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Rong-Hua Li

Rong-Hua Li contributes to research discovery and scholarly infrastructure.

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Machine Learning Artificial Intelligence Databases math.CO Computer Vision Data Structures and Algorithms Distributed, Parallel, and Cluster Computing

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preprint2026arXiv

AlgBench: To What Extent Do Large Reasoning Models Understand Algorithms?

Reasoning ability has become a central focus in the advancement of Large Reasoning Models (LRMs). Although notable progress has been achieved on several reasoning benchmarks such as MATH500 and LiveCodeBench, existing benchmarks for algorithmic reasoning remain limited, failing to answer a critical question: Do LRMs truly master algorithmic reasoning? To answer this question, we propose AlgBench, an expert-curated benchmark that evaluates LRMs under an algorithm-centric paradigm. AlgBench consists of over 3,000 original problems spanning 27 algorithms, constructed by ACM algorithmic experts and organized under a comprehensive taxonomy, including Euclidean-structured, non-Euclidean-structured, non-optimized, local-optimized, global-optimized, and heuristic-optimized categories. Empirical evaluations on leading LRMs (e.g., Gemini-3-Pro, DeepSeek-v3.2-Speciale and GPT-o3) reveal substantial performance heterogeneity: while models perform well on non-optimized tasks (up to 92%), accuracy drops sharply to around 49% on globally optimized algorithms such as dynamic programming. Further analysis uncovers \textbf{strategic over-shifts}, wherein models prematurely abandon correct algorithmic designs due to necessary low-entropy tokens. These findings expose fundamental limitations of problem-centric reinforcement learning and highlight the necessity of an algorithm-centric training paradigm for robust algorithmic reasoning.

preprint2026arXiv

CAMPA: Efficient and Aligned Multimodal Graph Learning via Decoupled Propagation and Aggregation

Multimodal Graph Neural Networks (MGNNs) have shown strong potential for learning from multimodal attributed graphs, yet most existing approaches rely on tightly coupled architectures that suffer from prohibitive computational overhead. In this paper, we present a systematic empirical analysis showing that decoupled MGNNs are substantially more efficient and scalable for large-scale graph learning. However, we identify a critical bottleneck in existing decoupled pipelines, namely modal conflict, which arises in both the propagation and aggregation stages. Specifically, independent multi-hop diffusion causes cross-modal semantic divergence during propagation, while naive fusion fails to align multi-hop feature trajectories during aggregation, jointly limiting effective representation learning. To address this challenge, we propose CAMPA, a Cross-modal Aligned Multimodal Propagation & Aggregation framework for decoupled multimodal graph learning. Concretely, CAMPA introduces a two-stage alignment mechanism: (1) cross-modal aligned propagation, which injects cross-modal similarity priors into message passing to preserve semantic consistency without additional parameter overhead; (2) trajectory aligned aggregation, which leverages trajectory-level self-attention and cross-attention to capture and align long-range dependencies across modalities and hops. Extensive experiments on diverse benchmark datasets and tasks demonstrate that CAMPA consistently outperforms strong coupled and decoupled baselines while preserving the efficiency advantages of the decoupled paradigm.

preprint2026arXiv

GOMA: Toward Structure-Driven Multimodal Alignment from a Graph Signal Smoothing Perspective

Multimodal alignment is commonly learned from isolated image-text pairs via CLIP-style dual encoders, leaving the relational context among entities largely unused. Multimodal attributed graphs (MAGs), where nodes carry multimodal attributes and edges encode corpus structure, provide a natural setting for refining frozen vision-language embeddings. This refinement is challenging: visual, textual, and cross-modal relations often induce different neighborhood geometries, while unrestricted graph propagation can quickly over-smooth retrieval representations. Effectively leveraging graph context therefore requires simultaneously breaking modality-specific topological barriers, controlling the smoothing regime, and preserving informative smoothing before semantic boundaries collapse. We propose Graph-Optimized Multimodal Alignment (GOMA), a structure-driven post-alignment framework that views frozen multimodal embeddings as graph signals and addresses these requirements through a unified retrieval-oriented design. GOMA decouples three key design choices: where messages should flow, how multimodal evidence should propagate, and which smoothing depth should be retained. Concretely, it learns modality-aware propagation operators, performs finite-step coupled smoothing without diagonal cross-modal shortcuts, and adaptively reads out node-specific smoothing trajectories to preserve useful smoothing before collapse. All experiments follow a transductive MAG retrieval protocol where the graph serves only as unlabeled context and diagonal self-pair edges are removed. On seven MAG benchmarks, GOMA achieves state-of-the-art or tied state-of-the-art retrieval and remains substantially more stable than the strongest graph competitor, demonstrating that MAG structure can serve as an effective post-encoder for frozen multimodal embeddings.

preprint2026arXiv

STAGE: Tackling Semantic Drift in Multimodal Federated Graph Learning

Federated graph learning (FGL) enables collaborative training on graph data across multiple clients. As graph data increasingly contain multimodal node attributes such as text and images, multimodal federated graph learning (MM-FGL) has become an important yet substantially harder setting. The key challenge is that clients from different modality domains may not share a common semantic space: even for the same concept, their local encoders can produce inconsistent representations before collaboration begins. This makes direct parameter coordination unreliable and further causes two downstream problems: forcing heterogeneous client representations into a naively shared semantic space may create false semantic agreement, and graph message passing may amplify residual inconsistency across neighborhoods. To address this issue, we propose \textbf{STAGE}, a protocol-first framework for MM-FGL. Instead of relying on direct parameter averaging, STAGE builds a shared semantic space that first translates heterogeneous multimodal features into comparable representations and then regulates how these representations propagate over local graph structures. In this way, STAGE not only improves cross-client semantic calibration, but also reduces the risk of inconsistency amplification during graph learning. Extensive experiments on 8 multimodal-attributed graphs across 5 graph-centric and modality-centric tasks show that STAGE consistently achieves state-of-the-art performance while reducing per-round communication payload.

preprint2026arXiv

Theoretically and Practically Efficient Resistance Distance Computation on Large Graphs

The computation of resistance distance is pivotal in a wide range of graph analysis applications, including graph clustering, link prediction, and graph neural networks. Despite its foundational importance, efficient algorithms for computing resistance distances on large graphs are still lacking. Existing state-of-the-art (SOTA) methods, including power iteration-based algorithms and random walk-based local approaches, often struggle with slow convergence rates, particularly when the condition number of the graph Laplacian matrix, denoted by $κ$, is large. To tackle this challenge, we propose two novel and efficient algorithms inspired by the classic Lanczos method: Lanczos Iteration and Lanczos Push, both designed to reduce dependence on $κ$. Among them, Lanczos Iteration is a near-linear time global algorithm, whereas Lanczos Push is a local algorithm with a time complexity independent of the size of the graph. More specifically, we prove that the time complexity of Lanczos Iteration is $\tilde{O}(\sqrtκ m)$ ($m$ is the number of edges of the graph and $\tilde{O}$ means the complexity omitting the $\log$ terms) which achieves a speedup of $\sqrtκ$ compared to previous power iteration-based global methods. For Lanczos Push, we demonstrate that its time complexity is $\tilde{O}(κ^{2.75})$ under certain mild and frequently established assumptions, which represents a significant improvement of $κ^{0.25}$ over the SOTA random walk-based local algorithms. We validate our algorithms through extensive experiments on eight real-world datasets of varying sizes and statistical properties, demonstrating that Lanczos Iteration and Lanczos Push significantly outperform SOTA methods in terms of both efficiency and accuracy.

preprint2026arXiv

Towards Robust Federated Multimodal Graph Learning under Modality Heterogeneity

Recently, multimodal graph learning (MGL) has garnered significant attention for integrating diverse modality information and structured context to support various network applications. However, real-world graphs are often isolated due to data-sharing limitations across multiple parties, and their modalities are frequently incomplete. This highlights an urgent need to develop a robust federated approach. However, we find that existing methods remain insufficient. On the one hand, centralized MGL methods that handle missing modalities overlook the knowledge sharing and generalization in federated scenarios. On the other hand, while federated MGL methods have become increasingly mature, they primarily target non-graph data. Based on these technologies, we identify a two-stage pipeline wherein client-side completion reconstructs missing modalities, and server-side aggregation integrates the client-updated parameters of both the modality generator and the backbone models. Although this serves as a general solution, we identify two primary challenges in achieving greater robustness: (1) Topology-Isolated Local Completion: Client-side modality generation struggles to effectively leverage global semantics. (2) Reliability-Imbalanced Global Aggregation: Server-side multi-party collaboration is hindered by client updates with varying modality availability and recovery reliability. To address these challenges, we propose \textsc{FedMPO}, which utilizes topology-aware cross-modal generation to recover missing features using comprehensive graph context, missing-aware expert routing to locally filter out noisy recovered signals, and reliability-aware aggregation to appropriately down-weight unreliable updates. Extensive experiments on 3 tasks across 6 datasets demonstrate that FedMPO outperforms baselines, achieving performance gains of up to 4.10% and 5.65% in high-missing and non-IID settings.

preprint2025arXiv

Knowledge-Driven Federated Graph Learning on Model Heterogeneity

Federated graph learning (FGL) has emerged as a promising paradigm for collaborative graph representation learning, enabling multiple parties to jointly train models while preserving data privacy. However, most existing approaches assume homogeneous client models and largely overlook the challenge of model-centric heterogeneous FGL (MHtFGL), which frequently arises in practice when organizations employ graph neural networks (GNNs) of different scales and architectures.Such architectural diversity not only undermines smooth server-side aggregation, which presupposes a unified representation space shared across clients' updates, but also further complicates the transfer and integration of structural knowledge across clients. To address this issue, we propose the Federated Graph Knowledge Collaboration (FedGKC) framework. FedGKC introduces a lightweight Copilot Model on each client to facilitate knowledge exchange while local architectures are heterogeneous across clients, and employs two complementary mechanisms: Client-side Self-Mutual Knowledge Distillation, which transfers effective knowledge between local and copilot models through bidirectional distillation with multi-view perturbation; and Server-side Knowledge-Aware Model Aggregation, which dynamically assigns aggregation weights based on knowledge provided by clients. Extensive experiments on eight benchmark datasets demonstrate that FedGKC achieves an average accuracy gain of 3.88% over baselines in MHtFGL scenarios, while maintaining excellent performance in homogeneous settings.

preprint2022arXiv

Biharmonic distance of graphs

Lipman et al. [ACM Transactions on Graphics 29 (3) (2010), 1--11] introduced the concept of biharmonic distance to measure the distances between pairs of points on a 3D surface. Biharmonic distance has some advantages over resistance distance and geodesic distance in some realistic contexts. Nevertheless, limited work has been done on the biharmonic distance in the discrete case. In this paper, we give some characterizations of the biharmonic distance of a graph. Some basic mathematical properties of biharmonic distance and biharmonic index are established.

preprint2022arXiv

Fairness-aware Maximal Clique in Large Graphs: Concepts and Algorithms

Cohesive subgraph mining on attributed graphs is a fundamental problem in graph data analysis. Existing cohesive subgraph mining algorithms on attributed graphs do not consider the fairness of attributes in the subgraph. In this paper, we, for the first time, introduce fairness into the widely-used clique model to mine fairness-aware cohesive subgraphs. In particular, we propose three novel fairness-aware maximal clique models on attributed graphs, called weak fair clique, strong fair clique and relative fair clique, respectively. To enumerate all weak fair cliques, we develop an efficient backtracking algorithm called WFCEnum equipped with a novel colorful k-core based pruning technique. We also propose an efficient enumeration algorithm called SFCEnum to find all strong fair cliques based on a new attribute-alternatively-selection search technique. To further improve the efficiency, we also present several non-trivial ordering techniques for both weak and strong fair clique enumerations. To enumerate all relative fair cliques, we design an enhanced colorful k-core based pruning technique for 2D attribute, and then develop two efficient search algorithms: RFCRefineEnum and RFCAlterEnum based on the ideas of WFCEnum and SFCEnum for arbitrary dimension attribute. The results of extensive experiments on four real-world graphs demonstrate the efficiency, scalability and effectiveness of the proposed algorithms.

preprint2022arXiv

Scaling Up Maximal k-plex Enumeration

Finding all maximal $k$-plexes on networks is a fundamental research problem in graph analysis due to many important applications, such as community detection, biological graph analysis, and so on. A $k$-plex is a subgraph in which every vertex is adjacent to all but at most $k$ vertices within the subgraph. In this paper, we study the problem of enumerating all large maximal $k$-plexes of a graph and develop several new and efficient techniques to solve the problem. Specifically, we first propose several novel upper-bounding techniques to prune unnecessary computations during the enumeration procedure. We show that the proposed upper bounds can be computed in linear time. Then, we develop a new branch-and-bound algorithm with a carefully-designed pivot re-selection strategy to enumerate all $k$-plexes, which outputs all $k$-plexes in $O(n^2γ_k^n)$ time theoretically, where $n$ is the number of vertices of the graph and $γ_k$ is strictly smaller than 2. In addition, a parallel version of the proposed algorithm is further developed to scale up to process large real-world graphs. Finally, extensive experimental results show that the proposed sequential algorithm can achieve up to $2\times$ to $100\times$ speedup over the state-of-the-art sequential algorithms on most benchmark graphs. The results also demonstrate the high scalability of the proposed parallel algorithm. For example, on a large real-world graph with more than 200 million edges, our parallel algorithm can finish the computation within two minutes, while the state-of-the-art parallel algorithm cannot terminate within 24 hours.

preprint2020arXiv

The $g$-extra edge-connectivity of balanced hypercubes

The $g$-extra edge-connectivity is an important measure for the reliability of interconnection networks. Recently, Yang et al. [Appl. Math. Comput. 320 (2018) 464--473] determined the $3$-extra edge-connectivity of balanced hypercubes $BH_n$ and conjectured that the $g$-extra edge-connectivity of $BH_n$ is $λ_g(BH_n)=2(g+1)n-4g+4$ for $2\leq g\leq 2n-1$. In this paper, we confirm their conjecture for $n\geq 6-\dfrac{12}{g+1}$ and $2\leq g\leq 8$, and disprove their conjecture for $n\geq \dfrac{3e_g(BH_n)}{g+1}$ and $9\leq g\leq 2n-1$, where $e_g(BH_n)=\max\{|E(BH_n[U])|\mid U\subseteq V(BH_n), |U|=g+1\}$.

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