \textbf{(II)} integrates seamlessly into existing multi-agent frameworks with $28.1\%\sim72.8\%\downarrow$ token reduction, and \textbf{(III)} successfully defend against two types of agent-based adversarial attacks with $3.5\%\sim10.8\%\uparrow$ performance boost.

Proximity graphs (PG) have gained increasing popularity as the state-of-the-art (SOTA) solutions to $k$-approximate nearest neighbor ($k$-ANN) search on high-dimensional data, which serves as a fundamental function in various fields, e.g. information retrieval and retrieval-augmented generation~(RAG). Although PG-based approaches have the best $k$-ANN search performance, their index construction cost is superlinear to the number of points, since they have to identify close neighbors for each point to establish the edges. Such superlinear cost substantially limits their scalability in the era of big data. Hence, the goal of this paper is to accelerate the construction of PG-based methods without compromising their $k$-ANN search performance. To achieve this goal, two mainstream categories of PG are revisited: relative neighborhood graph (RNG) and navigable small world graph (NSWG). By revisiting their construction process, we find the issues of construction efficiency. To address these issues, we propose a new construction framework with a novel pruning strategy for edge selection, which accelerates RNG construction while keeping its $k$-ANN search performance. Then, we integrate this framework into NSWG construction to enhance both the construction efficiency and $k$-ANN search performance. Moreover, extensive experiments are conducted to validate our construction framework for both RNG and NSWG. The results demonstrate that it significantly reduces the PG construction cost, achieving up to 5.6x speedup while not compromising the $k$-ANN search performance.

With the emergence of various molecular tasks and massive datasets, how to perform efficient training has become an urgent yet under-explored issue in the area. Data pruning (DP), as an oft-stated approach to saving training burdens, filters out less influential samples to form a coreset for training. However, the increasing reliance on pretrained models for molecular tasks renders traditional in-domain DP methods incompatible. Therefore, we propose a Molecular data Pruning framework for enhanced Generalization (MolPeg), which focuses on the source-free data pruning scenario, where data pruning is applied with pretrained models. By maintaining two models with different updating paces during training, we introduce a novel scoring function to measure the informativeness of samples based on the loss discrepancy. As a plug-and-play framework, MolPeg realizes the perception of both source and target domain and consistently outperforms existing DP methods across four downstream tasks. Remarkably, it can surpass the performance obtained from full-dataset training, even when pruning up to 60-70% of the data on HIV and PCBA dataset. Our work suggests that the discovery of effective data-pruning metrics could provide a viable path to both enhanced efficiency and superior generalization in transfer learning., Comment: 20 pages, under review

Enhancing the efficiency of iterative computation on graphs has garnered considerable attention in both industry and academia. Nonetheless, the majority of efforts focus on expediting iterative computation by minimizing the running time per iteration step, ignoring the optimization of the number of iteration rounds, which is a crucial aspect of iterative computation. We experimentally verified the correlation between the vertex processing order and the number of iterative rounds, thus making it possible to reduce the number of execution rounds for iterative computation. In this paper, we propose a graph reordering method, GoGraph, which can construct a well-formed vertex processing order effectively reducing the number of iteration rounds and, consequently, accelerating iterative computation. Before delving into GoGraph, a metric function is introduced to quantify the efficiency of vertex processing order in accelerating iterative computation. This metric reflects the quality of the processing order by counting the number of edges whose source precedes the destination. GoGraph employs a divide-and-conquer mindset to establish the vertex processing order by maximizing the value of the metric function. Our experimental results show that GoGraph outperforms current state-of-the-art reordering algorithms by 1.83x on average (up to 3.34x) in runtime., Comment: 14 pages, 13 figures, 2 tables; accepted for publication in ICDE 2024

Driven by the powerful representation ability of Graph Neural Networks (GNNs), plentiful GNN models have been widely deployed in many real-world applications. Nevertheless, due to distribution disparities between different demographic groups, fairness in high-stake decision-making systems is receiving increasing attention. Although lots of recent works devoted to improving the fairness of GNNs and achieved considerable success, they all require significant architectural changes or additional loss functions requiring more hyper-parameter tuning. Surprisingly, we find that simple re-balancing methods can easily match or surpass existing fair GNN methods. We claim that the imbalance across different demographic groups is a significant source of unfairness, resulting in imbalanced contributions from each group to the parameters updating. However, these simple re-balancing methods have their own shortcomings during training. In this paper, we propose FairGB, Fair Graph Neural Network via re-Balancing, which mitigates the unfairness of GNNs by group balancing. Technically, FairGB consists of two modules: counterfactual node mixup and contribution alignment loss. Firstly, we select counterfactual pairs across inter-domain and inter-class, and interpolate the ego-networks to generate new samples. Guided by analysis, we can reveal the debiasing mechanism of our model by the causal view and prove that our strategy can make sensitive attributes statistically independent from target labels. Secondly, we reweigh the contribution of each group according to gradients. By combining these two modules, they can mutually promote each other. Experimental results on benchmark datasets show that our method can achieve state-of-the-art results concerning both utility and fairness metrics. Code is available at https://github.com/ZhixunLEE/FairGB., Comment: Accepted by SIGKDD 2024, research track

In health, most large language model (LLM) research has focused on clinical tasks. However, mobile and wearable devices, which are rarely integrated into such tasks, provide rich, longitudinal data for personal health monitoring. Here we present Personal Health Large Language Model (PH-LLM), fine-tuned from Gemini for understanding and reasoning over numerical time-series personal health data. We created and curated three datasets that test 1) production of personalized insights and recommendations from sleep patterns, physical activity, and physiological responses, 2) expert domain knowledge, and 3) prediction of self-reported sleep outcomes. For the first task we designed 857 case studies in collaboration with domain experts to assess real-world scenarios in sleep and fitness. Through comprehensive evaluation of domain-specific rubrics, we observed that Gemini Ultra 1.0 and PH-LLM are not statistically different from expert performance in fitness and, while experts remain superior for sleep, fine-tuning PH-LLM provided significant improvements in using relevant domain knowledge and personalizing information for sleep insights. We evaluated PH-LLM domain knowledge using multiple choice sleep medicine and fitness examinations. PH-LLM achieved 79% on sleep and 88% on fitness, exceeding average scores from a sample of human experts. Finally, we trained PH-LLM to predict self-reported sleep quality outcomes from textual and multimodal encoding representations of wearable data, and demonstrate that multimodal encoding is required to match performance of specialized discriminative models. Although further development and evaluation are necessary in the safety-critical personal health domain, these results demonstrate both the broad knowledge and capabilities of Gemini models and the benefit of contextualizing physiological data for personal health applications as done with PH-LLM., Comment: 72 pages

Cold-start rating prediction is a fundamental problem in recommender systems that has been extensively studied. Many methods have been proposed that exploit explicit relations among existing data, such as collaborative filtering, social recommendations and heterogeneous information network, to alleviate the data insufficiency issue for cold-start users and items. However, the explicit relations constructed based on data between different roles may be unreliable and irrelevant, which limits the performance ceiling of the specific recommendation task. Motivated by this, in this paper, we propose a flexible framework dubbed heterogeneous interaction rating network (HIRE). HIRE dose not solely rely on the pre-defined interaction pattern or the manually constructed heterogeneous information network. Instead, we devise a Heterogeneous Interaction Module (HIM) to jointly model the heterogeneous interactions and directly infer the important interactions via the observed data. In the experiments, we evaluate our model under three cold-start settings on three real-world datasets. The experimental results show that HIRE outperforms other baselines by a large margin. Furthermore, we visualize the inferred interactions of HIRE to confirm the contribution of our model., Comment: 14 pages, 9 figures

With the development of foundation models such as large language models, zero-shot transfer learning has become increasingly significant. This is highlighted by the generative capabilities of NLP models like GPT-4, and the retrieval-based approaches of CV models like CLIP, both of which effectively bridge the gap between seen and unseen data. In the realm of graph learning, the continuous emergence of new graphs and the challenges of human labeling also amplify the necessity for zero-shot transfer learning, driving the exploration of approaches that can generalize across diverse graph data without necessitating dataset-specific and label-specific fine-tuning. In this study, we extend such paradigms to zero-shot transferability in graphs by introducing ZeroG, a new framework tailored to enable cross-dataset generalization. Addressing the inherent challenges such as feature misalignment, mismatched label spaces, and negative transfer, we leverage a language model to encode both node attributes and class semantics, ensuring consistent feature dimensions across datasets. We also propose a prompt-based subgraph sampling module that enriches the semantic information and structure information of extracted subgraphs using prompting nodes and neighborhood aggregation, respectively. We further adopt a lightweight fine-tuning strategy that reduces the risk of overfitting and maintains the zero-shot learning efficacy of the language model. The results underscore the effectiveness of our model in achieving significant cross-dataset zero-shot transferability, opening pathways for the development of graph foundation models. Codes and data are available at https://github.com/NineAbyss/ZeroG., Comment: Accepted by SIGKDD 2024, research track

Graph plays a significant role in representing and analyzing complex relationships in real-world applications such as citation networks, social networks, and biological data. Recently, Large Language Models (LLMs), which have achieved tremendous success in various domains, have also been leveraged in graph-related tasks to surpass traditional Graph Neural Networks (GNNs) based methods and yield state-of-the-art performance. In this survey, we first present a comprehensive review and analysis of existing methods that integrate LLMs with graphs. First of all, we propose a new taxonomy, which organizes existing methods into three categories based on the role (i.e., enhancer, predictor, and alignment component) played by LLMs in graph-related tasks. Then we systematically survey the representative methods along the three categories of the taxonomy. Finally, we discuss the remaining limitations of existing studies and highlight promising avenues for future research. The relevant papers are summarized and will be consistently updated at: https://github.com/yhLeeee/Awesome-LLMs-in-Graph-tasks., Comment: IJCAI 2024 Survey Track

Graph Structure Learning (GSL) has recently garnered considerable attention due to its ability to optimize both the parameters of Graph Neural Networks (GNNs) and the computation graph structure simultaneously. Despite the proliferation of GSL methods developed in recent years, there is no standard experimental setting or fair comparison for performance evaluation, which creates a great obstacle to understanding the progress in this field. To fill this gap, we systematically analyze the performance of GSL in different scenarios and develop a comprehensive Graph Structure Learning Benchmark (GSLB) curated from 20 diverse graph datasets and 16 distinct GSL algorithms. Specifically, GSLB systematically investigates the characteristics of GSL in terms of three dimensions: effectiveness, robustness, and complexity. We comprehensively evaluate state-of-the-art GSL algorithms in node- and graph-level tasks, and analyze their performance in robust learning and model complexity. Further, to facilitate reproducible research, we have developed an easy-to-use library for training, evaluating, and visualizing different GSL methods. Empirical results of our extensive experiments demonstrate the ability of GSL and reveal its potential benefits on various downstream tasks, offering insights and opportunities for future research. The code of GSLB is available at: https://github.com/GSL-Benchmark/GSLB., Comment: Accepted by NeurIPS Datasets and Benchmarks Track 2023

Querying cohesive subgraphs on temporal graphs (e.g., social network, finance network, etc.) with various conditions has attracted intensive research interests recently. In this paper, we study a novel Temporal $(k,\mathcal{X})$-Core Query (TXCQ) that extends a fundamental Temporal $k$-Core Query (TCQ) proposed in our conference paper by optimizing or constraining an arbitrary metric $\mathcal{X}$ of $k$-core, such as size, engagement, interaction frequency, time span, burstiness, periodicity, etc. Our objective is to address specific TXCQ instances with conditions on different $\mathcal{X}$ in a unified algorithm framework that guarantees scalability. For that, this journal paper proposes a taxonomy of measurement $\mathcal{X}(\cdot)$ and achieve our objective using a two-phase framework while $\mathcal{X}(\cdot)$ is time-insensitive or time-monotonic. Specifically, Phase 1 still leverages the query processing algorithm of TCQ to induce all distinct $k$-cores during a given time range, and meanwhile locates the ``time zones'' in which the cores emerge. Then, Phase 2 conducts fast local search and $\mathcal{X}$ evaluation in each time zone with respect to the time insensitivity or monotonicity of $\mathcal{X}(\cdot)$. By revealing two insightful concepts named tightest time interval and loosest time interval that bound time zones, the redundant core induction and unnecessary $\mathcal{X}$ evaluation in a zone can be reduced dramatically. Our experimental results demonstrate that TXCQ can be addressed as efficiently as TCQ, which achieves the latest state-of-the-art performance, by using a general algorithm framework that leaves $\mathcal{X}(\cdot)$ as a user-defined function., Comment: arXiv admin note: substantial text overlap with arXiv:2301.03770

Despite the popularity of product recommendations on online investment platforms, few studies have explored their impact on investor behaviors. Using data from a global e-commerce platform, we apply regression discontinuity design to causally examine the effects of product recommendations on online investors' mutual fund investments. Our findings indicate that recommended funds experience a significant rise in purchases, especially among low socioeconomic status investors who are most influenced by these recommendations. However, investors tend to suffer significantly worse investment returns after purchasing recommended funds, and this negative impact is also most significant for investors with low socioeconomic status. To explain this disparity, we find investors tend to gather less information and expend reduced effort in fund research when buying recommended funds. Furthermore, investors' redemption timing of recommended funds is less optimal than non-recommended funds. We also find that recommended funds experience a larger return reversal than non-recommended funds. In conclusion, product recommendations make investors behave more irrationally and these negative consequences are most significant for investors with low socioeconomic status, which can amplify wealth inequality among investors in financial markets.

On-demand service platforms face a challenging problem of forecasting a large collection of high-frequency regional demand data streams that exhibit instabilities. This paper develops a novel forecast framework that is fast and scalable, and automatically assesses changing environments without human intervention. We empirically test our framework on a large-scale demand data set from a leading on-demand delivery platform in Europe, and find strong performance gains from using our framework against several industry benchmarks, across all geographical regions, loss functions, and both pre- and post-Covid periods. We translate forecast gains to economic impacts for this on-demand service platform by computing financial gains and reductions in computing costs.

Querying cohesive subgraphs on temporal graphs with various time constraints has attracted intensive research interests recently. In this paper, we study a novel Temporal k-Core Query (TCQ) problem: given a time interval, find all distinct k-cores that exist within any subintervals from a temporal graph, which generalizes the previous historical k-core query. This problem is challenging because the number of subintervals increases quadratically to the span of time interval. For that, we propose a novel Temporal Core Decomposition (TCD) algorithm that decrementally induces temporal k-cores from the previously induced ones and thus reduces "intra-core" redundant computation significantly. Then, we introduce an intuitive concept named Tightest Time Interval (TTI) for temporal k-core, and design an optimization technique with theoretical guarantee that leverages TTI as a key to predict which subintervals will induce duplicated k-cores and prunes the subintervals completely in advance, thereby eliminating "inter-core" redundant computation. The complexity of optimized TCD (OTCD) algorithm no longer depends on the span of query time interval but only the scale of final results, which means OTCD algorithm is scalable. Moreover, we propose a compact in-memory data structure named Temporal Edge List (TEL) to implement OTCD algorithm efficiently in physical level with bounded memory requirement. TEL organizes temporal edges in a "timeline" and can be updated instantly when new edges arrive, and thus our approach can also deal with dynamic temporal graphs. We compare OTCD algorithm with the incremental historical k-core query on several real-world temporal graphs, and observe that OTCD algorithm outperforms it by three orders of magnitude, even though OTCD algorithm needs none precomputed index., Comment: This paper has been accepted by PVLDB(2023)

In modern graph analytics, the shortest path is a fundamental concept. Numerous \rrev{recent works} concentrate mostly on the distance of these shortest paths. Nevertheless, in the era of betweenness analysis, the counting of the shortest path between $s$ and $t$ is equally crucial. \rrev{It} is \rev{also} an important issue in the area of graph databases. In recent years, several studies have been conducted in an effort to tackle such issues. Nonetheless, the present technique faces a considerable barrier to parallel due to the dependencies in the index construction stage, hence limiting its application possibilities and wasting the potential hardware performance. To address this problem, we provide a parallel shortest path counting method that could avoid these dependencies and obtain approximately linear index time speedup as the number of threads increases. Our empirical evaluations verify the efficiency and effectiveness.

Community search is a problem that seeks cohesive and connected subgraphs in a graph that satisfy certain topology constraints, e.g., degree constraints. The majority of existing works focus exclusively on the topology and ignore the nodes' influence in the communities. To tackle this deficiency, influential community search is further proposed to include the node's influence. Each node has a weight, namely influence value, in the influential community search problem to represent its network influence. The influence value of a community is produced by an aggregated function, e.g., max, min, avg, and sum, over the influence values of the nodes in the same community. The objective of the influential community search problem is to locate the top-r communities with the highest influence values while satisfying the topology constraints. Existing studies on influential community search have several limitations: (i) they focus exclusively on simple aggregation functions such as min, which may fall short of certain requirements in many real-world scenarios, and (ii) they impose no limitation on the size of the community, whereas most real-world scenarios do. This motivates us to conduct a new study to fill this gap. We consider the problem of identifying the top-r influential communities with/without size constraints while using more complicated aggregation functions such as sum or avg. We give a theoretical analysis demonstrating the hardness of the problems and propose efficient and effective heuristic solutions for our topr influential community search problems. Extensive experiments on real large graphs demonstrate that our proposed solution is significantly more efficient than baseline solutions.

Deep Learning (DL) has achieved great success in many real applications. Despite its success, there are some main problems when deploying advanced DL models in database systems, such as hyper-parameters tuning, the risk of overfitting, and lack of prediction uncertainty. In this paper, we study cardinality estimation for SQL queries with a focus on uncertainty, which we believe is important in database systems when dealing with a large number of user queries on various applications. With uncertainty ensured, instead of trusting an estimator learned as it is, a query optimizer can explore other options when the estimator learned has a large variance, and it also becomes possible to update the estimator to improve its prediction in areas with high uncertainty. The approach we explore is different from the direction of deploying sophisticated DL models in database systems to build cardinality estimators. We employ Bayesian deep learning (BDL), which serves as a bridge between Bayesian inference and deep learning.The prediction distribution by BDL provides principled uncertainty calibration for the prediction. In addition, when the network width of a BDL model goes to infinity, the model performs equivalent to Gaussian Process (GP). This special class of BDL, known as Neural Network Gaussian Process (NNGP), inherits the advantages of Bayesian approach while keeping universal approximation of neural network, and can utilize a much larger model space to model distribution-free data as a nonparametric model. We show that our uncertainty-aware NNGP estimator achieves high accuracy, can be built very fast, and is robust to query workload shift, in our extensive performance studies by comparing with the existing approaches.

In this work, we study the problem of co-optimize communication, pre-computing, and computation cost in one-round multi-way join evaluation. We propose a multi-way join approach ADJ (Adaptive Distributed Join) for complex join which finds one optimal query plan to process by exploring cost-effective partial results in terms of the trade-off between pre-computing, communication, and computation.We analyze the input relations for a given join query and find one optimal over a set of query plans in some specific form, with high-quality cost estimation by sampling. Our extensive experiments confirm that ADJ outperforms the existing multi-way join methods by up to orders of magnitude., Comment: Long Version

Integrating machine learning techniques into RDBMSs is an important task since there are many real applications that require modeling (e.g., business intelligence, strategic analysis) as well as querying data in RDBMSs. In this paper, we provide an SQL solution that has the potential to support different machine learning modelings. As an example, we study how to support unsupervised probabilistic modeling, that has a wide range of applications in clustering, density estimation and data summarization, and focus on Expectation-Maximization (EM) algorithms, which is a general technique for finding maximum likelihood estimators. To train a model by EM, it needs to update the model parameters by an E-step and an M-step in a while-loop iteratively until it converges to a level controled by some threshold or repeats a certain number of iterations. To support EM in RDBMSs, we show our answers to the matrix/vectors representations in RDBMSs, the relational algebra operations to support the linear algebra operations required by EM, parameters update by relational algebra, and the support of a while-loop. It is important to note that the SQL'99 recursion cannot be used to handle such a while-loop since the M-step is non-monotonic. In addition, assume that a model has been trained by an EM algorithm, we further design an automatic in-database model maintenance mechanism to maintain the model when the underlying training data changes.We have conducted experimental studies and will report our findings in this paper., Comment: 12 pages

The Travelling Salesman Problem (TSP) is a classical NP-hard problem and has broad applications in many disciplines and industries. In a large scale location-based services system, users issue TSP queries concurrently, where a TSP query is a TSP instance with $n$ points. In the literature, many advanced TSP solvers are developed to find high-quality solutions. Such solvers can solve some TSP instances efficiently but may take an extremely long time for some other instances. Due to the diversity of TSP instances, it is well-known that there exists no universal best solver dominating all other solvers on all possible TSP instances. To solve TSP efficiently, in addition to developing new TSP solvers, it needs to find a per-instance solver for each TSP instance, which is known as the TSP solver selection problem. In this paper, for the first time, we propose a deep learning framework, \CTAS, for TSP solver selection in an end-to-end manner. Specifically, \CTAS exploits deep convolutional neural networks to extract informative features from TSP instances and involves data argumentation strategies to handle the scarcity of labeled TSP instances. Moreover, to support large scale TSP solver selection, we construct a challenging TSP benchmark dataset with 6,000 instances, which is known as the largest TSP benchmark. Our \CTAS achieves over 2$\times$ speedup of the average running time, comparing the single best solver, and outperforms the state-of-the-art statistical models.

Named entity linking is to map an ambiguous mention in documents to an entity in a knowledge base. The named entity linking is challenging, given the fact that there are multiple candidate entities for a mention in a document. It is difficult to link a mention when it appears multiple times in a document, since there are conflicts by the contexts around the appearances of the mention. In addition, it is difficult since the given training dataset is small due to the reason that it is done manually to link a mention to its mapping entity. In the literature, there are many reported studies among which the recent embedding methods learn vectors of entities from the training dataset at document level. To address these issues, we focus on how to link entity for mentions at a sentence level, which reduces the noises introduced by different appearances of the same mention in a document at the expense of insufficient information to be used. We propose a new unified embedding method by maximizing the relationships learned from knowledge graphs. We confirm the effectiveness of our method in our experimental studies.

Graph representation learning has achieved a remarkable success in many graph-based applications, such as node classification, link prediction, and community detection. These models are usually designed to preserve the vertex information at different granularity and reduce the problems in discrete space to some machine learning tasks in continuous space. However, regardless of the fruitful progress, for some kind of graph applications, such as graph compression and edge partition, it is very hard to reduce them to some graph representation learning tasks. Moreover, these problems are closely related to reformulating a global layout for a specific graph, which is an important NP-hard combinatorial optimization problem: graph ordering. In this paper, we propose to attack the graph ordering problem behind such applications by a novel learning approach. Distinguished from greedy algorithms based on predefined heuristics, we propose a neural network model: Deep Order Network (DON) to capture the hidden locality structure from partial vertex order sets. Supervised by sampled partial order, DON has the ability to infer unseen combinations. Furthermore, to alleviate the combinatorial explosion in the training space of DON and make the efficient partial vertex order sampling , we employ a reinforcement learning model: the Policy Network, to adjust the partial order sampling probabilities during the training phase of DON automatically. To this end, the Policy Network can improve the training efficiency and guide DON to evolve towards a more effective model automatically. Comprehensive experiments on both synthetic and real data validate that DON-RL outperforms the current state-of-the-art heuristic algorithm consistently. Two case studies on graph compression and edge partitioning demonstrate the potential power of DON-RL in real applications., Comment: 11 pages

The graph isomorphism is to determine whether two graphs are isomorphic. A closely related problem is automorphism detection, where an isomorphism between two graphs is a bijection between their vertex sets that preserves adjacency, and an automorphism is an isomorphism from a graph to itself. Applications of graph isomorphism/automorphism include database indexing, network simplification, network anonymization. By graph automorphism, we deal with symmetric subgraph matching (SSM), which is to find all subgraphs that are symmetric to a given subgraph in G. An application of SSM is to identify multiple seed sets that have the same influence power as a seed set found by influence maximization in a social network. To test two graphs for isomorphism, canonical labeling has been studied to relabel a graph in such a way that isomorphic graphs are identical after relabeling. Efficient canonical labeling algorithms have been designed by individualization-refinement. They enumerate all permutations using a search tree, and select the minimum as the canonical labeling, which prunes candidates during enumeration. Despite high performance in benchmark graphs, these algorithms face difficulties in handling massive graphs. In this paper, we design a new efficient canonical labeling algorithm DviCL. Different from previous algorithms, we take a divide-&-conquer approach to partition G. By partitioning G, an AutoTree is constructed, which preserves symmetric structures and the automorphism group of G. The canonical labeling for a tree node can be obtained by the canonical labeling of its child nodes, and the canonical labeling for the root is the one for G. Such AutoTree can also be effectively used to answer the automorphism group, symmetric subgraphs. We conducted extensive performance studies using 22 large graphs, and confirmed that DviCL is much more efficient and robust than the state-of-the-art.

We study the classic subgraph enumeration problem under distributed settings. Existing solutions either suffer from severe memory crisis or rely on large indexes, which makes them impractical for very large graphs. Most of them follow a synchronous model where the performance is often bottlenecked by the machine with the worst performance. Motivated by this, in this paper, we propose RADS, a Robust Asynchronous Distributed Subgraph enumeration system. RADS first identifies results that can be found using single-machine algorithms. This strategy not only improves the overall performance but also reduces network communication and memory cost. Moreover, RADS employs a novel region-grouped multi-round expand verify & filter framework which does not need to shuffle and exchange the intermediate results, nor does it need to replicate a large part of the data graph in each machine. This feature not only reduces network communication cost and memory usage, but also allows us to adopt simple strategies for memory control and load balancing, making it more robust. Several heuristics are also used in RADS to further improve the performance. Our experiments verified the superiority of RADS to state-of-the-art subgraph enumeration approaches.

Keyword search provides ordinary users an easy-to-use interface for querying RDF data. Given the input keywords, in this paper, we study how to assemble a query graph that is to represent user's query intention accurately and efficiently. Based on the input keywords, we first obtain the elementary query graph building blocks, such as entity/class vertices and predicate edges. Then, we formally define the query graph assembly (QGA) problem. Unfortunately, we prove theoretically that QGA is a NP-complete problem. In order to solve that, we design some heuristic lower bounds and propose a bipartite graph matching-based best-first search algorithm. The algorithm's time complexity is $O(k^{2l} \cdot l^{3l})$, where $l$ is the number of the keywords and $k$ is a tunable parameter, i.e., the maximum number of candidate entity/class vertices and predicate edges allowed to match each keyword. Although QGA is intractable, both $l$ and $k$ are small in practice. Furthermore, the algorithm's time complexity does not depend on the RDF graph size, which guarantees the good scalability of our system in large RDF graphs. Experiments on DBpedia and Freebase confirm the superiority of our system on both effectiveness and efficiency.