Enqiang Zhu

Enqiang Zhu, Yizi Liu, Yilong Luo et al.

Accurate prediction of protein-protein interaction sites (PPIS) is essential for understanding cellular processes, disease mechanisms, and therapeutic target discovery. Graph-based deep learning has advanced PPIS prediction by incorporating residue-level structural context. However, most graph-based models still rely on fixed propagation schemes that treat all residues similarly, despite the structural and functional heterogeneity of protein interfaces. Such propagation may limit the ability to adapt information diffusion to local geometric environments, making it difficult to distinguish true interaction sites from structurally similar non-interacting neighbors. We present SGAP-PPIS, a structure-guided adaptive propagation model for PPIS prediction. Rather than using a fixed propagation mechanism, SGAP-PPIS leverages multi-scale geometric states from an equivariant graph neural network to generate residue-wise propagation coefficients. This design allows each residue to adaptively balance local feature preservation and neighborhood diffusion according to its geometric microenvironment. Experimental results show that SGAP-PPIS achieves competitive performance among the state-of-the-art methods on Test\_60. Ablation studies show that geometry-conditioned adaptive propagation, scale-aligned geometric guidance, and multi-step propagation-state representation jointly drive these improvements.

Enqiang Zhu, Yu Zhang, Shengzhi Wang et al.

Given a graph, the minimum dominating set (MinDS) problem is to identify a smallest set $D$ of vertices such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The MinDS problem is a classic $\mathcal{NP}$-hard problem and has been extensively studied because of its many disparate applications in network analysis. To solve this problem efficiently, many heuristic approaches have been proposed to obtain a good solution within an acceptable time limit. However, existing MinDS heuristic algorithms are always limited by various tie-breaking cases when selecting vertices, which slows down the effectiveness of the algorithms. In this paper, we design an efficient local search algorithm for the MinDS problem, named DmDS -- a dual-mode local search framework that probabilistically chooses between two distinct vertex-swapping schemes. We further address limitations of other algorithms by introducing vertex selection criterion based on the frequency of vertices added to solutions to address tie-breaking cases, and a new strategy to improve the quality of the initial solution via a greedy-based strategy integrated with perturbation. We evaluate DmDS against the state-of-the-art algorithms on seven datasets, consisting of 346 instances (or families) with up to tens of millions of vertices. Experimental results show that DmDS obtains the best performance in accuracy for almost all instances and finds much better solutions than state-of-the-art MinDS algorithms on a broad range of large real-world graphs.

Enqiang Zhu, Xiang Li, Chanjuan Liu et al.

The extraction of biomedical data has significant academic and practical value in contemporary biomedical sciences. In recent years, drug repositioning, a cost-effective strategy for drug development by discovering new indications for approved drugs, has gained increasing attention. However, many existing drug repositioning methods focus on mining information from adjacent nodes in biomedical networks without considering the potential inter-relationships between the feature spaces of drugs and diseases. This can lead to inaccurate encoding, resulting in biased mined drug-disease association information. To address this limitation, we propose a new model called Dual-Feature Drug Repurposing Neural Network (DFDRNN). DFDRNN allows the mining of two features (similarity and association) from the drug-disease biomedical networks to encode drugs and diseases. A self-attention mechanism is utilized to extract neighbor feature information. It incorporates two dual-feature extraction modules: the single-domain dual-feature extraction (SDDFE) module for extracting features within a single domain (drugs or diseases) and the cross-domain dual-feature extraction (CDDFE) module for extracting features across domains. By utilizing these modules, we ensure more appropriate encoding of drugs and diseases. A cross-dual-domain decoder is also designed to predict drug-disease associations in both domains. Our proposed DFDRNN model outperforms six state-of-the-art methods on four benchmark datasets, achieving an average AUROC of 0.946 and an average AUPR of 0.597. Case studies on two diseases show that the proposed DFDRNN model can be applied in real-world scenarios, demonstrating its significant potential in drug repositioning.

Yu Zhang, Witold Pedrycz, Chanjuan Liu et al.

The Maximum Independent Set problem is fundamental for extracting conflict-free structure from large graphs, with applications in scheduling, recommendation, and network analysis. However, existing heuristics can stagnate when search schedules are fixed and information from past solutions is underused, leading to wasted effort in low-quality regions of the search space. We present ARCIS, an efficient algorithm for mining large independent sets on massive graphs. ARCIS couples two main components. The first is an adaptive restart policy that refreshes exploration when progress slows. The second is Consensus-Guided Vertex Fixing, which restricts the search to the non-consensus region of the graph by fixing vertices consistently observed within a round. The consensus is maintained as a running intersection within each round, and because it is recomputed at every restart, the fixing is reversible. Vertices that later lose support are automatically unfixed and their neighborhoods re-enter the working graph, which corrects occasional mistakes while preserving progress. Experiments on 222 graphs from four benchmark suites show that ARCIS attains the best or tied-best solution quality in most instances while delivering competitive runtime and low variability. Ablation studies isolate the impact of each component, indicating that ARCIS is a practical and robust method for large-scale graph mining.

Chanjuan Liu, Shengzhi Wang, Enqiang Zhu

Time series forecasting is crucial in strategic planning and decision-making across various industries. Traditional forecasting models mainly concentrate on numerical time series data, often overlooking important textual information such as events and news, which can significantly affect forecasting accuracy. While large language models offer a promise for integrating multimodal data, existing single-prompt frameworks struggle to effectively capture the semantics of timestamped text, introducing redundant information that can hinder model performance. To address this limitation, we introduce DP-GPT4MTS (Dual-Prompt GPT2-base for Multimodal Time Series), a novel dual-prompt large language model framework that combines two complementary prompts: an explicit prompt for clear task instructions and a textual prompt for context-aware embeddings from time-stamped data. The tokenizer generates the explicit prompt while the embeddings from the textual prompt are refined through self-attention and feed-forward networks. Comprehensive experiments conducted on diverse textural-numerical time series datasets demonstrate that this approach outperforms state-of-the-art algorithms in time series forecasting. This highlights the significance of incorporating textual context via a dual-prompt mechanism to achieve more accurate time series predictions.

Chanjuan Liu, Jinmiao Cong, Bingcai Chen et al.

Multi-agent hierarchical reinforcement learning (MAHRL) has been studied as an effective means to solve intelligent decision problems in complex and large-scale environments. However, most current MAHRL algorithms follow the traditional way of using reward functions in reinforcement learning, which limits their use to a single task. This study aims to design a multi-agent cooperative algorithm with logic reward shaping (LRS), which uses a more flexible way of setting the rewards, allowing for the effective completion of multi-tasks. LRS uses Linear Temporal Logic (LTL) to express the internal logic relation of subtasks within a complex task. Then, it evaluates whether the subformulae of the LTL expressions are satisfied based on a designed reward structure. This helps agents to learn to effectively complete tasks by adhering to the LTL expressions, thus enhancing the interpretability and credibility of their decisions. To enhance coordination and cooperation among multiple agents, a value iteration technique is designed to evaluate the actions taken by each agent. Based on this evaluation, a reward function is shaped for coordination, which enables each agent to evaluate its status and complete the remaining subtasks through experiential learning. Experiments have been conducted on various types of tasks in the Minecraft-like environment. The results demonstrate that the proposed algorithm can improve the performance of multi-agents when learning to complete multi-tasks.

Chanjuan Liu, Shengzhi Wang, Enqiang Zhu

In real-world applications, multimodal time series data often suffer from interference, especially in the textual modality. Existing methods for multimodal time series forecasting often neglect the inherent perturbations within textual data, where irrelevant, noisy, or ambiguous content can significantly degrade model performance, particularly when the noise exhibits varying intensity or stems from structural inconsistencies. To address this challenge, we propose PA-RNet (Perturbation-Aware Reasoning Network for Multimodal Time Series Forecasting), a robust multimodal forecasting framework. PA-RNet features a perturbation-aware projection module and a cross-modal attention mechanism to effectively separate noise from the textual embeddings while maintaining semantically meaningful representations, thereby enhancing the model's generalization ability. Theoretically, we establish the Lipschitz continuity of PA-RNet with respect to textual inputs and prove that the proposed perturbation module can reduce expected prediction error, offering strong guarantees of stability under noisy conditions. Furthermore, we introduce a textual perturbation pipeline that can be seamlessly incorporated into existing multimodal time series forecasting tasks, allowing for systematic evaluation of the model's robustness in the presence of varying levels of textual noise. Extensive experiments across diverse domains and temporal settings demonstrate that PA-RNet consistently outperforms state-of-the-art baselines.

Yu Zhang, Yilong Luo, Mingyuan Ma et al.

Discovering quasi-cliques -- subgraphs whose edge density exceeds a given threshold -- is a fundamental task in graph mining with applications to web spam detection, fraud screening, and e-commerce recommendation. However, existing methods for quasi-clique discovery on large-scale web graphs are often sensitive to random seeds or lack of explicit edge-density guarantees, making the task challenging in practice. This paper presents EDQC, an energy diffusion-based method for quasi-clique discovery. EDQC first employs an adaptive energy diffusion process to generate an energy ranking that highlights structurally cohesive regions. Guided by this energy ranking, the algorithm identifies a high-quality subgraph by minimizing conductance, a standard measure from community detection. This subgraph is then refined to meet the specified density threshold. Extensive experiments on 75 real-world graphs show that EDQC finds larger quasi-cliques on most datasets, with consistently lower variance across runs and competitive runtime. To the best of our knowledge, EDQC is the first method to incorporate energy diffusion into quasi-clique discovery.

Enqiang Zhu, Yu Zhang, Haopeng Sun et al.

The graph coloring problem (GCP) is a classic combinatorial optimization problem that aims to find the minimum number of colors assigned to vertices of a graph such that no two adjacent vertices receive the same color. GCP has been extensively studied by researchers from various fields, including mathematics, computer science, and biological science. Due to the NP-hard nature, many heuristic algorithms have been proposed to solve GCP. However, existing GCP algorithms focus on either small hard graphs or large-scale sparse graphs (with up to 10^7 vertices). This paper presents an efficient hybrid heuristic algorithm for GCP, named HyColor, which excels in handling large-scale sparse graphs while achieving impressive results on small dense graphs. The efficiency of HyColor comes from the following three aspects: a local decision strategy to improve the lower bound on the chromatic number; a graph-reduction strategy to reduce the working graph; and a k-core and mixed degree-based greedy heuristic for efficiently coloring graphs. HyColor is evaluated against three state-of-the-art GCP algorithms across four benchmarks, comprising three large-scale sparse graph benchmarks and one small dense graph benchmark, totaling 209 instances. The results demonstrate that HyColor consistently outperforms existing heuristic algorithms in both solution accuracy and computational efficiency for the majority of instances. Notably, HyColor achieved the best solutions in 194 instances (over 93%), with 34 of these solutions significantly surpassing those of other algorithms. Furthermore, HyColor successfully determined the chromatic number and achieved optimal coloring in 128 instances.

Enqiang Zhu, Chenkai Hao, Chanjuan Liu et al.

While Artificial intelligence (AI), including Generative AI, are effective at generating high-quality traffic data and optimization solutions in intelligent transportation systems (ITSs), these techniques often demand significant training time and computational resources, especially in large-scale and complex scenarios. To address this, we introduce a novel and efficient algorithm for solving the maximum weighted independent set (MWIS) problem, which can be used to model many ITSs applications, such as traffic signal control and vehicle routing. Given the NP-hard nature of the MWIS problem, our proposed algorithm, DynLS, incorporates three key innovations to solve it effectively. First, it uses a scores-based adaptive vertex perturbation (SAVP) technique to accelerate convergence, particularly in sparse graphs. Second, it includes a region location mechanism (RLM) to help escape local optima by dynamically adjusting the search space. Finally, it employs a novel variable neighborhood descent strategy, ComLS, which combines vertex exchange strategies with a reward mechanism to guide the search toward high-quality solutions. Our experimental results demonstrate DynLS's superior performance, consistently delivering high-quality solutions within 1000 seconds. DynLS outperformed five leading algorithms across 360 test instances, achieving the best solution for 350 instances and surpassing the second-best algorithm, Cyclic-Fast, by 177 instances. Moreover, DynLS matched Cyclic-Fast's convergence speed, highlighting its efficiency and practicality. This research represents a significant advancement in heuristic algorithms for the MWIS problem, offering a promising approach to aid AI techniques in optimizing intelligent transportation systems.

Enqiang Zhu, Qiqi Bao, Yu Zhang et al.

The problem of finding a minimum vertex cover (MVC) in a graph is a well-known NP-hard problem with significant practical applications in optimization and scheduling. Its complexity, combined with the increasing scale of problems, underscores the need for efficient and effective algorithms. However, existing heuristic algorithms for MVC often rely on simplistic initialization strategies and overlook the impact of edge attributes and neighborhood information on vertex selection. In this paper, we introduce GCNIVC, a novel heuristic search algorithm designed to address the limitations of existing methods for solving MVC problems in large-scale graphs. Our approach features two main innovations. First, it utilizes a Graph Convolutional Network (GCN) to capture the global structure of graphs, which enables the generation of high-quality initial solutions that enhance the efficiency of the subsequent search process. Second, GCNIVC introduces a new heuristic that employs three containers and the concept of double-covered edges (dc-edges), improving search efficiency and providing greater flexibility for adding and removing operations based on edge attributes. Through extensive experiments on benchmark datasets, we demonstrate that GCNIVC outperforms state-of-the-art MVC algorithms in terms of both accuracy and efficiency. Our results highlight the effectiveness of GCNIVC's GCN-assisted initialization and its edge-informed search strategy. This study not only advances the understanding of MVC problem-solving but also contributes a new tool for addressing large-scale graph optimization challenges.