Approximate nearest neighbor (ANN) searches are commonly employed in various machine learning applications, such as recommendation systems, but traditional ANN searches typically involve only a single reference vector in a query. To broaden the capabilities of ANN search and support multi-reference-vector queries, thereby enabling a wider range of machine learning applications, we introduce all/any-k ANN search. They aim to find vectors that are similar to all or any of the multi-reference vectors in a query, respectively. To effectively and efficiently support all/any-k ANN search, we first propose distance metrics to evaluate the ranking of vectors among those in the dataset for exact all/any-k NN. Building on this, we introduce search algorithms and prove they can search according to the proposed distance metrics on graph indexes designed for traditional ANN. Additionally, we further introduce two-stage search algorithms for all/any-k ANN search to further enhance their search performance. We conduct extensive experiments on real-world datasets to validate the efficiency and effectiveness of our proposed algorithms compared to existing approaches.

In the era of cloud computing and AI, data owners outsource ubiquitous vectors to the cloud, which furnish approx-imate k-nearest neighbors (k-ANNS) services to users. To protect data privacy against the untrusted server, privacy-preserving k-ANNS (PP-ANNS) on vectors has been a fundamental and urgent problem. However, existing PP-ANNS solutions fall short of meeting the requirements of data privacy, efficiency, accuracy, and minimal user involvement concurrently. To tackle this challenge, we introduce a novel solution that primarily executes PP-ANNS on a single cloud server to avoid the heavy communication overhead between the cloud and the user. To ensure data privacy, we introduce a novel encryption method named distance comparison encryption, facilitating secure, efficient, and exact distance comparisons. To optimize the trade-off between data privacy and search performance, we design a privacy-preserving index that combines the state-of-the-art k-ANNS method with an approximate distance computation method. Then, we devise a search method using a filter-and - refine strategy based on the index. Moreover, we provide the security analysis of our solution and conduct extensive experiments to demonstrate its superiority over existing solutions. Based on our experimental results, our method accelerates PP-ANNS by up to 3 orders of magnitude compared to state-of-the-art methods, while not compromising the accuracy.

Recent advancements in deep learning, particularly in embedding models, have enabled the effective representation of various data types such as text, images, and audio as vectors, thereby facilitating semantic analysis. A large number of massive vector datasets are maintained in vector databases. Approximate similarity join is a core operation in vector database systems that joins two datasets, and outputs all pairs of vectors from the two datasets, if the distance between such a pair of two vectors is no more than a specified value. Existing approaches for similarity join are selection-based such that they treat each data point in a dataset as an individual query point to search data points by an approximate range query in another dataset. Such methods do not fully capitalize on the inherent properties of the join operation itself. In this paper, we propose a new join algorithm, SimJoin. Our join algorithm aims at boosting join processing efficiency by leveraging relationships between partial join results (e.g., join windows). In brief, our join algorithm accelerates the join processing to process a join window by utilizing the join windows from the processed data points. Then, we discuss optimizing join window order to minimize join costs. In addition, we discuss how to support k -similarity join, and how to maintain proximity graph index based on k-similarity join. Extensive experiments on real-world and synthetic datasets demonstrate the significant performance superiority of our proposed algorithms over existing state-of-the-art methods.

k -ANN search has been extensively studied to find k approximate nearest neighbors for a given query vector in a high-dimensional dataset, where a data item is represented as a vector. As there are many new emerging real-world applications that have categorical/numerical attributes associated with vectors, it is highly needed to support k -ANN search with additional predicates on such attributes. In this paper, we study k -ANN queries, q = (v q , c q ), where v q is a query vector and c q is a predicate on categorical/numerical attributes. Note that the conventional k -ANN search is a k -ANN query when c q = ∅. In the literature, some can support the cases when c q = ∅, some can support the cases when c q is on categorical attributes, and some can support the cases when c q is on numerical attributes. But none of them can support all cases efficiently. In this paper, we propose an all-in-one approach. Our approach supports conventional k -ANN search in the same way as the state-of-the-art approaches, and supports the predicates in a similar or even better way compared to the approaches that are tailored to support either categorical attributes or numerical attributes. We conduct extensive performance studies and confirm the accuracy and the efficiency of our approach in comparison with the state-of-the-art approaches.

Proximity graphs (PG) have gained increasing popularity as the state-of-the-art solutions to k -approximate nearest neighbor ( k -ANN) search on high-dimensional data, which serves as a fundamental function in various fields, e.g., retrieval-augmented generation. Although PG-based approaches have the best k -ANN search performance, their index construction cost is superlinear to the number of points. 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 of NSWG. Extensive experiments are conducted to validate our construction framework for both RNG and NSWG, and that it significantly reduces the PG construction cost, achieving up to 5.6x speedup, while not compromising the k -ANN search performance.

The problem of k -nearest neighbor ( k -NN) search is a fundamental problem to find the exact k nearest neighbor points for a user-given query point q in a d -dimensional large dataset D with n points, and the approximate k -NN ( k -ANN) search problem is to find the approximate k -NN. Both are extensively studied to support real applications. Among all approaches, the graph-based approaches have been seen as the best to support k -NN/ANN in recent studies. The state-of-the-art graph-based approach, τ-MG, finds 1-NN, \(\bar{p}_1\) , over a graph index G τ constructed for D based on a predetermined parameter τ where the distance between \(\bar{p}_1\) and q is less than τ, and finds k -ANN based on the approach taken for 1-NN. There are some main issues in τ-MG and other graph-based approaches. One is that it is difficult to predetermine τ which can ensure to find 1-NN and can do it efficiently. This is because the accuracy/efficiency is related to the size of the graph index G τ constructed. To achieve high accuracy is at the expense of efficiency. In addition, like all the other existing graph-based approaches, it does not have a theoretical guarantee to ensure k -NN for the same reason to use the same graph index, G τ , for both 1-NN and k -NN ( k > 1). In this article, we propose a new graph-based approach for k -NN with a theoretical guarantee. We construct a labeled graph, \(\mathcal {G}\) , and we do not need to predetermine τ. Instead, we find 1-NN over a subgraph, \(\mathcal {G}_{\dot{\tau }}\) , of \(\mathcal {G}\) , virtually constructed in a dynamic manner. Here, \(\dot{\tau }\) we use is query-dependent and can be smaller than τ, and the subgraph \(\mathcal {G}_{\dot{\tau }}\) is smaller than G τ when \(\dot{\tau }= \tau\) . We find k -NN in two phases. In the navigation phase, we find 1-NN, \(\bar{p}_1\) , of q over \(\mathcal {G}_{\dot{\tau }}\) . In the second refinement phase, for k > 1, we explore the neighbors within the vicinity region of \(\bar{p}_1\) in \(\mathcal {G}\) . Based on our solution for k -NN in theory, we propose new algorithms to support k -ANN efficiently in practice. We conduct extensive performance studies and confirm the effectiveness and efficiency of our new approach.

Network resilience is a critical ability of a network to maintain its functionality against disturbances. A network is resilient/robust when a large portion of the nodes are to be better engaged in the network, i.e., they are less likely to leave given the changes on the network. Existing studies validate that the engagement of a node can be well captured by its coreness on network topology. Therefore, it is promising to maximize the number of nodes with increasing coreness values. In this paper, we propose and study thefollower maximization problem: maximizing the resilience gain (the number of coreness-increased vertices) via anchoring a set of vertices within a given budget. We prove that the problem is NP-hard and W[2]-hard, and it is NP-hard to approximate within an O(n^1-ε ) factor. We first propose an advanced greedy approach, followed by a time-dependent framework designed to quickly find high-quality results. The framework is initialized by the advanced greedy algorithm and incorporates novel techniques for optimizing the search space. The effectiveness and efficiency of our solution are verified with extensive experiments on 8 real-life datasets. Our source codes are available at https://github.com/Tsyxxxka/Follower-Maximization.

Competitive viral marketing considers the product competition of multiple companies, where each user may adopt one product and propagate the product to other users. Existing studies focus on a traditional seeding strategy where a company only selects seeds from the users with no adopted product to maximize its influence (i.e., the number of users who will adopt its product). However, influential users are often rare, and the gain from traditional seeding will degrade as the number of seeds increases. Therefore, in this paper, we study the promisingcounteringstrategy which is to counter some users who initially use other products s.t. they will turn to adopting the target product and recommending it to others. We propose the problem ofinfluence countering: given a graph, a budgetb, a target companyCt, and a setSof the seeds adopting different companies (where each seed adopts one company), we counterbusers inSwho do not adoptCtto turn to adoptCts.t. the expected number of users who eventually adoptCtin the influence diffusion is maximized. Following existing studies, we formalize the diffusion process by the Multi-Campaigner Independent Cascade model. We prove the influence countering problem is #P-complete and its influence computation is #P-hard. Then, we propose two novel algorithmsMICandMIC+to address the problem. In general,MICestimates seed influence by its empirical average influence in multiple graph samplings, whileMIC+improvesMICby reducing the cost of influence estimation and the required number of samples. Given pre-setεandl, both algorithms return a (1 -ε)-approximate solution with at least 1 -n-lprobability. We also design an index forMIC+to efficiently process graphs that are frequently updated. The experiments on 8 real-world datasets show that our algorithms are efficient in practice while offering strong result quality.

The rapid rise and prevalence of social platforms have created great demands on effective schemes to limit the influence of negative information, e.g., blocking key vertices for influence minimization. However, there is currently no system providing practical schemes to solve the negative influence minimization problem with a blocking budget effectively and efficiently in the literature. In this demo, we present IMinimize, the first interactive system that provides audiences with vertex-blocking schemes over different budgets and demonstrates via visualization for comparison vividly and directly, aiming to help minimize the negative influence spreading in networks. Our IMinimize system applies an advanced greedy algorithm to select blocked vertices with both high efficiency and effectiveness. Furthermore, we extend IMinimize to the application of epidemic controlling and prevention and show the usability of IMinimize through two case studies of real-life applications.

Information cascade in online social networks can be rather negative, e.g., the spread of rumors may trigger panic. To limit the influence of misinformation in an effective and efficient manner, the influence minimization (IMIN) problem is studied in the literature: given a graph G and a seed set S, blocking at most b vertices such that the influence spread of the seed set is minimized. In this paper, we are the first to prove the IMIN problem is NP-hard and hard to approximate. Due to the hardness of the problem, existing works resort to greedy solutions and use Monte-Carlo Simulations to solve the problem. However, they are cost-prohibitive on large graphs since they have to enumerate all the candidate blockers and compute the decrease of expected spread when blocking each of them. To improve the efficiency, we propose the AdvancedGreedy algorithm (AG) based on a new graph sampling technique that applies the dominator tree structure, which can compute the decrease of the expected spread of all candidate blockers at once. Besides, we further propose the GreedyReplace algorithm (GR) by considering the relationships among candidate blockers. Extensive experiments on 8 real-life graphs demonstrate that our AG and GR algorithms are significantly faster than the state-of-the-art by up to 6 orders of magnitude, and GR can achieve better effectiveness with its time cost close to AG.

Quantifying node importance on engagement dynamics is critical to support network stability. We can motivate or retain the users in a social platform according to their importance s.t. the network is more sustainable. Existing studies validate that the coreness of a node is the "best practice" on network topology to estimate the engagement of the node. In this paper, the importance of a node is the effect on the engagement of other nodes when its engagement is strengthened or weakened. Specifically, the importance of a node is quantified via two novel concepts: the anchor power to measure the engagement effect of node strengthening (i.e., the overall coreness gain) and the collapse power to measure the engagement effect of node weakening (i.e., the overall coreness loss). We find the computation of the two concepts can be naturally integrated into a shell component-based framework, and propose a unified static algorithm to compute both the anchored and collapsed followers. For evolving networks, efficient maintenance techniques are designed to update the follower sets of each node, which is faster than redoing the static algorithm by around 3 orders of magnitude. Extensive experiments on real-life data demonstrate the effectiveness of our model and the efficiency of our algorithms.

Considering the rapid spread of incidents like rumours or epidemics, it is important to hinder their influence diffusion. However, none of the existing works can well control the influence diffusion of a community. Based on a novel metric named interaction frequency that can measure the influence diffusion of a community, we aim to remove b nodes from a given community such that the interaction frequency of the remaining nodes is minimized. We also design a polynomial-time algorithm for the problem. The experiments show our algorithm can efficiently hinder the influence diffusion.