Euclidean k-center Fair Clusterings

📝 Original Info

• Title: Euclidean k-center Fair Clusterings
• ArXiv ID: 2511.07660
• Date: 2025-11-10
• Authors: ** 논문에 명시된 저자 정보가 제공되지 않았습니다. **

📝 Abstract

Many approximation algorithms and heuristic algorithms to find a fair clustering have emerged. In this paper we define a new and natural variant of fair clustering problem and design a polynomial time algorithm to compute an optimal fair clustering. Let P be a set of n points on a plane, and each point has a color in C, corresponding to a group. For each color q in C, a lower bound l(q) and an upper bound u(q) are given. Then we define the fair clustering problem as follows. The fair k-clustering problem is to find a partition of P into a set of k clusters with a minimum cost such that each cluster contains at least l(q) and at most u(q) points in P with color q. By l(q) and u(q) each cluster cannot contain too few or too many points with a specific color. If we regard a color to a gender or a minority ethnic group, the clustering corresponds to a fair clustering.

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