Abstract Cyclic animation is widely used in computer graphics and interactive content. It supports seamless playback in games, VR, and interactive simulation, where short clips must repeat smoothly over long durations. Converting an observed non‐cyclic trajectory into a seamless loop is challenging because the endpoint states of the observed sequence rarely match exactly, and the governing equations of the underlying system are often unavailable. We therefore propose an equation‐free framework that identifies a Koopman surrogate from the observed trajectory and computes a cyclic trajectory by applying a Fourier‐parameterized, time‐varying control input under a hard temporal periodicity constraint. The resulting formulation reduces cyclic synthesis to a linearly constrained quadratic program that can be solved efficiently through a structured KKT system. Our method is applicable to a diverse range of examples, including N‐body systems, cloth, deformable objects, shallow water, etc.

In this paper, given a user's query set and budget, we aim to use the limited budget to help users assemble a set of datasets that can enrich a base dataset by introducing the maximum number of distinct tuples (i.e., maximizing distinctiveness). We prove this problem to be NP-hard. A greedy algorithm using exact distinctiveness computation attains an approximation ratio of (1-e-1 )/2, but it lacks efficiency and scalability due to its frequent computation of the exact distinctiveness marginal gain of any candidate dataset for selection. This requires scanning through every tuple in candidate datasets and thus is unaffordable in practice. To overcome this limitation, we propose an efficient machine learning (ML)-based method for estimating the distinctiveness marginal gain of any candidate dataset. This effectively eliminates the need to test each tuple individually. Estimating the distinctiveness marginal gain of a dataset involves estimating the number of distinct tuples in the tuple sets returned by each query in a query set across multiple datasets. This can be viewed as the cardinality estimation for a query set on a set of datasets, and the proposed method is the first to tackle this cardinality estimation problem. This is a significant advancement over prior methods that were limited to single-query cardinality estimation on a single dataset and struggled with identifying overlaps among tuple sets returned by each query in a query set across multiple datasets. Extensive experiments using five real-world data pools demonstrate that our algorithm, which utilizes ML-based distinctiveness estimation, outperforms all relevant baselines in effectiveness, efficiency, and scalability. A case study on two downstream ML tasks also highlights its potential to find datasets with more useful tuples to enhance the performance of ML tasks.

Balanced k -means ensures representative centroids by forming equal-sized clusters, but struggles with slow clustering of massive distributed attributes and data-sharing restrictions. A common approach is adapting it to a vertical federated learning (VFL) framework, preventing raw data exposure by only intermediate result exchange and accelerating clustering via parallelism, yet it remains unexplored. In this paper, we propose a time-efficient, federated, and balanced k -means algorithm, called Teb-means, to bridge the gap. We first formulate the balanced k -means problem as a trace maximization problem (TMP) and propose an efficient coordinate-wise optimization (CO) scheme to solve it. We then integrate TMP and CO into the VFL framework by demonstrating that TMP can be decomposed into multiple subproblems based on each party's data, which can be solved using CO while exchanging only intermediate results. Notably, we build a trade-off between utility and communication efficiency by designing a greedy block-based strategy for CO (GBCO). Our theoretical analysis shows that Teb-means achieves linear time complexity on each client, and our communication round is constant in the mild condition. Experiments show that Teb-means is on average 12.18× faster than other balanced clustering algorithms that can be federated, while achieving better balance without disrupting the cluster structure.

Active learning (AL), that aims to label limited data samples to effectively train the model, stands as a very cost-effective data labelling strategy in machine learning. Given the state-of-the-art performance GNNs have achieved in graph-based tasks, it is critical to design proper AL methods for graph neural networks (GNNs). However, existing GNN-based AL methods require considerable supervised information to guide the AL process, such as the GNN model to use, and initially labelled nodes and labels of newly selected nodes. Such dependency on supervised information limits both flexibility and scalabilty. In this paper, we propose an unsupervised, scalable and flexible AL method - it incurs low memory footprints and time cost, is flexible to the choice of underlying GNNs, and operates without requiring GNN-model-specific knowledge or labels of selected nodes. Specifically, we leverage the commonality of existing GNNs to reformulate the unsupervised AL problem as the Aggregation Involvement Maximization (AIM) problem. The objective of AIM is to maximize the involvement or participation of all nodes during the feature aggregation process of GNNs for nodes to be labelled. In this way, the aggregated features of labelled nodes can be diversified to a large extent, thereby benefiting the training of feature transformation matrices which are major trainable components in GNNs. We prove that the AIM problem is NP-hard and propose an efficient solution with theoretical guarantees. Extensive experiments on public datasets demonstrate the effectiveness, scalability and flexibility of our method. Our study is highly relevant to the track "Graph Algorithms and Modeling for the Web" since we focus one of the major listed topics "Graph Embedding and GNNs for the Web" and AL for GNNs, as an important research problem, is faced by aforementioned challenges to be tackled in this paper.

In this paper, we study the problem of cardinality estimation for similarity search on high-dimensional data (CE4HD). We aim to perform CE4HD with high data robustness (i.e., robust to different datasets), query robustness (i.e., robust to large cardinality variance and scale) and efficiency. We propose to leverage the cardinality estimation of selected objects (called reference objects) in the database to achieve the above. Specifically, we propose two techniques that adopt different strategies to select and leverage reference objects, as well as strategies to support efficient computation in dynamic databases. Extensive experiments on datasets from diverse domains show that our methods achieve up to ~10x speed-up and up to ~136x smaller mean Q-error compared to existing studies.

In this work, we address the critical task of discovering representative time series in exploratory data mining. We define a representative time series, referred to as similarity-bounded representative time series, as one that represents other time series if their similarity meets a user-defined threshold. Building on this definition, we study the problem of finding the smallest set of such time series that can represent a specified proportion of all time series within the dataset. The representativeness of each similarity-bounded representative time series is controllable and determined by the specified level of similarity, and only the minimum number of such representatives needed to collectively represent the specified proportion of entire set are identified. Identifying representative time series over large-scale data in an efficient and effective manner facilitates exploratory data analysis and summary generation, serving a wide range of data exploration applications across diverse domains. We first prove the NP-hardness of this problem and propose a range of approximation methods with theoretical guarantees, and we refer to them as non-learning-based methods. While effective, these methods often excel in either running time or memory efficiency, but not both concurrently. To overcome these limitations, we further propose a learning-based method that simultaneously optimizes both time and memory efficiency. This method leverages novel data preparation and training strategies, providing adaptability to user-specified representativeness requirements with low memory usage and computational overhead. We conduct extensive experiments across four real-world datasets to demonstrate that our learning-based method is highly competitive with non-learning-based methods in terms of effectiveness (produces similar number of representative time series), while achieving significantly higher efficiency (up to 21× speedups) and lower memory consumption (saving up to 101× memory space).

In this paper, we study how to acquire labeled data points from a large data pool to enrich a training set for enhancing supervised machine learning (ML) performance. The state-of-the-art solution is the clustering-based training set selection (CTS) algorithm, which initially clusters the data points in a data pool and subsequently selects new data points from clusters. The efficiency of CTS is constrained by its frequent retraining of the target ML model, and the effectiveness is limited by the selection criteria, which represent the state of data points within each cluster and impose a restriction of selecting only one cluster in each iteration. To overcome these limitations, we propose a new algorithm, called CTS with incremental estimation of adaptive score (IAS). IAS employs online learning, enabling incremental model updates by using new data, and eliminating the need to fully retrain the target model, and hence improves the efficiency. To enhance the effectiveness of IAS, we introduce adaptive score estimation, which serves as novel selection criteria to identify clusters and select new data points by balancing trade-offs between exploitation and exploration during data acquisition. To further enhance the effectiveness of IAS, we introduce a new adaptive mini-batch selection method that, in each iteration, selects data points from multiple clusters rather than a single cluster, hence eliminating the potential bias due to using only one cluster. By integrating this method into the IAS algorithm, we propose a novel algorithm termed IAS with adaptive mini-batch selection (IAS-AMS). Experimental results highlight the superior effectiveness of IAS-AMS, with IAS also outperforming other competing algorithms. In terms of efficiency, IAS takes the lead, while the efficiency of IAS-AMS is on par with that of the existing CTS algorithm.

With the rise of 5G technology, Mobile (or Multi-Access) Edge Computing (MEC) has become crucial in modern network architecture. One key research area is the effective placement of edge nodes, which has attracted significant attention. Service providers strive to minimize deployment costs for these nodes within a network. Although many studies have explored optimal strategies for reducing these costs, most overlook the allocation of computational resources and the users’ tolerance for delays. These factors add complexity, making previous methods less adaptable. In this paper, we define the Cost Minimization in MEC Edge Node Placement problem. Our goal is to find the optimal strategy for deploying edge nodes that minimize costs while cater to users’ delay tolerance limits. We prove the NP-hardness of this problem and provide a range of solutions, including Cluster-based Mixed Integer Programming, Coverage First Search, and Distance-Aware Coverage First Search, to address this challenge effectively and efficiently. Additionally, we propose a fine-grained optimization approach for allocating computational resources to edge nodes based on user service requests, significantly lowering deployment costs. Extensive experiments on a large-scale real-world dataset show that our solutions outperform the state-of-the-art in efficiency, effectiveness, and scalability.

Due to various reasons such as noisy measurement and privacy preservation, a network/graph is often uncertain such that each edge in the network has a probability of existence. In this paper, we study finding the most probable shortest path which has the highest probability of being the shortest path between a given pair of nodes in an uncertain network. Despite significant progress being made, this problem still suffers from the efficiency and scalability issue. To solve this problem, the state-of-the-art adopts a two-phase approach where Phase 1 generates some candidate paths and Phase 2 estimates their probabilities of being the shortest path and returns the one with the highest probability as the solution. Notably, Phase 2 requires a large number of simulations over all edges in the network and can easily dominate the cost of the whole process. In this paper, we aim to resolve the efficiency and scalability issue by optimizing Phase 2. Specifically, we first propose a non-learning based fast approximation technique which significantly reduces the number of samples for the probability estimation in each simulation. Afterwards, we further propose a learning-based method which can directly estimate the probability of each candidate path without costly simulations. Extensive experiments show that (1) compared to the state-of-the-art, our fast approximation technique and learning-based method can achieve up to 5x and 210x speedups in Phase 2 respectively while maintaining highly competitive or even equivalent results, (2) the training process is highly scalable and (3) the prediction function can work effectively under the problem settings different from the one it was trained.

A successful campaign should be able to attract investment from the brand, and meanwhile manage the conflicting interests in the campaign cost between the brand and the influencers. As such, the agency between these two stakeholders plays a vital role. Motivated by the above, we stand in the agency's shoes to formulate an interesting yet practical problem, namely Profit Divergence Minimization in Investment-Persuasive Influencer Marketing Campaign (PDMIC). This problem aims to (i) minimize the divergence of the actual hiring prices from the asking prices of the influencers and meanwhile (ii) maintain the attractiveness of the pricing scheme for the influencers to the brand. We show that this problem is NP-hard. To mitigate the challenge of the extremely large searching space of the hiring prices of the influencers, we solve this problem by firstly considering a restrictive searching sub-space and then gradually expanding the searching sub-space to the whole space in the end (specifically, from binary price choices to a set of integer prices and then to any price in the feasible price range). We propose effective yet efficient approximate algorithms for solving the problem in each of these settings. Extensive experiments demonstrate the superiority of our methods.

In this work, we study how to find the k most representative routes over large scale trajectory data, which is a fundamental operation that benefits various real-world applications, such as traffic monitoring and public transportation planning. The operator is time-sensitive as it must be able to adapt the results as traffic conditions change. We first prove the NP-hardness of the problem, and then propose a range of effective approximate solutions that have rapid response times. Specifically, we first build a lookup table that stores the trajectories covered by each edge in a given road network. Rather than performing a depth-first search for all possible routes, we find a 1/η approximate solution by developing a maximum-weight algorithm. Since each edge in a route may be close to several trajectories, we further propose a coverage-first algorithm to locate the edges with the greatest coverage gain in the solution route set. By observing that in the real world each edge is connected to only a few other edges in a road network, we have developed a connect-first algorithm that finds consecutive edges for k representative routes by greedily selecting edges with the maximum marginal gain for each route. Finally, comprehensive experiments over two real-world datasets are conducted to verify the effectiveness and efficiency of our proposed algorithms, and provide evidence of the usefulness of our solution and rapid response times in traffic monitoring tasks.

In the last few years, many closed social networks such as WhatsAPP and WeChat have emerged to cater for people's growing demand of privacy and independence. In a closed social network, the posted content is not available to all users or senders can set limits on who can see the posted content. Under such a constraint, we study the problem of influence maximization in a closed social network. It aims to recommend users (not just the seed users) a limited number of existing friends who will help propagate the information, such that the seed users' influence spread can be maximized. We first prove that this problem is NP-hard. Then, we propose a highly effective yet efficient method to augment the diffusion network, which initially consists of seed users only. The augmentation is done by iteratively and intelligently selecting and inserting a limited number of edges from the original network. Through extensive experiments on real-world social networks including deployment into a real-world application, we demonstrate the effectiveness and efficiency of our proposed method.

In this paper, we study the problem of efficient motif-based graph partitioning (MGP). We observe that existing methods require to enumerate all motif instances to compute the exact edge weights for partitioning. However, the enumeration is prohibitively expensive against large graphs. We thus propose a sampling-based MGP (SMGP) framework that employs an unbiased sampling mechanism to efficiently estimate the edge weights while trying to preserve the partitioning quality. To further improve the effectiveness, we propose a novel adaptive sampling framework called SMGP+. SMGP+ iteratively partitions the input graph based on up-to-date estimated edge weights, and adaptively adjusts the sampling distribution so that edges that are more likely to affect the partitioning outcome will be prioritized for weight estimation. To our best knowledge, this is the first attempt to solve the MGP problem without employing exact edge weight computations, which gives hope for existing MGP methods to perform on complicated motifs in a scalable yet effective manner. Extensive experiments on seven real-world datasets have validated that our framework delivers competitive partitioning quality compared to existing workflows based on exact edge weights, while achieving orders of magnitude speedup.

Network embedding is an effective method to learn low-dimensional representations of nodes, which can be applied to various real-life applications such as visualization, node classification, and link prediction. Although significant progress has been made on this problem in recent years, several important challenges remain, such as how to properly capture temporal information in evolving networks. In practice, most networks are continually evolving. Some networks only add new edges or nodes such as authorship networks, while others support removal of nodes or edges such as internet data routing. If patterns exist in the changes of the network structure, we can better understand the relationships between nodes and the evolution of the network, which can be further leveraged to learn node representations with more meaningful information. In this paper, we propose the Embedding via Historical Neighborhoods Aggregation (EHNA) algorithm. More specifically, we first propose a temporal random walk that can identify relevant nodes in historical neighborhoods which have impact on edge formations. Then we apply a deep learning model which uses a custom attention mechanism to induce node embeddings that directly capture temporal information in the underlying feature representation. We perform extensive experiments on a range of real-world datasets, and the results demonstrate the effectiveness of our new approach in the network reconstruction task and the link prediction task.

Influence maximization (IM) continues to be a key research problem in social networks. The goal is to find a small seed set of target users that have the greatest influence in the network under various stochastic diffusion models. While significant progress has been made on the IM problem in recent years, several interesting challenges remain. For example, social networks in reality are constantly evolving, and "important" users with the most influence also change over time. As a result, several recent studies have proposed approaches to update the seed set as the social networks evolve. However, this seed set is not guaranteed to be the best seed set over a period of time. In this paper we study the problem of Distinct Influence Maximization (DIM) where the goal is to identify a seed set of influencers who maximize the number of distinct users influenced over a predefined window of time. Our new approach allows social network providers to make fewer incremental changes to targeted advertising while still maximizing the coverage of the advertisements. It also provides finer grained control over service level agreements where a certain number of impressions for an advertisement must be displayed in a specific time period. We propose two different strategies HCS and VCS with novel graph compression techniques to solve this problem. Additionally, VCS can also be applied directly to the traditional IM problem. Extensive experiments on real-world datasets verify the efficiency, accuracy and scalability of our solutions on both the DIM and IM problems.

In this paper we study the problem of efficiently and effectively extracting induced planar subgraphs. Edwards and Farr proposed an algorithm with O(mn) time complexity to find an induced planar subgraph of at least 3n/(d+1) vertices in a graph of maximum degree d. They also proposed an alternative algorithm with O(mn) time complexity to find an induced planar subgraph graph of at least 3n/(bar{d}+1) vertices, where bar{d} is the average degree of the graph. These two methods appear to be best known when d and bar{d} are small. Unfortunately, they sacrifice accuracy for lower time complexity by using indirect indicators of planarity. A limitation of those approaches is that the algorithms do not implicitly test for planarity, and the additional costs of this test can be significant in large graphs. In contrast, we propose a linear-time algorithm that finds an induced planar subgraph of n-nu vertices in a graph of n vertices, where nu denotes the total number of vertices shared by the detected Kuratowski subdivisions. An added benefit of our approach is that we are able to detect when a graph is planar, and terminate the reduction. The resulting planar subgraphs also do not have any rigid constraints on the maximum degree of the induced subgraph. The experiment results show that our method achieves better performance than current methods on graphs with small skewness.

This paper studies the location-based web search and aims to build a unified processing paradigm for two purposes: (1) efficiently support each of the various types of location-based queries (kNN query, top-k spatial-textual query, etc.) on two major forms of geo-tagged data, i.e., spatial point data such as geo-tagged web documents, and spatial trajectory data such as a sequence of geo-tagged travel blogs by a user; (2) support interactive search to provide quick response for a query session, within which a user usually keeps refining her query by either issuing different query types or specifying different constraints (e.g., adding a keyword and/or location, changing the choice of k, etc.) until she finds the desired results. To achieve this goal, we first propose a general Top-k query called Monotone Aggregate Spatial Keyword query-MASK, which is able to cover most types of location-based web search. Next, we develop a unified indexing (called Textual-Grid-Point Inverted Index) and query processing paradigm (called ETAIL Algorithm) to answer a single MASK query efficiently. Furthermore, we extend ETAIL to provide interactive search for multiple queries within one query session, by exploiting the commonality of textual and/or spatial dimension among queries. Last, extensive experiments on four real datasets verify the robustness and efficiency of our approach.