A Unified Framework of FPT Approximation Algorithms for Clustering Problems

Authors Qilong Feng, Zhen Zhang, Ziyun Huang, Jinhui Xu, Jianxin Wang



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Author Details

Qilong Feng
  • School of Computer Science and Engineering, Central South University, Changsha, China
Zhen Zhang
  • School of Computer Science and Engineering, Central South University, Changsha, China
Ziyun Huang
  • Department of Computer Science and Software Engineering, Penn State Erie, The Behrend College, PA, USA
Jinhui Xu
  • Department of Computer Science and Engineering, State University of New York at Buffalo, NY, USA
Jianxin Wang
  • School of Computer Science and Engineering, Central South University, Changsha, China

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Qilong Feng, Zhen Zhang, Ziyun Huang, Jinhui Xu, and Jianxin Wang. A Unified Framework of FPT Approximation Algorithms for Clustering Problems. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ISAAC.2020.5

Abstract

In this paper, we present a framework for designing FPT approximation algorithms for many k-clustering problems. Our results are based on a new technique for reducing search spaces. A reduced search space is a small subset of the input data that has the guarantee of containing k clients close to the facilities opened in an optimal solution for any clustering problem we consider. We show, somewhat surprisingly, that greedily sampling O(k) clients yields the desired reduced search space, based on which we obtain FPT(k)-time algorithms with improved approximation guarantees for problems such as capacitated clustering, lower-bounded clustering, clustering with service installation costs, fault tolerant clustering, and priority clustering.

Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
Keywords
  • clustering
  • approximation algorithms
  • fixed-parameter tractability

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