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Graph representation learning (GRL) is to encode graph elements into informative vector representations, which can be used in downstream tasks for analyzing graph-structured data and has seen extensive applications in various domains. However, the majority of extant studies on GRL are geared towards generating node representations, which cannot be readily employed to perform edge-based analytics tasks in edge-attributed bipartite graphs (EABGs) that pervade the real world, e.g., spam review detection in customer-product reviews and identifying fraudulent transactions in user-merchant networks. Compared to node-wise GRL, learning edge representations (ERL) on such graphs is challenging due to the need to incorporate the structure and attribute semantics from the perspective of edges while considering the separate influence of two heterogeneous node sets U and V in bipartite graphs. To our knowledge, despite its importance, limited research has been devoted to this frontier, and existing workarounds all suffer from sub-par results. Motivated by this, this paper designs EAGLE, an effective ERL method for EABGs. Building on an in-depth and rigorous theoretical analysis, we propose the factorized feature propagation (FFP) scheme for edge representations with adequate incorporation of long-range dependencies of edges/features without incurring tremendous computation overheads. We further ameliorate FFP as a dual-view FFP by taking into account the influences from nodes in U and V severally in ERL. Extensive experiments on 5 real datasets showcase the effectiveness of the proposed EAGLE models in semi-supervised edge classification tasks. In particular, EAGLE can attain a considerable gain of at most 38.11% in AP and 1.86% in AUC when compared to the best baselines., Comment: 11 pages. Full version of the research paper accepted to KDD 2024

In this paper, we study cascading failures in power grids through the lens of information diffusion models. Similar to the spread of rumors or influence in an online social network, it has been observed that failures (outages) in a power grid can spread contagiously, driven by viral spread mechanisms. We employ a stochastic diffusion model that is Markovian (memoryless) and local (the activation of one node, i.e., transmission line, can only be caused by its neighbors). Our model integrates viral diffusion principles with physics-based concepts, by correlating the diffusion weights (contagion probabilities between transmission lines) with the hyperparametric Information Cascades (IC) model. We show that this diffusion model can be learned from traces of cascading failures, enabling accurate modeling and prediction of failure propagation. This approach facilitates actionable information through well-understood and efficient graph analysis methods and graph diffusion simulations. Furthermore, by leveraging the hyperparametric model, we can predict diffusion and mitigate the risks of cascading failures even in unseen grid configurations, whereas existing methods falter due to a lack of training data. Extensive experiments based on a benchmark power grid and simulations therein show that our approach effectively captures the failure diffusion phenomena and guides decisions to strengthen the grid, reducing the risk of large-scale cascading failures. Additionally, we characterize our model's sample complexity, improving upon the existing bound., Comment: KDD 2024

The study of continuous-time information diffusion has been an important area of research for many applications in recent years. When only the diffusion traces (cascades) are accessible, cascade-based network inference and influence estimation are two essential problems to explore. Alas, existing methods exhibit limited capability to infer and process networks with more than a few thousand nodes, suffering from scalability issues. In this paper, we view the diffusion process as a continuous-time dynamical system, based on which we establish a continuous-time diffusion model. Subsequently, we instantiate the model to a scalable and effective framework (FIM) to approximate the diffusion propagation from available cascades, thereby inferring the underlying network structure. Furthermore, we undertake an analysis of the approximation error of FIM for network inference. To achieve the desired scalability for influence estimation, we devise an advanced sampling technique and significantly boost the efficiency. We also quantify the effect of the approximation error on influence estimation theoretically. Experimental results showcase the effectiveness and superior scalability of FIM on network inference and influence estimation.

Influence maximization (IM) aims to identify a small number of influential individuals to maximize the information spread and finds applications in various fields. It was first introduced in the context of viral marketing, where a company pays a few influencers to promote the product. However, apart from the cost factor, the capacity of individuals to consume content poses challenges for implementing IM in real-world scenarios. For example, players on online gaming platforms can only interact with a limited number of friends. In addition, we observe that in these scenarios, (i) the initial adopters of promotion are likely to be the friends of influencers rather than the influencers themselves, and (ii) existing IM solutions produce sub-par results with high computational demands. Motivated by these observations, we propose a new IM variant called capacity constrained influence maximization (CIM), which aims to select a limited number of influential friends for each initial adopter such that the promotion can reach more users. To solve CIM effectively, we design two greedy algorithms, MG-Greedy and RR-Greedy, ensuring the $1/2$-approximation ratio. To improve the efficiency, we devise the scalable implementation named RR-OPIM+ with $(1/2-\epsilon)$-approximation and near-linear running time. We extensively evaluate the performance of 9 approaches on 6 real-world networks, and our solutions outperform all competitors in terms of result quality and running time. Additionally, we deploy RR-OPIM+ to online game scenarios, which improves the baseline considerably., Comment: The technical report of the paper entitled 'Capacity Constrained Influence Maximization in Social Networks' in SIGKDD'23

Graph Neural Networks (GNNs) have shown superior performance for semi-supervised learning of numerous web applications, such as classification on web services and pages, analysis of online social networks, and recommendation in e-commerce. The state of the art derives representations for all nodes in graphs following the same diffusion (message passing) model without discriminating their uniqueness. However, (i) labeled nodes involved in model training usually account for a small portion of graphs in the semisupervised setting, and (ii) different nodes locate at different graph local contexts and it inevitably degrades the representation qualities if treating them undistinguishedly in diffusion. To address the above issues, we develop NDM, a universal node-wise diffusion model, to capture the unique characteristics of each node in diffusion, by which NDM is able to yield high-quality node representations. In what follows, we customize NDM for semisupervised learning and design the NIGCN model. In particular, NIGCN advances the efficiency significantly since it (i) produces representations for labeled nodes only and (ii) adopts well-designed neighbor sampling techniques tailored for node representation generation. Extensive experimental results on various types of web datasets, including citation, social and co-purchasing graphs, not only verify the state-of-the-art effectiveness of NIGCN but also strongly support the remarkable scalability of NIGCN. In particular, NIGCN completes representation generation and training within 10 seconds on the dataset with hundreds of millions of nodes and billions of edges, up to orders of magnitude speedups over the baselines, while achieving the highest F1-scores on classification.

Existing graph contrastive learning (GCL) techniques typically require two forward passes for a single instance to construct the contrastive loss, which is effective for capturing the low-frequency signals of node features. Such a dual-pass design has shown empirical success on homophilic graphs, but its effectiveness on heterophilic graphs, where directly connected nodes typically have different labels, is unknown. In addition, existing GCL approaches fail to provide strong performance guarantees. Coupled with the unpredictability of GCL approaches on heterophilic graphs, their applicability in real-world contexts is limited. Then, a natural question arises: Can we design a GCL method that works for both homophilic and heterophilic graphs with a performance guarantee? To answer this question, we theoretically study the concentration property of features obtained by neighborhood aggregation on homophilic and heterophilic graphs, introduce the single-pass augmentation-free graph contrastive learning loss based on the property, and provide performance guarantees for the minimizer of the loss on downstream tasks. As a direct consequence of our analysis, we implement the Single-Pass Graph Contrastive Learning method (SP-GCL). Empirically, on 14 benchmark datasets with varying degrees of homophily, the features learned by the SP-GCL can match or outperform existing strong baselines with significantly less computational overhead, which demonstrates the usefulness of our findings in real-world cases., Comment: This article has been accepted for publication by the Transactions on Machine Learning Research. OpenReview at: https://openreview.net/forum?id=244KePn09i

Measuring the closeness of friendships is an important problem that finds numerous applications in practice. For example, online gaming platforms often host friendship-enhancing events in which a user (called the source) only invites his/her friend (called the target) to play together. In this scenario, the measure of friendship closeness is the backbone for understanding source invitation and target adoption behaviors, and underpins the recommendation of promising targets for the sources. However, most existing measures for friendship closeness only consider the information between the source and target but ignore the information of groups where they are located, which renders inferior results. To address this issue, we present new measures for friendship closeness based on the social identity theory (SIT), which describes the inclination that a target endorses behaviors of users inside the same group. The core of SIT is the process that a target assesses groups of users as them or us. Unfortunately, this process is difficult to be captured due to perceptual factors. To this end, we seamlessly reify the factors of SIT into quantitative measures, which consider local and global information of a target's group. We conduct extensive experiments to evaluate the effectiveness of our proposal against 8 state-of-the-art methods on 3 online gaming datasets. In particular, we demonstrate that our solution can outperform the best competitor on the behavior prediction (resp. online target recommendation) by up to 23.2% (resp. 34.2%) in the corresponding evaluation metric., Comment: CIKM 2022

Graph visualization is a vital component in many real-world applications (e.g., social network analysis, web mining, and bioinformatics) that enables users to unearth crucial insights from complex data. Lying in the core of graph visualization is the node distance measure, which determines how the nodes are placed on the screen. A favorable node distance measure should be informative in reflecting the full structural information between nodes and effective in optimizing visual aesthetics. However, existing node distance measures yield sub-par visualization quality as they fall short of these requirements. Moreover, most existing measures are computationally inefficient, incurring a long response time when visualizing large graphs. To overcome such deficiencies, we propose a new node distance measure, PDist, geared towards graph visualization by exploiting a well-known node proximity measure, personalized PageRank. Moreover, we propose an efficient algorithm Tau-Push for estimating PDist under both single- and multi-level visualization settings. With several carefully-designed techniques, Tau-Push offers non-trivial theoretical guarantees for estimation accuracy and computation complexity. Extensive experiments show that our proposal significantly outperforms 13 state-of-the-art graph visualization solutions on 12 real-world graphs in terms of both efficiency and effectiveness (including aesthetic criteria and user feedback). In particular, our proposal can interactively produce satisfactory visualizations within one second for billion-edge graphs., Comment: The technical report of the paper entitled 'Effective and Efficient PageRank-based Positioning for Graph Visualization' in SIGMOD'23

Given a graph G where each node is associated with a set of attributes, and a parameter k specifying the number of output clusters, k-attributed graph clustering (k-AGC) groups nodes in G into k disjoint clusters, such that nodes within the same cluster share similar topological and attribute characteristics, while those in different clusters are dissimilar. This problem is challenging on massive graphs, e.g., with millions of nodes and billions of edges. For such graphs, existing solutions either incur prohibitively high costs, or produce clustering results with compromised quality. In this paper, we propose ACMin, an effective approach to k-AGC that yields high-quality clusters with cost linear to the size of the input graph G. The main contributions of ACMin are twofold: (i) a novel formulation of the k-AGC problem based on an attributed multi-hop conductance quality measure custom-made for this problem setting, which effectively captures cluster coherence in terms of both topological proximities and attribute similarities, and (ii) a linear-time optimization solver that obtains high-quality clusters iteratively, based on efficient matrix operations such as orthogonal iterations, an alternative optimization approach, as well as an initialization technique that significantly speeds up the convergence of ACMin in practice. Extensive experiments, comparing 11 competitors on 6 real datasets, demonstrate that ACMin consistently outperforms all competitors in terms of result quality measured against ground-truth labels, while being up to orders of magnitude faster. In particular, on the Microsoft Academic Knowledge Graph dataset with 265.2 million edges and 1.1 billion attribute values, ACMin outputs high-quality results for 5-AGC within 1.68 hours using a single CPU core, while none of the 11 competitors finish within 3 days., Comment: This is the full version of the paper appearing in TheWebConf 2021. The DOI assigned: https://doi.org/10.1145/3442381.3449875

Node classification on graphs is an important task in many practical domains. It usually requires labels for training, which can be difficult or expensive to obtain in practice. Given a budget for labelling, active learning aims to improve performance by carefully choosing which nodes to label. Previous graph active learning methods learn representations using labelled nodes and select some unlabelled nodes for label acquisition. However, they do not fully utilize the representation power present in unlabelled nodes. We argue that the representation power in unlabelled nodes can be useful for active learning and for further improving performance of active learning for node classification. In this paper, we propose a latent space clustering-based active learning framework for node classification (LSCALE), where we fully utilize the representation power in both labelled and unlabelled nodes. Specifically, to select nodes for labelling, our framework uses the K-Medoids clustering algorithm on a latent space based on a dynamic combination of both unsupervised features and supervised features. In addition, we design an incremental clustering module to avoid redundancy between nodes selected at different steps. Extensive experiments on five datasets show that our proposed framework LSCALE consistently and significantly outperforms the stateof-the-art approaches by a large margin., Comment: ECML-PKDD 2022

Given a graph $G$ with $n$ nodes and two nodes $u,v\in G$, the {\em CoSimRank} value $s(u,v)$ quantifies the similarity between $u$ and $v$ based on graph topology. Compared to SimRank, CoSimRank is shown to be more accurate and effective in many real-world applications, including synonym expansion, lexicon extraction, and entity relatedness in knowledge graphs. The computation of all pairwise CoSimRanks in $G$ is highly expensive and challenging. Existing solutions all focus on devising approximate algorithms for the computation of all pairwise CoSimRanks. To attain a desired absolute accuracy guarantee $\epsilon$, the state-of-the-art approximate algorithm for computing all pairwise CoSimRanks requires $O(n^3\log_2(\ln(\frac{1}{\epsilon})))$ time, which is prohibitively expensive even though $\epsilon$ is large. In this paper, we propose \rsim, a fast randomized algorithm for computing all pairwise CoSimRank values. The basic idea of \rsim is to approximate the $n\times n$ matrix multiplications in CoSimRank computation via random projection. Theoretically, \rsim runs in $O(\frac{n^2\ln(n)}{\epsilon^2}\ln(\frac{1}{\epsilon}))$ time and meanwhile ensures an absolute error of at most $\epsilon$ in each CoSimRank value in $G$ with a high probability. Extensive experiments using six real graphs demonstrate that \rsim is more than orders of magnitude faster than the state of the art. In particular, on a million-edge Twitter graph, \rsim answers the $\epsilon$-approximate ($\epsilon=0.1$) all pairwise CoSimRank query within 4 hours, using a single commodity server, while existing solutions fail to terminate within a day., Comment: full version of the paper titled "Fast Approximate All Pairwise CoSimRanks via Random Projection" published at WISE 2021

Given a graph G where each node is associated with a set of attributes, attributed network embedding (ANE) maps each node v in G to a compact vector Xv, which can be used in downstream machine learning tasks. Ideally, Xv should capture node v's affinity to each attribute, which considers not only v's own attribute associations, but also those of its connected nodes along edges in G. It is challenging to obtain high-utility embeddings that enable accurate predictions; scaling effective ANE computation to massive graphs pushes the difficulty of the problem to a whole new level. Existing solutions largely fail on such graphs, leading to prohibitive costs, low-quality embeddings, or both. This paper proposes PANE, an effective and scalable approach to ANE computation for massive graphs that achieves state-of-the-art result quality on multiple benchmark datasets. PANE obtains high scalability and effectiveness through 3 main algorithmic designs. First, it formulates the learning objective based on a novel random walk model for attributed networks. Second, PANE includes a highly efficient solver for the above optimization problem, whose key module is a carefully designed initialization of the embeddings, which drastically reduces the number of iterations required to converge. Finally, PANE utilizes multi-core CPUs through non-trivial parallelization of the above solver, which achieves scalability while retaining the high quality of the resulting embeddings. The performance of PANE depends upon the number of attributes in the input network. To handle large networks with numerous attributes, we further extend PANE to PANE++. Extensive experiments, comparing 10 existing approaches on 8 real datasets, demonstrate that PANE and PANE++ consistently outperform all existing methods in terms of result quality, while being orders of magnitude faster., Comment: Paper published in VLDBJ 2023. Extended version of PVLDB Vol. 14 (VLDB 2021) paper titled "Scaling Attributed Network Embedding to Massive Graphs"

Given a social network $G$ and an integer $k$, the influence maximization (IM) problem asks for a seed set $S$ of $k$ nodes from $G$ to maximize the expected number of nodes influenced via a propagation model. The majority of the existing algorithms for the IM problem are developed only under the non-adaptive setting, i.e., where all $k$ seed nodes are selected in one batch without observing how they influence other users in real world. In this paper, we study the adaptive IM problem where the $k$ seed nodes are selected in batches of equal size $b$, such that the $i$-th batch is identified after the actual influence results of the former $i-1$ batches are observed. In this paper, we propose the first practical algorithm for the adaptive IM problem that could provide the worst-case approximation guarantee of $1-\mathrm{e}^{\rho_b(\varepsilon-1)}$, where $\rho_b=1-(1-1/b)^b$ and $\varepsilon \in (0, 1)$ is a user-specified parameter. In particular, we propose a general framework AdaptGreedy that could be instantiated by any existing non-adaptive IM algorithms with expected approximation guarantee. Our approach is based on a novel randomized policy that is applicable to the general adaptive stochastic maximization problem, which may be of independent interest. In addition, we propose a novel non-adaptive IM algorithm called EPIC which not only provides strong expected approximation guarantee, but also presents superior performance compared with the existing IM algorithms. Meanwhile, we clarify some existing misunderstandings in recent work and shed light on further study of the adaptive IM problem. We conduct experiments on real social networks to evaluate our proposed algorithms comprehensively, and the experimental results strongly corroborate the superiorities and effectiveness of our approach., Comment: This paper is accepted by The VLDB Journal

Given a graph G and a node u in G, a single source SimRank query evaluates the similarity between u and every node v in G. Existing approaches to single source SimRank computation incur either long query response time, or expensive pre-computation, which needs to be performed again whenever the graph G changes. Consequently, to our knowledge none of them is ideal for scenarios in which (i) query processing must be done in realtime, and (ii) the underlying graph G is massive, with frequent updates. Motivated by this, we propose SimPush, a novel algorithm that answers single source SimRank queries without any pre-computation, and at the same time achieves significantly higher query processing speed than even the fastest known index-based solutions. Further, SimPush provides rigorous result quality guarantees, and its high performance does not rely on any strong assumption of the underlying graph. Specifically, compared to existing methods, SimPush employs a radically different algorithmic design that focuses on (i) identifying a small number of nodes relevant to the query, and subsequently (ii) computing statistics and performing residue push from these nodes only. We prove the correctness of SimPush, analyze its time complexity, and compare its asymptotic performance with that of existing methods. Meanwhile, we evaluate the practical performance of SimPush through extensive experiments on 8 real datasets. The results demonstrate that SimPush consistently outperforms all existing solutions, often by over an order of magnitude. In particular, on a commodity machine, SimPush answers a single source SimRank query on a web graph containing over 133 million nodes and 5.4 billion edges in under 62 milliseconds, with 0.00035 empirical error, while the fastest index-based competitor needs 1.18 seconds., Comment: To appear in PVLDB 2020

Given a social network $G$, the profit maximization (PM) problem asks for a set of seed nodes to maximize the profit, i.e., revenue of influence spread less the cost of seed selection. The target profit maximization (TPM) problem, which generalizes the PM problem, aims to select a subset of seed nodes from a target user set $T$ to maximize the profit. Existing algorithms for PM mostly consider the nonadaptive setting, where all seed nodes are selected in one batch without any knowledge on how they may influence other users. In this paper, we study TPM in adaptive setting, where the seed users are selected through multiple batches, such that the selection of a batch exploits the knowledge of actual influence in the previous batches. To acquire an overall understanding, we study the adaptive TPM problem under both the oracle model and the noise model, and propose ADG and AddATP algorithms to address them with strong theoretical guarantees, respectively. In addition, to better handle the sampling errors under the noise model, we propose the idea of hybrid error based on which we design a novel algorithm HATP that boosts the efficiency of AddATP significantly. We conduct extensive experiments on real social networks to evaluate the performance, and the experimental results strongly confirm the superiorities and effectiveness of our solutions., Comment: A short version of the paper will appear in the 36th IEEE International Conference on Data Engineering (ICDE '20), April 20--24, 2020, Dallas, Texas, USA

Given a graph $G$, a source node $s$ and a target node $t$, the personalized PageRank (PPR) of $t$ with respect to $s$ is the probability that a random walk starting from $s$ terminates at $t$. An important variant of the PPR query is single-source PPR (SSPPR), which enumerates all nodes in $G$, and returns the top-$k$ nodes with the highest PPR values with respect to a given source $s$. PPR in general and SSPPR in particular have important applications in web search and social networks, e.g., in Twitter's Who-To-Follow recommendation service. However, PPR computation is known to be expensive on large graphs, and resistant to indexing. Consequently, previous solutions either use heuristics, which do not guarantee result quality, or rely on the strong computing power of modern data centers, which is costly. Motivated by this, we propose effective index-free and index-based algorithms for approximate PPR processing, with rigorous guarantees on result quality. We first present FORA, an approximate SSPPR solution that combines two existing methods Forward Push (which is fast but does not guarantee quality) and Monte Carlo Random Walk (accurate but slow) in a simple and yet non-trivial way, leading to both high accuracy and efficiency. Further, FORA includes a simple and effective indexing scheme, as well as a module for top-$k$ selection with high pruning power. Extensive experiments demonstrate that the proposed solutions are orders of magnitude more efficient than their respective competitors. Notably, on a billion-edge Twitter dataset, FORA answers a top-500 approximate SSPPR query within 1 second, using a single commodity server., Comment: Accepted in the ACM Transactions on Database Systems (TODS)

As a dual problem of influence maximization, the seed minimization problem asks for the minimum number of seed nodes to influence a required number $\eta$ of users in a given social network $G$. Existing algorithms for seed minimization mostly consider the non-adaptive setting, where all seed nodes are selected in one batch without observing how they may influence other users. In this paper, we study seed minimization in the adaptive setting, where the seed nodes are selected in several batches, such that the choice of a batch may exploit information about the actual influence of the previous batches. We propose a novel algorithm, ASTI, which addresses the adaptive seed minimization problem in $O\Big(\frac{\eta \cdot (m+n)}{\varepsilon^2}\ln n \Big)$ expected time and offers an approximation guarantee of $\frac{(\ln \eta+1)^2}{(1 - (1-1/b)^b) (1-1/e)(1-\varepsilon)}$ in expectation, where $\eta$ is the targeted number of influenced nodes, $b$ is size of each seed node batch, and $\varepsilon \in (0, 1)$ is a user-specified parameter. To the best of our knowledge, ASTI is the first algorithm that provides such an approximation guarantee without incurring prohibitive computation overhead. With extensive experiments on a variety of datasets, we demonstrate the effectiveness and efficiency of ASTI over competing methods., Comment: A short version of the paper appeared in 2019 International Conference on Management of Data (SIGMOD '19), June 30--July 5, 2019, Amsterdam, Netherlands. ACM, New York, NY, USA, 18 pages

Given an input graph G and a node v in G, homogeneous network embedding (HNE) maps the graph structure in the vicinity of v to a compact, fixed-dimensional feature vector. This paper focuses on HNE for massive graphs, e.g., with billions of edges. On this scale, most existing approaches fail, as they incur either prohibitively high costs, or severely compromised result utility. Our proposed solution, called Node-Reweighted PageRank (NRP), is based on a classic idea of deriving embedding vectors from pairwise personalized PageRank (PPR) values. Our contributions are twofold: first, we design a simple and efficient baseline HNE method based on PPR that is capable of handling billion-edge graphs on commodity hardware; second and more importantly, we identify an inherent drawback of vanilla PPR, and address it in our main proposal NRP. Specifically, PPR was designed for a very different purpose, i.e., ranking nodes in G based on their relative importance from a source node's perspective. In contrast, HNE aims to build node embeddings considering the whole graph. Consequently, node embeddings derived directly from PPR are of suboptimal utility. The proposed NRP approach overcomes the above deficiency through an effective and efficient node reweighting algorithm, which augments PPR values with node degree information, and iteratively adjusts embedding vectors accordingly. Overall, NRP takes O(mlogn) time and O(m) space to compute all node embeddings for a graph with m edges and n nodes. Our extensive experiments that compare NRP against 18 existing solutions over 7 real graphs demonstrate that NRP achieves higher result utility than all the solutions for link prediction, graph reconstruction and node classification, while being up to orders of magnitude faster. In particular, on a billion-edge Twitter graph, NRP terminates within 4 hours, using a single CPU core., Comment: full version of a paper published in PVLDB 2020, Volume 13, Number 5, pages 670-683, https://doi.org/10.14778/3377369.3377376, 17 pages

Given an undirected graph G and a seed node s, the local clustering problem aims to identify a high-quality cluster containing s in time roughly proportional to the size of the cluster, regardless of the size of G. This problem finds numerous applications on large-scale graphs. Recently, heat kernel PageRank (HKPR), which is a measure of the proximity of nodes in graphs, is applied to this problem and found to be more efficient compared with prior methods. However, existing solutions for computing HKPR either are prohibitively expensive or provide unsatisfactory error approximation on HKPR values, rendering them impractical especially on billion-edge graphs. In this paper, we present TEA and TEA+, two novel local graph clustering algorithms based on HKPR, to address the aforementioned limitations. Specifically, these algorithms provide non-trivial theoretical guarantees in relative error of HKPR values and the time complexity. The basic idea is to utilize deterministic graph traversal to produce a rough estimation of exact HKPR vector, and then exploit Monte-Carlo random walks to refine the results in an optimized and non-trivial way. In particular, TEA+ offers practical efficiency and effectiveness due to non-trivial optimizations. Extensive experiments on real-world datasets demonstrate that TEA+ outperforms the state-of-the-art algorithm by more than four times on most benchmark datasets in terms of computational time when achieving the same clustering quality, and in particular, is an order of magnitude faster on large graphs including the widely studied Twitter and Friendster datasets., Comment: The technical report for the full research paper accepted in the SIGMOD 2019

We study the min-cost seed selection problem in online social networks, where the goal is to select a set of seed nodes with the minimum total cost such that the expected number of influenced nodes in the network exceeds a predefined threshold. We propose several algorithms that outperform the previous studies both on the theoretical approximation ratios and on the experimental performance. Under the case where the nodes have heterogeneous costs, our algorithms are the first bi- criteria approximation algorithms with polynomial running time and provable logarithmic performance bounds using a general contagion model. Under the case where the users have uniform costs, our algorithms achieve logarithmic approximation ratio and provable time complexity which is smaller than that of existing algorithms in orders of magnitude. We conduct extensive experiments using real social networks. The experimental results show that, our algorithms significantly outperform the existing algorithms both on the total cost and on the running time, and also scale well to billion-scale networks., Comment: submitted

In a recent SIGMOD paper titled "Debunking the Myths of Influence Maximization: An In-Depth Benchmarking Study", Arora et al. [1] undertake a performance benchmarking study of several well-known algorithms for influence maximization. In the process, they contradict several published results, and claim to have unearthed and debunked several "myths" that existed around the research of influence maximization. It is the goal of this article to examine their claims objectively and critically, and refute the erroneous ones. Our investigation discovers that first, the overall experimental methodology in Arora et al. [1] is flawed and leads to scientifically incorrect conclusions. Second, the paper [1] is riddled with issues specific to a variety of influence maximization algorithms, including buggy experiments, and draws many misleading conclusions regarding those algorithms. Importantly, they fail to appreciate the trade-off between running time and solution quality, and did not incorporate it correctly in their experimental methodology. In this article, we systematically point out the issues present in [1] and refute 11 of their misclaims., Comment: 13 pages, 6 figures

SimRank is a similarity measure for graph nodes that has numerous applications in practice. Scalable SimRank computation has been the subject of extensive research for more than a decade, and yet, none of the existing solutions can efficiently derive SimRank scores on large graphs with provable accuracy guarantees. In particular, the state-of-the-art solution requires up to a few seconds to compute a SimRank score in million-node graphs, and does not offer any worst-case assurance in terms of the query error. This paper presents SLING, an efficient index structure for SimRank computation. SLING guarantees that each SimRank score returned has at most $\varepsilon$ additive error, and it answers any single-pair and single-source SimRank queries in $O(1/\varepsilon)$ and $O(n/\varepsilon)$ time, respectively. These time complexities are near-optimal, and are significantly better than the asymptotic bounds of the most recent approach. Furthermore, SLING requires only $O(n/\varepsilon)$ space (which is also near-optimal in an asymptotic sense) and $O(m/\varepsilon + n\log \frac{n}{\delta}/\varepsilon^2)$ pre-computation time, where $\delta$ is the failure probability of the preprocessing algorithm. We experimentally evaluate SLING with a variety of real-world graphs with up to several millions of nodes. Our results demonstrate that SLING is up to $10000$ times (resp. $110$ times) faster than competing methods for single-pair (resp. single-source) SimRank queries, at the cost of higher space overheads., Comment: A short version of this paper will appear in SIGMOD 2016

Given a social network G and a constant k, the influence maximization problem asks for k nodes in G that (directly and indirectly) influence the largest number of nodes under a pre-defined diffusion model. This problem finds important applications in viral marketing, and has been extensively studied in the literature. Existing algorithms for influence maximization, however, either trade approximation guarantees for practical efficiency, or vice versa. In particular, among the algorithms that achieve constant factor approximations under the prominent independent cascade (IC) model or linear threshold (LT) model, none can handle a million-node graph without incurring prohibitive overheads. This paper presents TIM, an algorithm that aims to bridge the theory and practice in influence maximization. On the theory side, we show that TIM runs in O((k+\ell) (n+m) \log n / \epsilon^2) expected time and returns a (1-1/e-\epsilon)-approximate solution with at least 1 - n^{-\ell} probability. The time complexity of TIM is near-optimal under the IC model, as it is only a \log n factor larger than the \Omega(m + n) lower-bound established in previous work (for fixed k, \ell, and \epsilon). Moreover, TIM supports the triggering model, which is a general diffusion model that includes both IC and LT as special cases. On the practice side, TIM incorporates novel heuristics that significantly improve its empirical efficiency without compromising its asymptotic performance. We experimentally evaluate TIM with the largest datasets ever tested in the literature, and show that it outperforms the state-of-the-art solutions (with approximation guarantees) by up to four orders of magnitude in terms of running time. In particular, when k = 50, \epsilon = 0.2, and \ell = 1, TIM requires less than one hour on a commodity machine to process a network with 41.6 million nodes and 1.4 billion edges., Comment: Revised Sections 1, 2.3, and 5 to remove incorrect claims about reference [3]. Updated experiments accordingly. A shorter version of the paper will appear in SIGMOD 2014