arXiv subjects

Enqiang Zhu

Publications and source records attributed to Enqiang Zhu.

At least 19 recordsLinked to original sources

arXiv2026

Total-coloring of planar graphs with maximum degree 6 and without prescribed 4-cycles

The Total Coloring Conjecture (TCC) is a challenging unsolved problem posed by Behzad and Vizing independently, which states that every simple graph $G$ admits a ($Δ(G)$ +2)-total-coloring, where $Δ(G)$ denotes the maximum degree of $G$. This conjecture has been confirmed for graphs with $Δ(G)\leq 5$. However, for planar graphs, the only open case is $Δ(G)=6$. It was known that planar graphs with maximum degree 6 and without 4-cycles are 7-totally-colorable. In this paper, we improve this result by showing that any planar graph $G$ of maximum degree 6, which does not contain some special 4-cycles, is 7-totally-colorable.

math.CO↗

arXiv2026

GRALS: GCN-Guided Redundancy-Aware Local Search for Minimum Vertex Cover

The minimum vertex cover (MVC) problem seeks to identify the smallest set of vertices that cover all edges in an undirected graph. As a fundamental NP-hard combinatorial optimization problem, MVC has been widely studied due to its applications in network analysis and system design. For large-scale instances, local search heuristics are among the most effective approaches, offering a practical trade-off between solution quality and computational efficiency. Most existing high-performance local search algorithms adopt a break-and-repair framework, where the repair process mainly restores feasibility but provides limited opportunities for enhancing the current solution's structure. We introduce GRALS, a local search framework that integrates vertex probability priors learned from a graph convolutional network with an expansion revelation elimination (ERE) operator. The learned priors guide the search toward promising regions, while the ERE operator dynamically identifies and eliminates redundant vertices to further enhance solution quality. Experiments conducted on 346 benchmark instances demonstrate that GRALS achieves the best-known solution for 335 instances, compared to 302 instances achieved by the strongest baseline. The advantage of GRALS is maintained across different time limits and is particularly evident on large-scale graphs with millions of vertices.

cs.AI↗

arXiv2026

Structure-Guided Adaptive Propagation for Protein-Protein Interaction Site Prediction

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.

cs.AI↗

arXiv2026

PA-RNet: Perturbation-Aware Residual Network for Robust Multimodal Time Series Forecasting

In real-world applications, multimodal time-series forecasting faces a key challenge: textual information is often useful but unreliable. Auxiliary texts may contain irrelevant, ambiguous, incomplete, or structurally corrupted content, making direct text integration prone to introducing noisy semantic signals and degrading forecasting performance. Therefore, robust multimodal forecasting requires a model that can exploit useful textual context while suppressing misleading perturbations. To address this challenge, we propose PA-RNet, a carefully designed perturbation-aware residual network for robust multimodal time-series forecasting. Rather than directly fusing textual and numerical representations, PA-RNet first refines multimodal features in a perturbation-aware manner, preserving stable contextual information while reducing unstable or misleading signals. The refined textual representations are then aligned with temporal dynamics, enabling more reliable forecasting under noisy multimodal conditions. Theoretically, we prove that PA-RNet is Lipschitz continuous with respect to textual embeddings and show that the proposed spectral residual correction can reduce the expected prediction error under zero-mean textual perturbations. We further conduct supplementary experiments with injected textual perturbations to examine the robustness of PA-RNet. The results across diverse domains demonstrate that PA-RNet consistently outperforms state-of-the-art baselines and maintains stable forecasting performance under both original and noise-perturbed textual conditions.

cs.LG↗

arXiv2026

DNA Ternary Full Adder

As transistor dimensions continue to shrink, binary devices are rapidly approaching their fundamental limits in power density. In response, multi-valued systems have attracted significant attention due to their enhanced information density. Among these, the ternary system stands out as the most practical option, being the closest integer base to (e), which is considered optimal for information efficiency. Despite the intrinsic advantages of DNA nanomaterials, such as programmability, energy efficiency, and massive parallelism, their application in ternary logic remains largely unexplored, particularly in the realm of ternary addition circuits. This gap can be attributed to a fundamental challenge: ternary logic requires circuits capable of recognizing and processing a far larger set of input combinations than binary systems, a task that existing models and techniques often struggle to accomplish. In this work, we propose a novel architecture for a ternary full adder. Our design includes a competitive blocking (CB) circuit that enables the recognition and computation of all possible three-input ternary combinations. Coupled with a dynamic concentration adjustment (CA) strategy, this approach significantly enhances the number of trits that can be processed. Biochemical experiments demonstrate that the CB circuit successfully yields the correct output digits for a ternary full adder, achieving 17-trit ternary addition. To our knowledge, this work represents the first successful DNA-based ternary adder, establishing a new methodological foundation for DNA computing and highlighting its considerable potential for scalable digital information processing.

q-bio.MN↗

arXiv2026

Cohesive Group Discovery in Interaction Graphs under Explicit Density Constraints

Discovering cohesive groups is a fundamental primitive in graph-based recommender systems, underpinning tasks such as social recommendation, bundle discovery, and community-aware modeling. In interaction graphs, cohesion is often modeled as the $γ$-quasi-clique, an induced subgraph whose internal edge density meets a user-defined threshold $γ$. This formulation provides explicit control over within-group connectivity while accommodating the sparsity inherent in real-world data. This paper presents EDQC, an effective framework for cohesive group discovery under explicit density constraints. EDQC leverages a lightweight energy diffusion process to rank vertices for localizing promising candidate regions. Guided by this ranking, the framework extracts and refines a candidate subgraph to ensure the output strictly satisfies the target density requirement. Extensive experiments on 75 real-world graphs across varying density thresholds demonstrate that EDQC identifies the largest mean $γ$-quasi-cliques in the vast majority of cases, achieving lower variance than the state-of-the-art methods while maintaining competitive runtime. Furthermore, statistical analysis confirms that EDQC significantly outperforms the baselines, underscoring its robustness and practical utility for cohesive group discovery in graph-based recommender systems.

cs.SI↗

arXiv2025

Mining Large Independent Sets on Massive Graphs

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.

cs.AI↗

arXiv2025

Exact Optimization for Minimum Dominating Sets

The Minimum Dominating Set (MDS) problem is a well-established combinatorial optimization problem with numerous real-world applications. Its NP-hard nature makes it increasingly difficult to obtain exact solutions as the graph size grows. This paper introduces ParDS, an exact algorithm developed to address the MDS problem within the branch-and-bound framework. ParDS features two key innovations: an advanced linear programming technique that yields tighter lower bounds and a set of novel reduction rules that dynamically simplify instances throughout the solving process. Compared to the leading exact algorithms presented at IJCAI 2023 and 2024, ParDS demonstrates theoretically superior lower-bound quality. Experimental results on standard benchmark datasets highlight several significant advantages of ParDS: it achieves fastest solving times in 70% of graph categories, especially on large, sparse graphs, delivers a speed-up of up to 3,411 times on the fastest individual instance, and successfully solves 16 out of 43 instances that other algorithms were unable to resolve within the 5-hour time limit. These findings establish ParDS as a state-of-the-art solution for exactly solving the MDS problem.

cs.DS↗

arXiv2025

DP-GPT4MTS: Dual-Prompt Large Language Model for Textual-Numerical Time Series Forecasting

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.

cs.CL↗

arXiv2025

The Total Coloring Conjecture holds for planar graphs without three special subgraphs

The Total Coloring Conjecture (TCC) for planar graphs with a maximum degree of six remains open. Previous studies suggest that TCC is valid for such graphs if they do not contain any subgraph isomorphic to a 4-fan. In this paper, we present an improved conclusion by establishing that TCC holds for planar graphs that are free of three particular substructures, namely the mushroom, the tent, and the cone. This advancement enhances previous findings by demonstrating that TCC is applicable to planar graphs with a maximum degree of six, which can accommodate sparse 4-fans, 5-fans, 5-wheels, and 6-wheels.

math.CO↗

arXiv2025

HyColor: An Efficient Heuristic Algorithm for Graph Coloring

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.

cs.DM↗

arXiv2025

Dynamic Location Search for Identifying Maximum Weighted Independent Sets in Complex Networks

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.

cs.AI↗

arXiv2025

Boosting drug-disease association prediction for drug repositioning via dual-feature extraction and cross-dual-domain decoding

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.

cs.LG↗

arXiv2024

Guiding Multi-agent Multi-task Reinforcement Learning by a Hierarchical Framework with Logical Reward Shaping

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.

cs.AI↗

arXiv2024

Improving Critical Node Detection Using Neural Network-based Initialization in a Genetic Algorithm

The Critical Node Problem (CNP) is concerned with identifying the critical nodes in a complex network. These nodes play a significant role in maintaining the connectivity of the network, and removing them can negatively impact network performance. CNP has been studied extensively due to its numerous real-world applications. Among the different versions of CNP, CNP-1a has gained the most popularity. The primary objective of CNP-1a is to minimize the pair-wise connectivity in the remaining network after deleting a limited number of nodes from a network. Due to the NP-hard nature of CNP-1a, many heuristic/metaheuristic algorithms have been proposed to solve this problem. However, most existing algorithms start with a random initialization, leading to a high cost of obtaining an optimal solution. To improve the efficiency of solving CNP-1a, a knowledge-guided genetic algorithm named K2GA has been proposed. Unlike the standard genetic algorithm framework, K2GA has two main components: a pretrained neural network to obtain prior knowledge on possible critical nodes, and a hybrid genetic algorithm with local search for finding an optimal set of critical nodes based on the knowledge given by the trained neural network. The local search process utilizes a cut node-based greedy strategy. The effectiveness of the proposed knowledgeguided genetic algorithm is verified by experiments on 26 realworld instances of complex networks. Experimental results show that K2GA outperforms the state-of-the-art algorithms regarding the best, median, and average objective values, and improves the best upper bounds on the best objective values for eight realworld instances.

cs.NE↗

arXiv2023

A Dual-mode Local Search Algorithm for Solving the Minimum Dominating Set Problem

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.

cs.SI↗

arXiv2022

A universal DNA computing model for solving NP-hard subset problems

DNA computing, a nontraditional computing mechanism, provides a feasible and effective method for solving NP-hard problems because of the vast parallelism and high-density storage of DNA molecules. Although DNA computing has been exploited to solve various intractable computational problems, such as the Hamiltonian path problem, SAT problem, and graph coloring problem, there has been little discussion of designing universal DNA computing-based models, which can solve a class of problems. In this paper, by leveraging the dynamic and enzyme-free properties of DNA strand displacement, we propose a universal model named DCMSubset for solving subset problems in graph theory. The model aims to find a minimum (or maximum) set satisfying given constraints. For each element x involved in a given problem, DCMSubset uses an exclusive single-stranded DNA molecule to model x as well as a specific DNA complex to model the relationship between x and other elements. Based on the proposed model, we conducted simulation and biochemical experiments on three kinds of subset problems, a minimum dominating set, maximum independent set, and minimum vertex cover. We observed that DCMSubset can also be used to solve the graph coloring problem. Moreover, we extended DCMSubset to a model for solving the SAT problem. The results of experiments showed the feasibility and university of the proposed method. Our results highlighted the potential for DNA strand displacement to act as a computation tool to solve NP-hard problems.

q-bio.MN↗

arXiv2022

PHEE: A phased hybrid evaluation-enhanced approach for identifying influential users in social networks

For the purpose of maximizing the spread of influence caused by a certain small number k of nodes in a social network, we are asked to find a k-subset of nodes (i.e., a seed set) with the best capacity to influence the nodes not in it. This problem of influence maximization (IM) has wide application, belongs to subset problems, and is NP-hard. To solve it, we should theoretically examine all seed sets and evaluate their influence spreads, which is time-consuming. Therefore, metaheuristic strategies are generally employed to gain a good seed set within a reasonable time. We observe that many algorithms for the IM problem only adopt a uniform mechanism in the whole solution search process, which lacks a response measure when the algorithm becomes trapped in a local optimum. To address this issue, we propose a phased hybrid evaluation-enhanced (PHEE) approach for IM, which utilizes two distinct search strategies to enhance the search of optimal solutions: a randomized range division evolutionary (RandRDE) algorithm to improve the solution quality, and a fast convergence strategy. Our approach is evaluated on 10 real-world social networks of different sizes and types. Experimental results demonstrate that our algorithm is efficient and obtains the best influence spread for all the datasets compared with three state-of-the-art algorithms, outperforms the time consuming CELF algorithm on four datasets, and performs worse than CELF on only two networks.

cs.SI↗