Exponential Inapproximability of Selecting a Maximum Volume Sub-matrix

Ali Civril; Malik Magdon-Ismail

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arXiv · 1006.4349

Exponential Inapproximability of Selecting a Maximum Volume Sub-matrix

Ali Civril·Malik Magdon-Ismail

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Abstract

Given a matrix $A \in \mathbb{R}^{m \times n}$ ($n$ 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 $\delta<1$ and $c>0$ such that this problem is not approximable within $2^{-ck}$ for $k = \delta n$, unless $P=NP$.

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Ali Civril, Malik Magdon-Ismail. 2010-06-22. Exponential Inapproximability of Selecting a Maximum Volume Sub-matrix. https://arxiv.org/abs/1006.4349

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