arXiv subjects

Tianle Jiang

Publications and source records attributed to Tianle Jiang.

6 recordsLinked to original sources

arXiv2026

On the Communication Complexity of Maximum Matching and Negative-Weight Shortest Paths

We revisit several fundamental graph problems in the deterministic two-party communication model. Our main contributions include: (1) a new $\widetilde{O}(n^{3/2})$-bit protocol for computing a maximum matching in general graphs. While the same upper bound can be obtained by simulating the classic algorithms of Micali-Vazirani and Gabow, our protocol is conceptually simple and avoids the intricacies of finding a maximal set of shortest augmenting paths; (2) a new $\widetilde{O}(n)$-bit protocol for negative-cycle detection and negative-weight single-source shortest paths. Our protocol simplifies that of Blikstad et al. by replacing a long chain of reductions with a more direct approach based on vertex potentials; (3) a combinatorial $\widetilde{O}(n)$-bit protocol for computing a maximum matching in bipartite graphs, obtained by reinterpreting the near-linear communication protocol of Blikstad et al. through a discretized analysis. Together, these results provide simpler protocols for several basic graph problems. We hope they will inspire further advances on the communication complexity of a wide range of graph problems.

cs.DS↗

arXiv2026

On the Cost of Non-Adaptivity in Matroid Prophet Inequalities

Matroid prophet inequalities admit an optimal 2-competitive algorithm, which relies on adaptively updating thresholds based on previous outcomes. Motivated by applications to posted-price mechanisms and the structural simplicity of fixed-threshold policies, recent work initiated the study of non-adaptive matroid prophet inequalities. The central question is to understand how much the performance deteriorates when thresholds must be fixed in advance. We explore the fundamental limits of non-adaptive algorithms and show new structural barriers and algorithmic insights. We first identify a simple case where non-adaptive algorithms admit a lower bound strictly above $2$: for truncated partition matroids where every local partition has rank $1$, there is an instance giving a lower bound of $\approx 2.179$, and we give a non-adaptive OCRS-style algorithm that exactly matches this ratio. We then show that richer matroid structures can amplify this barrier: we obtain stronger lower bounds of $2.217$ for laminar matroids and $3$ for graphic matroids, and complement the hardness results with improved upper bounds for these matroids.

cs.DS↗

arXiv2026

Simple KNN-Based Outlier Detection Achieves Robust Clustering

Being robust to the presence of outliers is crucial for applying clustering algorithms in practice. In the $\textit{robust $k$-Means}$ problem (i.e., $k$-Means with outliers), the goal is to remove $z$ outliers and minimize the $k$-Means cost on the remaining points. Despite the close connection between robust $k$-Means and outlier detection, both theoretical and empirical understanding of the effectiveness of $\textit{classic outlier detection heuristics}$ for robust $k$-Means remains limited. In this paper, we prove that under a practical assumption on the optimal cluster sizes, simply removing points with large $K$-Nearest-Neighbor distances achieves performance comparable to prior work in terms of approximation guarantees: it yields a constant-factor reduction from robust $k$-Means to standard $k$-Means, without introducing additional centers or discarding extra outliers, as is commonly required by existing approaches. Empirically, experiments on real-world datasets show that our method outperforms or matches several more sophisticated algorithms in terms of clustering cost and runtime. These results demonstrate that simple KNN-based heuristics can be surprisingly effective for robust clustering, highlighting new opportunities to bridge techniques from outlier detection and clustering.

cs.LG↗

arXiv2026

PolyCrysDiff: Controllable Generation of Three-Dimensional Computable Polycrystalline Material Structures

The three-dimensional (3D) microstructures of polycrystalline materials exert a critical influence on their mechanical and physical properties. Realistic, controllable construction of these microstructures is a key step toward elucidating structure-property relationships, yet remains a formidable challenge. Herein, we propose PolyCrysDiff, a framework based on conditional latent diffusion that enables the end-to-end generation of computable 3D polycrystalline microstructures. Comprehensive qualitative and quantitative evaluations demonstrate that PolyCrysDiff faithfully reproduces target grain morphologies, orientation distributions, and 3D spatial correlations, while achieving an $R^2$ over 0.972 on grain attributes (e.g., size and sphericity) control, thereby outperforming mainstream approaches such as Markov random field (MRF)- and convolutional neural network (CNN)-based methods. The computability and physical validity of the generated microstructures are verified through a series of crystal plasticity finite element method (CPFEM) simulations. Leveraging PolyCrysDiff's controllable generative capability, we systematically elucidate how grain-level microstructural characteristics affect the mechanical properties of polycrystalline materials. This development is expected to pave a key step toward accelerated, data-driven optimization and design of polycrystalline materials.

cs.CV↗

arXiv2025

Mass-transport-limited reaction rates and molecular diffusion in the van der Waals gap beneath graphene

The confinement of molecules within the van der Waals (vdW) gap between a two-dimensional 2D material and a catalytic substrate offers a promising route toward the development of molecule-selective catalysts with increased reaction rates. However, identifying the kinetic limitations of such confined reactions remains challenging. Here, we employ an inverted wedding-cake configuration of multilayer graphene on platinum to study the dynamics of graphene etching in the vdW gap by various molecules (O2, H2, and CO), using in situ scanning electron microscopy. Under the experimental conditions explored (up to p = 1.4x10-3 Pa and T = 1000 °C), the etching reaction rates are limited by mass transport within the confined space. This limitation persists even for CO, despite its anomalously enhanced transport resulting from a significant lifting of the vdW gap. Reactive molecular dynamics simulations further reveal multiple etching pathways for CO, enabled by confinement within the vdW space. Once mass-transport limitations are overcome, the vdW gap acts as an effective nanoreactor, facilitating reaction pathways that would be otherwise inaccessible on a pristine surface without spatial confinement.

cond-mat.mes-hall↗

arXiv2024

Edge Arrival Online Matching: The Power of Free Disposal on Acyclic Graphs

Online matching is a fundamental problem in the study of online algorithms. We study the problem under a very general arrival model: the edge arrival model. Free disposal is an important notion in the online matching literature, which allows the algorithm to dispose of the previously matched edges. Without free disposal, we cannot achieve any bounded ratio, even with randomized algorithms, when edges are weighted. Our paper focuses on clarifying the power of free disposal in both the unweighted and the weighted setting. As far as we know, it's still uncertain if free disposal can give us extra leverage to enhance the competitive ratio in the unweighted scenario, even in specific instances such as Growing Trees, where every new edge adds a new leaf to the graph. Our study serves as a valuable initial exploration of this open question. The results are listed as follows: 1. With free disposal, we improve the competitive ratio for unweighted online matching on Growing Trees from $5/9$ to $2/3 \approx 0.66$, and show that the ratio is tight. For Forests, a more general setting where the underlying graph is a forest and edges may arrive in arbitrary order, we improve the competitive ratio from $5/9$ to $5/8 = 0.625$. 2. Both the ratios of $2/3$ and $0.625$ show a separation to the upper bound of the competitive ratio without free disposal on Growing Trees ($0.5914$). Therefore, we demonstrate the additional power of free disposal for the unweighted setting for the first time, at least in the special setting of Growing Trees and Forests. 3. We improve the competitive ratio for weighted online matching on Growing Trees from $1/3$ to $1/2$ using a very simple ordinal algorithm, and show that it is optimal among ordinal algorithms.

cs.DS↗