Scholarlink

We study k-center clustering with an additional fairness constraint: for any cluster \(\varGamma \) and any two groups a, b, the number of points of group a in \(\varGamma \) is at most t times the number of points of group b in \(\varGamma \) . The problem is known to admit O(1)-approximation in some special cases including (i) when the number of groups \(c=2\) and t is an integer, and (ii) when \(t=1\) and c is arbitrary. We obtain the first O(1)-approximation for this problem with arbitrary c and integer t. Our algorithm is based on a novel tree-based LP rounding scheme which also works in a more general setting with outliers. In contrast, we show an integrality gap of \(\varOmega (k)\) when t is not an integer, even when \(c=2\) .

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A Constant-Factor Approximation for Pairwise Fair k-Center Clustering

  • 会议论文

  • 发表日期：

    2025年

查看全文
  • Sayan Bandyapadhyay,
  • Tianzhi Chen,
  • Zachary Friggstad,
  • Mahya Jamshidian

摘要

We study k-center clustering with an additional fairness constraint: for any cluster \(\varGamma \) and any two groups a, b, the number of points of group a in \(\varGamma \) is at most t times the number of points of group b in \(\varGamma \) . The problem is known to admit O(1)-approximation in some special cases including (i) when the number of groups \(c=2\) and t is an integer, and (ii) when \(t=1\) and c is arbitrary. We obtain the first O(1)-approximation for this problem with arbitrary c and integer t. Our algorithm is based on a novel tree-based LP rounding scheme which also works in a more general setting with outliers. In contrast, we show an integrality gap of \(\varOmega (k)\) when t is not an integer, even when \(c=2\) .