A Greedy Algorithm for Subspace Approximation Problem

Author Nguyen Kim Thang

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Nguyen Kim Thang
  • IBISC, Univ Evry, University Paris Saclay, Evry, France

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Nguyen Kim Thang. A Greedy Algorithm for Subspace Approximation Problem. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 30:1-30:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


In the subspace approximation problem, given m points in R^{n} and an integer k <= n, the goal is to find a k-dimension subspace of R^{n} that minimizes the l_{p}-norm of the Euclidean distances to the given points. This problem generalizes several subspace approximation problems and has applications from statistics, machine learning, signal processing to biology. Deshpande et al. [Deshpande et al., 2011] gave a randomized O(sqrt{p})-approximation and this bound is proved to be tight assuming NP != P by Guruswami et al. [Guruswami et al., 2016]. It is an intriguing question of determining the performance guarantee of deterministic algorithms for the problem. In this paper, we present a simple deterministic O(sqrt{p})-approximation algorithm with also a simple analysis. That definitely settles the status of the problem in term of approximation up to a constant factor. Besides, the simplicity of the algorithm makes it practically appealing.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Approximation Algorithms
  • Subspace Approximation


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