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Zian Chen

Publications and source records attributed to Zian Chen.

6 recordsLinked to original sources
arXiv2026

I-Rex: An Interactive Debugger for SQL

SQL is declarative in nature and rich in its features. Writing semantically correct SQL queries and finding logical bugs in SQL are not easy, even for experienced programmers, who are often used to the mindset of working with general-purpose programming languages (GPLs). While there are many GPL debuggers, SQL debugging has received much less attention. In this paper, we present I-Rex, a SQL debugger that enables users to inspect the logical execution of SQL queries visually and interactively to identify and potentially fix logical bugs in the queries. I-Rex draws analogies to the debugging paradigm of GPLs (e.g., stepping, watchpoints, etc.), making it easier for programmers to adopt. However, unlike debugging GPLs, which involves executing the underlying program in full to the point of interest, I-Rex allows users to jump to arbitrary points of interest by leveraging the power of the database systems, through selective materialization and query rewrites. To simplify deployment, I-Rex acts as a lightweight middleware on top of the database system; it imposes no overhead to prepare a database for debugging and maintains no state in the database systems during debugging sessions. We demonstrate the effectiveness of I-Rex through performance experiments as well as a user study in an educational setting.

cs.DB↗
arXiv2026

The exact generalized Tur\'an number for \(C_6\) in \(C_8\)-free graphs

For graphs $F$ and $H$, let $\ex(n,F,H)$ denote the maximum number of copies of $F$ in an $n$-vertex $H$-free graph. Gerbner, Gy\H{o}ri, Methuku and Vizer proved that $\ex(n,C_6,C_8)=\Theta(n^3)$ and predicted that the unrestricted problem should have the same first-order asymptotics as the bipartite one. We determine the exact value for all sufficiently large $n$, showing that \[ \ex(n,C_6,C_8)=6\binom{n-3}{3}+12(n-5). \] Moreover, the unique extremal graph is $K_3\vee (K_2\cup I_{n-5})$. The main new ingredient is a codegree decomposition for $C_8$-free graphs: a packing lemma for triangles in the linear-codegree graph recovers an almost spanning common neighborhood, and a defect-absorption argument upgrades this stability to the exact extremal graph.

math.CO↗
arXiv2026

On saturation problems involving clique number and matching number

For a clique $K_r$, a graph is $K_r$-saturated if it contains no copy of $K_r$ and the addition of any edge from its complement creates a $K_r$. A classical result of Erd\H{o}s-Hajnal-Moon and Zykov shows that the number of edges of an $n$-vertex $K_r$-saturated graph is at least $(r-2)n-\binom{r-1}{2}$. In this paper, we focus on the number of edges of the $K_r$-saturated graphs with a fixed matching number. Let $G$ be an $n$-vertex $K_r$-saturated graph with matching number $\nu(G) = s$. For sufficiently large $n$, we prove that the number of edges \begin{equation*} e(G)\geq \left\{\begin{array}{cl}{(r-1)n-\frac{r}{2}(r-1)-1,}&{\quad\mathrm{if}~s=r-1;}\\{(r-1)n + (s-r)^2 - \frac{1}{2}(r+2)(r-3) - 5,}&{\quad\mathrm{if}~s>r-1.}\\\end{array}\right. \end{equation*} Moreover, we completely characterize the graphs attaining the equality.

math.CO↗
arXiv2025

Can LLMs Generate Reliable Test Case Generators? A Study on Competition-Level Programming Problems

Large Language Models (LLMs) have demonstrated remarkable capabilities in code generation, capable of tackling complex tasks during inference. However, the extent to which LLMs can be utilized for code checking or debugging through test case generation remains largely unexplored. We investigate this problem from the perspective of competition-level programming (CP) programs and propose TCGBench, a Benchmark for (LLM generation of) Test Case Generators. This benchmark comprises two tasks, aimed at studying the capabilities of LLMs in (1) generating valid test case generators for a given CP problem, and further (2) generating targeted test case generators that expose bugs in human-written code. Experimental results indicate that while state-of-the-art LLMs can generate valid test case generators in most cases, most LLMs struggle to generate targeted test cases that reveal flaws in human code effectively. Especially, even advanced reasoning models (e.g., o3-mini) fall significantly short of human performance in the task of generating targeted generators. Furthermore, we construct a high-quality, manually curated dataset of instructions for generating targeted generators. Analysis demonstrates that the performance of LLMs can be enhanced with the aid of this dataset, by both prompting and fine-tuning.

cs.CL↗
arXiv2024

Generalized Andr\'{a}sfai--Erd\H{o}s--S\'{o}s theorems for odd cycles

In this note, we establish Andr\'{a}sfai--Erd\H{o}s--S\'{o}s-type stability theorems for two generalized Tur\'{a}n problems involving odd cycles, both of which are extensions of the Erd\H{o}s Pentagon Problem. Our results strengthen previous results by Lidick\'{y}--Murphy~\cite{LM21} and Beke--Janzer~\cite{BJ24}, while also simplifying parts of their proofs.

math.CO↗
arXiv2024

Enhancing Large-Scale AI Training Efficiency: The C4 Solution for Real-Time Anomaly Detection and Communication Optimization

The emergence of Large Language Models (LLMs) has necessitated the adoption of distributed training techniques, involving the deployment of thousands of GPUs to train a single model. Unfortunately, the efficiency of large-scale distributed training systems is often suboptimal due to the increased likelihood of hardware errors in high-end GPU products and the heightened risk of network traffic collisions. Moreover, any local hardware failure can disrupt training tasks, and the inability to swiftly identify faulty components leads to a significant waste of GPU resources. And, prolonged communication due to traffic collisions can substantially increase GPU waiting times. To address these challenges, we propose a communication-driven solution, namely the C4. The key insights of C4 are twofold. First, the load in distributed training exhibits homogeneous characteristics and is divided into iterations through periodic synchronization, therefore hardware anomalies would incur certain syndrome in collective communication. By leveraging this feature, C4 can rapidly identify the faulty components, swiftly isolate the anomaly, and restart the task, thereby avoiding resource wastage caused by delays in anomaly detection. Second, the predictable communication model of collective communication, involving a limited number of long-lived flows, allows C4 to efficiently execute traffic planning, substantially reducing bandwidth competition among these flows. The C4 has been extensively deployed across real-world production systems in a hyperscale cloud provider, yielding a significant improvement in system efficiency, from 30% to 45%. This enhancement is attributed to a 30% reduction in error-induced overhead and a 15% reduction in communication costs.

cs.DC↗