Column subset selection is NP-complete
نویسندگان
چکیده
Let M be a real r × c matrix, and let k positive integer. In the column subset selection problem (CSSP), we need to minimize quantity ‖ − S A , where can an arbitrary runs over all submatrices of . This its applications in numerical linear algebra are being discussed for several decades, but algorithmic complexity remained open issue. We show that CSSP is NP-complete.
منابع مشابه
Column subset selection is NP-complete
Let M be a real r × c matrix and let k be a positive integer. In the column subset selection problem (CSSP), we need to minimize the quantity M − SA, where A can be an arbitrary k × c matrix, and S runs over all r × k submatrices of M. This problem and its applications in numerical linear algebra are being discussed for several decades, but its algorithmic complexity remained an open issue. We ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2021
ISSN: ['1873-1856', '0024-3795']
DOI: https://doi.org/10.1016/j.laa.2020.09.015