Algorithmica

, Volume 65, Issue 1, pp 159–176 | Cite as

Exponential Inapproximability of Selecting a Maximum Volume Sub-matrix

Article

Abstract

Given a matrix A∈ℝ m×n (n vectors in m dimensions), and a positive integer k<n, we consider the problem of selecting k column vectors from A such that the volume of the parallelepiped they define is maximum over all possible choices. We prove that there exists δ<1 and c>0 such that this problem is not approximable within 2ck for k=δn, unless P=NP.

Keywords

Matrices Volume Complexity Inapproximability 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Computer Engineering DepartmentMelikşah UniversityKayseriTurkey
  2. 2.Computer Science DepartmentRensselaer Polytechnic InstituteTroyUSA

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