Extracting cohesive subgraphs from complex networks is a fundamental task in graph analytics and is essential for understanding biological, social, and web graphs. The edge-based γ-quasi-clique model offers a flexible alternative by identifying subgraphs whose edge densities exceed a specified threshold γ. However, finding the exact maximum edge-based quasi-clique is computationally challenging, as the problem is NP-hard and lacks the hereditary property. These characteristics limit the effectiveness of conventional pruning methods and the development of efficient reduction rules. As a result, existing algorithms, such as QClique and FPCE, struggle to scale to large graphs. In this paper, we revisit the problem and propose a novel iterative framework that reformulates the problem as a sequence of hereditary subproblems, enabling more effective pruning and reduction strategies and improving the worst-case time complexity. Furthermore, we redesign the iterative process and introduce a novel heuristic to further improve practical efficiency. Extensive experiments on 253 large-scale real-world graphs demonstrate that our proposed algorithm EQC-Pro outperforms existing methods by up to four orders of magnitude.

Community search has widespread applications in areas such as advertising, friend recommendation, and protein complex identification. In this paper, we revisit the Size-bounded Community Search (SCS) problem, which aims to identify a connected subgraph containing a query vertex q and between l and h vertices, while maximizing the minimum degree of the subgraph. Existing state-of-the-art exact solutions for SCS face challenges in practical efficiency due to ineffective strategies for searching candidate solutions and suboptimal method for finding optimal solution. To address these challenges, we propose a novel branch-and-bound algorithm that efficiently locating a subset of candidate solutions with favorable structural properties, forming the basis for three progressively refined frameworks to determine the optimal solution. Furthermore, we enhance practical performance through a new heuristic, two reduction rules, and a query decomposition technique. Extensive experiments on 12 large real-world graphs demonstrate that our most efficient framework significantly outperforms state-of-the-art methods, achieving an average speedup of two orders of magnitude while consistently identifying communities with higher cohesion.

Deep neural networks (DNNs) are vulnerable to adversarial examples crafted by well-designed perturbations. This could lead to disastrous results on critical applications such as self-driving cars, surveillance security, and medical diagnosis. At present, adversarial training is one of the most effective defenses against adversarial examples. However, in traditional adversarial training, it is still difficult to achieve a good trade-off between clean accuracy and robustness since DNNs still learn spurious features. The intrinsic reason is that traditional adversarial training makes it difficult to fully learn core features from adversarial examples when noise and examples cannot be disentangled. In this paper, we disentangle the adversarial examples into natural and perturbed patterns by bit-plane slicing. We assume the higher bit-planes represent natural patterns and the lower bit-planes represent perturbed patterns, respectively. We propose Feature-Focusing Adversarial Training (F$^{2}$AT), which differs from previous work in that it enforces the model to focus on the core features from natural patterns and reduce the impact of spurious features from perturbed patterns. The experimental results demonstrated that the clean accuracy and adversarial robustness with our F$^{2}$AT can be significantly improved.

Deduplication-based techniques are popular in backup storage systems for reducing data volume. To maximize data reduction, existing fine-grained deduplication approaches not only eliminate duplicate chunks but also delta-compress non-duplicate chunks as delta relative to their similar (base) chunks. However, each chunk may have multiple similar chunks, and delta compression usually only selects one of them as the base chunk, i.e., a one-to-one scheme. This scheme benefits the restore performance because it needs to read only one (instead of multiple) base chunk in decompressing delta chunks, while it also wastes the potential compressibility among other similar chunks.In this paper, we propose SuperDelta to further exploit compressibility across multiple similar chunks and to preserve the restore performance advantage of the one-to-one scheme as much as possible. It is based on three techniques. (1) To further eliminate redundancy among similar chunks, SuperDelta applies a "Multiple Referenced Base Chunks" (MRBC) scheme instead of the one-to-one scheme. It combines several similar pairs of chunks in delta encoding to recover possibly lost compressibility in "boundary shift" problems. (2) To avoid the negative side effects of MRBC on restore performance, SuperDelta introduces a rebase scheme to rebuild simple reference paths among duplicate and similar chunks. It significantly simplifies the restore workflow, but also costs slightly more storage space because of impacting the workflow of redundancy detection. (3) To compensate for the additional storage cost, SuperDelta applies a space-recycle scheme to remove derived data when they become old while ensuring the optimized restore performance of the latest backups.Experiments on four real-world backup datasets show that SuperDelta increases the overall compression ratio by 1.05~2.40 times than the traditional one-to-one fine-grained deduplication without significantly affecting the backup and restore throughput.

Continuously monitoring structural patterns in streaming graphs is a critical task in many real-time graph-based applications. In this paper, we study the problem of time-constrained continuous subgraph matching (shorted as TCSM) over streaming graphs. Given a query graph Q with timing order constraint and a data graph stream G , TCSM aims to report all incremental matches of Q in G for each update of G , where a match should obey both structure constraint (i.e., isomorphism) and timing order constraint of Q. Although TCSM has a wide range of applications, such as cyber-attack detection and credit card fraud detection, we note that this problem has not been well addressed. The state-of-the-art bears the limitations of high index space cost and intermediate result maintenance cost. In this paper, we propose TC-Match, an effective approach to TCSM. First, we design a space and time cost-effective index CSS, which is essentially a k -partite graph structure where a node corresponds to an edge in G. By carefully creating links between nodes, we can encapsulate into CSS the partial embedding and timing order information between edges in G. We theoretically show that CSS has polynomial space and construction time complexities. Second, based on the property of CSS, we develop an efficient incremental matching algorithm with an effective node merging optimization. Extensive experiments show that TC-Match can achieve up to 3 orders of magnitude query performance improvement over the baseline methods, and meanwhile the memory consumption is reduced by 48.7%-86.7%.

In this paper, we study the problem of maximal biclique enumeration on large signed bipartite graphs. Given a signed bipartite graph$G=(U,V,E,s)$, a parameter$\theta \in [0.5, 1.0]$, our goal is to efficiently enumerate all maximal$\theta$-bicliques in$G$, where a maximal$\theta$-biclique$B(L,R)$is a complete subgraph of$G$with (1) the proportion of positive neighbors for each vertex in$B$is at least$\theta$, and (2)$B$is not contained in another biclique$B^{\prime }$, while$B^{\prime }$also satisfies (1). This problem has many applications, such as biclustering for genes, recommendation of similar groups, collaboration in communities, etc. However, it is computationally challenging due to its #P-completeness. Besides, we prove that even determining the maximality of a$\theta$-biclique is NP-hard. To the best of our knowledge, there is no efficient and scalable solution to this problem in the literature. In this paper, we first propose a branch-and-bound framework, namely${\sf MSiBE}$, which enumerates all maximal$\theta$-bicliques in a depth-first manner. Then, we develop three effective optimizations to improve the performance of${\sf MSiBE}$. (1) The local information of each search space is utilized to enhance the pruning capacity. (2) When expanding the partial biclique, we always focus on the side with fewer candidates first, by which fruitless search branches can be skipped early. (3) We implement${\sf MSiBE}$with efficient array reordering techniques and set intersection strategy. To further accelerate the computation, we introduce useful graph reduction techniques. Comprehensive performance studies on 10 real datasets demonstrate that our proposals can significantly outperform the baseline methods by up to 3 orders of magnitude.

Group recommendation has attracted significant research efforts for its importance in benefiting a group of users. This paper investigates the Group Recommendation problem from a novel aspect, which tries to maximize the satisfaction of each group member while minimizing the unfairness between them. In this work, we present several semantics of the individual utility and propose two concepts of social welfare and fairness for modeling the overall utilities and the balance between group members. We formulate the problem as a multiple objective optimization problem and show that it is NP-Hard in different semantics. Given the multiple-objective nature of fairness-aware group recommendation problem, we provide an optimization framework for fairness-aware group recommendation from the perspective of Pareto Efficiency. We conduct extensive experiments on real-world datasets and evaluate our algorithm in terms of standard accuracy metrics. The results indicate that our algorithm achieves superior performances and considering fairness in group recommendation can enhance the recommendation accuracy.