Mining cohesive subgraphs in bipartite graphs is of great importance to various real-world applications such as recommendation in e-commercial systems and fraud detections in social networks. In this paper, we study the problem of Bitruss Decomposition of a given bipartite graph G. The goal is to compute, for each edge e, the largest value of k such that e is still contained in a k-bitruss. Here, a k-bitruss is a maximal subgraph of G such that every edge of it is contained in at least k butterflies (i.e(2,2)-cliques) in the subgraph. All the previous state-of-the-art solutions are based on the well-known Peeling Process framework and have to ''touch'' every butterfly in the graph G for at least once, causing a O(⧖G) cost, where ⧖G is the number of butterflies in G. In the worst case, ⧖G can be as large as O(m2), where m is the number of edges in G. We propose the first algorithm called BiT-DT, whose running time is bounded by O(m^1.5 log m), significantly improving the state-of-the-art bound by roughly a factor of O(√m). The crucial idea of our algorithm is an efficient approach to identify the edges to be peeled next in the Peeling Process without maintaining a precise butterfly support for each edge. To further enhance the practical performance of our BiT-DT algorithm, we propose a heuristic to peel the edges in batch. Extensive experimental results on ten real-world datasets show that our proposed algorithm outperforms the state-of-the-art baselines by up to an order of magnitude in terms of running time.

We study structural clustering on graphs in dynamic scenarios, where graphs can be updated by arbitrary insertions or deletions of edges/vertices. Our goal is to efficiently compute structural clustering results under three conditions: 1) for any clustering parameters ε and μ provided on the fly, 2) for arbitrary graph update patterns, and 3) for all typical similarity measurements. To achieve this, we propose an algorithm named VD-STAR that is much simpler yet more efficient than state of the art. With a theoretical guarantee on clustering result's quality, VD-STAR can produce clustering results with up to 99.9% accuracy. Moreover, VD-STAR is easy to implement as it just needs to maintain sorted linked lists and hash tables, making it highly deployable in practice. Most importantly, VD-STAR improves the expected per-update time bound from state-of-the-art O(log2 n), which relies on specific assumption on update pattern, to O(log n) amortized in expectation without any assumption on update pattern. We further design two variants of VD-STAR to enhance its empirical performance. Experimental results show that our algorithms consistently outperform state-of-the-art competitors by up to 9,315 times in update time across nine real datasets, while maintaining similar update time and memory usage.

The uniqueness of trajectory data for user re-identification has received unprecedented attention as the increasing popularity of location-based services boosts the excessive collection of daily trajectories with sufficient spatiotemporal coverage. Consequently, leveraging or releasing personally-sensitive trajectories without proper protection severely threatens individual privacy despite simply removing IDs. Trajectory privacy protection is never a trivial task due to the trade-off between privacy protection, utility preservation, and computational efficiency. Furthermore,recovery attack, one of the most threatening attacks specific to trajectory data, has not been well studied in the current literature. To tackle these challenges, we propose a frequency-based randomization model with a rigorous differential privacy guarantee for privacy-preserving trajectory data publishing. In particular, two randomized mechanisms are introduced for perturbing the local/global frequency distributions of a limited number of significantly essential locations in trajectories by injecting special Laplace noises. To reflect the perturbed distributions on the trajectory level without losing privacy guarantee or data utility, we formulate the trajectory modification tasks as kNN search problems and design two hierarchical indices with powerful pruning strategies and a novel search algorithm to support efficient modification. Extensive experiments on a real-world dataset verify the effectiveness of our approaches in resisting individual re-identification and recovery attacks simultaneously while still preserving desirable data utility. The efficient performance on large-scale data demonstrates the feasibility and scalability in practice.

With the popularity of GPS-enabled devices, a huge amount of trajectory data has been continuously collected and a variety of location-based services have been developed that greatly benefit our daily life. However, the released trajectories also bring severe concern on personal privacy, and several recent studies have demonstrated the existence of personally-identifying information in spatial trajectories. Trajectory anonymization is nontrivial due to the trade-off between privacy protection and utility preservation. Furthermore, recovery attack has not been well studied in the current literature. To tackle these issues, we propose a frequency-based randomization model with a rigorous differential privacy guarantee for trajectory data publishing. In particular, we introduce two randomized mechanisms to perturb the local/global frequency distributions of significantly important locations in trajectories by injecting Laplace noise. We design a hierarchical indexing along with a novel search algorithm to support efficient trajectory modification, ensuring the modified trajectories satisfy the perturbed distributions without compromising privacy guarantee or data utility. Extensive experiments on a real-world trajectory dataset verify the effectiveness of our approaches in resisting individual re-identification and recovery attacks, and meanwhile preserving desirable data utility as well as the feasibility in practice.

\em Structural Clustering ($\strclu$) is one of the most popular graph clustering paradigms. In this paper, we consider $\strclu$ under Jaccard similarity on a dynamic graph, G = (V, E), subject to edge insertions and deletions (updates). The goal is to maintain certain information under updates, so that the strclu clustering result on~G can be retrieved in O(|V| + |E|)$ time, upon request. The state-of-the-art worst-case cost is~O(|V|) per update; we improve this update-time bound \em significantly with the ρ-approximate notion. Specifically, for a specified failure probability, δ^*, and \em every sequence of~M updates (no need to know M's value in advance), our algorithm, $\dynelm$, achieves~O(?og^2 |V| + og |V| \cdot ?og \fracM ?^* )$ amortized cost for each update, \em at all times in linear space. Moreover, $\dynelm$ provides a provable "sandwich'' guarantee on the clustering quality at all times after each update with probability at least 1 - ^*. We further develop dynelm into our ultimate algorithm, dynstr, which also supports \em cluster-group-by queries. Given Q \subseteq V, this puts the non-empty intersection of Q and each strclu cluster into a distinct group. dynstr not only achieves all the guarantees of dynelm, but also runs \em cluster-group-by queries in~O(|Q|\cdot og |V|) time. We demonstrate the performance of our algorithms via extensive experiments, on 15 real datasets. Experimental results confirm that our algorithms are up to three orders of magnitude more efficient than state-of-the-art competitors, and still provide quality structural clustering results.

Given a pair of Origin-Destination (OD) locations, the set of trajectories passing from the original to destination, usually possesses the nature to reflect different traveling patterns between OD. In general, the higher diversity these trajectories have, the more various traveling behaviors and greater robustness of the connectivity can be revealed, which highly raises the value of transportation analysis towards the corresponding OD pair. Therefore, in this paper, we introduce a comprehensive and rational measure for trajectory diversity, on top of which we propose a novel query, Top-k Diversified Search (TkDS), that aims to find a set of k OD pairs among all the given OD pairs such that the trajectories traversing in-between have the highest diversity. Owing to the intrinsic characteristics of trajectory data, the computational cost for diversity is considerably high. Thus we present an efficient bounding algorithm with early termination to filter the candidates that are impossible to contribute the result. Finally, we demonstrate some case studies for trajectory diversity on real world dataset and give a comprehensive performance evaluation on the Top-k Diversified Search.