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Removing Aspect Ratio on the Running Time for Constrained k-center Clustering

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 5.6Download Report PDF
Constrained Clustering; Approximation Algorithm
Abstract:

In this paper, we consider the constrained kk-center problems. Existing algorithms for these problems often rely on optimal radius guessing strategy, leading to an overall running time that is dependent on the aspect ratio Δ\Delta (the ratio between the maximum and minimum pairwise distances). This dependency may potentially limit the scalability of the algorithms for handling large-scale datasets. To overcome the aspect ratio dependency issue, we propose a multi-scaling method. Multi-scaling partitions the clustering instance based on relative distances between data points. It then generates a set of candidate radii whose size is independent of Δ\Delta, ensuring the existence of at least one radius that can closely approximate the optimal one for any constrained kk-center instance. This narrows the search space for radius guessing and removes the running time dependency on the aspect ratio. To further improve the efficiency of multi-scaling, we introduce a problem-specific data reduction method that allows multi-scaling to operate on a smaller unweighted instance while preserving theoretical guarantees. These techniques enable us to obtain approximation results for a series of constrained kk-center problems with near-linear running time in the data size. Empirical experiments show that our proposed methods achieve better performances compared with the SOTA algorithms on both small and large-scale clustering datasets.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper introduces a multi-scaling method to eliminate aspect ratio dependency in constrained k-center clustering, achieving running times independent of the ratio between maximum and minimum pairwise distances. According to the taxonomy, this work occupies the 'Aspect Ratio Independent Algorithms' leaf under 'Algorithmic Efficiency and Scalability Techniques'. Notably, this leaf contains only the original paper itself, with no sibling papers identified, suggesting this represents a relatively sparse or emerging research direction within the broader field of constrained k-center clustering.

The taxonomy reveals that the broader field divides into two main branches: algorithmic efficiency techniques and fairness-constrained methods. The original paper's branch includes neighboring leaves focused on coreset-based sliding window methods, with papers addressing general metric spaces and dimensionality-adaptive variants. These neighboring works tackle streaming models and dimensional adaptivity rather than aspect ratio independence directly. The fairness branch, by contrast, explores demographic constraints and matroid-based formulations, representing a distinct research trajectory that the original paper does not engage with.

Among the three identified contributions, the literature search examined twenty-two candidates total. The multi-scaling method examined two candidates with zero refutations; the data reduction method examined ten candidates with zero refutations; and the near-linear time approximation algorithms examined ten candidates with zero refutations. This suggests that within the limited search scope of top-K semantic matches, no prior work was found that clearly overlaps with or anticipates these specific technical contributions. The absence of refutable candidates across all three contributions indicates potential novelty, though the search scope remains constrained.

Based on the limited examination of twenty-two semantically related candidates, the work appears to occupy a relatively unexplored niche within constrained k-center clustering. The taxonomy structure confirms sparse coverage in the aspect ratio independence direction, with neighboring research focusing on different efficiency challenges. However, this assessment reflects only the top-K semantic search results and does not constitute an exhaustive survey of all potentially relevant prior work in clustering algorithms or computational geometry.

Taxonomy

Core-task Taxonomy Papers
4
3
Claimed Contributions
22
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: constrained k-center clustering with aspect ratio independent running time. The field of constrained k-center clustering has evolved along two main branches. The first branch, Algorithmic Efficiency and Scalability Techniques, focuses on developing methods that achieve strong theoretical guarantees—such as running times independent of geometric properties like aspect ratio or dimension—often through adaptive sliding window approaches and careful data structure design. Works such as Dimensionality Adaptive Sliding[3] and Adaptive Sliding k-center[2] exemplify this direction by addressing high-dimensional or streaming settings where traditional algorithms struggle. The second branch, Fairness-Constrained k-Center Clustering, emphasizes equitable treatment of different groups or protected attributes, ensuring that clustering solutions satisfy fairness criteria alongside the standard objective of minimizing maximum radius. Representative studies like Fair Range k-center[1] and Streaming Fair k-center[4] illustrate how fairness constraints can be integrated into both offline and online clustering frameworks. Recent work has increasingly sought to bridge efficiency and fairness, exploring trade-offs between computational complexity and the strength of fairness guarantees. A particularly active line of research investigates whether one can maintain aspect ratio independence—a desirable property for robustness across diverse data geometries—while also accommodating fairness or other side constraints. Aspect Ratio k-center[0] sits squarely within the Algorithmic Efficiency and Scalability Techniques branch, sharing the emphasis on aspect ratio independent running time with Dimensionality Adaptive Sliding[3] and Adaptive Sliding k-center[2]. However, while those neighboring works primarily target dimensionality or streaming challenges, Aspect Ratio k-center[0] appears to focus more directly on removing aspect ratio dependence in constrained settings, potentially offering a complementary perspective on how geometric robustness can be achieved without sacrificing theoretical efficiency.

Claimed Contributions

Multi-scaling method for aspect-ratio independent clustering

The authors introduce a multi-scaling technique that partitions data based on relative distances and constructs a candidate radii set of size independent of the aspect ratio. This method eliminates the running time dependency on aspect ratio for constrained k-center problems while preserving approximation guarantees.

2 retrieved papers
Problem-specific data reduction method

The authors propose data reduction methods that construct small summaries (compact unweighted point sets) to accelerate multi-scaling. By applying multi-scaling to these summaries, the running time overhead is further reduced while maintaining similar theoretical guarantees.

10 retrieved papers
Near-linear time approximation algorithms for constrained k-center variants

By combining multi-scaling with data reduction, the authors achieve near-linear running time approximation algorithms for various constrained k-center problems including k-center with outliers, individual fair k-center, proportionally fair k-center, and (α, β)-fair k-center.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Multi-scaling method for aspect-ratio independent clustering

The authors introduce a multi-scaling technique that partitions data based on relative distances and constructs a candidate radii set of size independent of the aspect ratio. This method eliminates the running time dependency on aspect ratio for constrained k-center problems while preserving approximation guarantees.

Contribution

Problem-specific data reduction method

The authors propose data reduction methods that construct small summaries (compact unweighted point sets) to accelerate multi-scaling. By applying multi-scaling to these summaries, the running time overhead is further reduced while maintaining similar theoretical guarantees.

Contribution

Near-linear time approximation algorithms for constrained k-center variants

By combining multi-scaling with data reduction, the authors achieve near-linear running time approximation algorithms for various constrained k-center problems including k-center with outliers, individual fair k-center, proportionally fair k-center, and (α, β)-fair k-center.

Table of Contents