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The dominant contribution to communication complexity in factorizing a matrix using QR with column pivoting is due to column-norm updates that are required to process pivot decisions.
Extensions of Lipschitz mappings into a Hilbert space
W. B. Johnson and J. Lindenstrauss · 1984
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The W Y WY representation for products of householder matrices
C. H. Bischof and C. V. Loan · 1987
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Rank revealing Q R QR factorizations
T. F. Chan · 1987
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A storage-efficient W Y WY representation for products of householder transformations
R. Schreiber and C. V. Loan · 1989
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A parallel Q R QR factorization algorithm with controlled local pivoting
C. H. Bischof · 1991
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Some applications of the rank revealing Q R QR factorization
T. F. Chan and P. C. Hansen · 1992
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Efficient algorithms for computing a strong rank-revealing Q R QR factorization
M. Gu and S. C. Eisenstat · 1996
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A BLAS-3 version of the Q R QR factorization with column pivoting
G. Quintana-Ortí, X. Sun, and C. H. Bischof · 1998
Cited alongside, same era.
The Q L P QLP approximation to the singular value decomposition
G. W. Stewart · 1999
Cited alongside, same era.
On the convergence of Stewart’s Q L P QLP algorithm for approximating the SVD
D. A. Huckaby and T. F. Chan · 2003
Cited alongside, same era.
Randomized algorithms for the low-rank approximation of matrices
E. Liberty, F. Woolfe, P. Martinsson, V. Rokhlin, and M. Tygert · 2007
Cited alongside, same era.
Minimizing communication in numerical linear algebra
G. Ballard, J. Demmel, O. Holtz, and O. Schwartz · 2011
Cited alongside, same era.
Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
Communication-optimal parallel and sequential Q R QR and L U LU factorizations
J. Demmel, L. Grigori, M. Hoemmen, and J. Langou · 2012
Later among the works it cites.
Communication avoiding rank revealing Q R QR factorization with column pivoting
J. Demmel, L. Grigori, M. Gu, and H. Xiang · 2013
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Matrix Computations
G. H. Golub and C. F. van Loan · 2013
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Randomized strong rank-revealing Q R QR factorization
J. A. Duersch and M. Gu · 2014
Later among the works it cites.
Blocked rank-revealing Q R QR factorizations: How randomized sampling can be used to avoid single-vector pivoting
P. G. Martinsson · 2015
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Differential gear, 2016
A. Kovach · 2016
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N. Halko, P.-G. Martinsson, and J. A. Tropp · 2011
Cited alongside, same era.
A randomized algorithm for the decomposition of matrices
P. G. Martinsson, V. Rokhlin, and M. Tygert · 2011
Cited alongside, same era.