arXiv subjects

Chaoqi Jia

Publications and source records attributed to Chaoqi Jia.

5 recordsLinked to original sources

arXiv2026

Parameterized and Streaming Algorithms for Euclidean Fair $k$-Center Clustering

Motivated by the growing importance of fairness in machine learning, fair $k$-center clustering has attracted considerable research attention as a fundamental problem. In this problem, a dataset is partitioned into $m$ disjoint groups, and the objective is to select $k$ data points as centers, subject to upper bounds on the number of centers chosen from each group, aiming to minimize the maximum distance between any data point and its assigned center. Focusing on Euclidean spaces, which are ubiquitous in machine learning applications, we first develop a parameterized approximation algorithm for Euclidean fair $k$-center with an approximation ratio of $2.732$. By incorporating this algorithm as a post-processing stage into a one-pass streaming framework for large-scale data, we obtain an approximation ratio of $4.464$. These ratios can be further respectively improved to $2.414$ and $3.828$ with a runtime exponential on $k$. To ensure polynomial-time complexity, we further design a one-pass streaming algorithm with an approximation ratio of $4.732$, which can be further improved to $4.42$, outperforming the state-of-the-art ratio. Finally, extensive experiments show that our methods significantly outperform state-of-the-art approaches in terms of clustering accuracy.

cs.LG↗

arXiv2026

Approximation Algorithm for Constrained $k$-Center Clustering: A Local Search Approach

Clustering is a long-standing research problem and a fundamental tool in AI and data analysis. The traditional k-center problem, a fundamental theoretical challenge in clustering, has a best possible approximation ratio of 2, and any improvement to a ratio of 2 - ε would imply P = NP. In this work, we study the constrained k-center clustering problem, where instance-level cannot-link (CL) and must-link (ML) constraints are incorporated as background knowledge. Although general CL constraints significantly increase the hardness of approximation, previous work has shown that disjoint CL sets permit constant-factor approximations. However, whether local search can achieve such a guarantee in this setting remains an open question. To this end, we propose a novel local search framework based on a transformation to a dominating matching set problem, achieving the best possible approximation ratio of 2. The experimental results on both real-world and synthetic datasets demonstrate that our algorithm outperforms baselines in solution quality.

cs.LG↗

arXiv2026

Improved Streaming Algorithm for Fair $k$-Center Clustering

Many real-world applications pose challenges in incorporating fairness constraints into the $k$-center clustering problem, where the dataset consists of $m$ demographic groups, each with a specified upper bound on the number of centers to ensure fairness. Focusing on big data scenarios, this paper addresses the problem in a streaming setting, where data points arrive one by one sequentially in a continuous stream. Leveraging a structure called the $λ$-independent center set, we propose a one-pass streaming algorithm that first computes a reserved set of points during the streaming process. Then, for the post-streaming process, we propose an approach for selecting centers from the reserved point set by analyzing all three possible cases, transforming the most complicated one into a specially constrained vertex cover problem in an auxiliary graph. Our algorithm achieves a tight approximation ratio of 5 while consuming $O(k\log n)$ memory. It can also be readily adapted to solve the offline fair $k$-center problem, achieving a 3-approximation ratio that matches the current state of the art. Furthermore, we extend our approach to a semi-structured data stream, where data points from each group arrive in batches. In this setting, we present a 3-approximation algorithm for $m = 2$ and a 4-approximation algorithm for general $m$. Lastly, we conduct extensive experiments to evaluate the performance of our approaches, demonstrating that they outperform existing baselines in both clustering cost and runtime efficiency.

cs.DS↗

arXiv2026

Optimized Algorithms for Text Clustering with LLM-Generated Constraints

Clustering is a fundamental tool that has garnered significant interest across a wide range of applications including text analysis. To improve clustering accuracy, many researchers have incorporated background knowledge, typically in the form of must-link and cannot-link constraints, to guide the clustering process. With the recent advent of large language models (LLMs), there is growing interest in improving clustering quality through LLM-based automatic constraint generation. In this paper, we propose a novel constraint-generation approach that reduces resource consumption by generating constraint sets rather than using traditional pairwise constraints. This approach improves both query efficiency and constraint accuracy compared to state-of-the-art methods. We further introduce a constrained clustering algorithm tailored to the characteristics of LLM-generated constraints. Our method incorporates a confidence threshold and a penalty mechanism to address potentially inaccurate constraints. We evaluate our approach on five text datasets, considering both the cost of constraint generation and the overall clustering performance. The results show that our method achieves clustering accuracy comparable to the state-of-the-art algorithms while reducing the number of LLM queries by more than 20 times.

cs.LG↗

arXiv2025

Near-Optimal Algorithms for Constrained k-Center Clustering with Instance-level Background Knowledge

Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work, we build on widely adopted $k$-center clustering and model its input background knowledge as must-link (ML) and cannot-link (CL) constraint sets. However, most clustering problems including $k$-center are inherently $\mathcal{NP}$-hard, while the more complex constrained variants are known to suffer severer approximation and computation barriers that significantly limit their applicability. By employing a suite of techniques including reverse dominating sets, linear programming (LP) integral polyhedron, and LP duality, we arrive at the first efficient approximation algorithm for constrained $k$-center with the best possible ratio of 2. We also construct competitive baseline algorithms and empirically evaluate our approximation algorithm against them on a variety of real datasets. The results validate our theoretical findings and demonstrate the great advantages of our algorithm in terms of clustering cost, clustering quality, and running time.

cs.LG↗