Parameterized Algorithms for the Matrix Completion Problem

Robert Ganian, Iyad Kanj, Sebastian Ordyniak, Stefan Szeider
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:1656-1665, 2018.

Abstract

We consider two matrix completion problems, in which we are given a matrix with missing entries and the task is to complete the matrix in a way that (1) minimizes the rank, or (2) minimizes the number of distinct rows. We study the parameterized complexity of the two aforementioned problems with respect to several parameters of interest, including the minimum number of matrix rows, columns, and rows plus columns needed to cover all missing entries. We obtain new algorithmic results showing that, for the bounded domain case, both problems are fixed-parameter tractable with respect to all aforementioned parameters. We complement these results with a lower-bound result for the unbounded domain case that rules out fixed-parameter tractability w.r.t. some of the parameters under consideration.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-ganian18a, title = {Parameterized Algorithms for the Matrix Completion Problem}, author = {Ganian, Robert and Kanj, Iyad and Ordyniak, Sebastian and Szeider, Stefan}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {1656--1665}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/ganian18a/ganian18a.pdf}, url = {https://proceedings.mlr.press/v80/ganian18a.html}, abstract = {We consider two matrix completion problems, in which we are given a matrix with missing entries and the task is to complete the matrix in a way that (1) minimizes the rank, or (2) minimizes the number of distinct rows. We study the parameterized complexity of the two aforementioned problems with respect to several parameters of interest, including the minimum number of matrix rows, columns, and rows plus columns needed to cover all missing entries. We obtain new algorithmic results showing that, for the bounded domain case, both problems are fixed-parameter tractable with respect to all aforementioned parameters. We complement these results with a lower-bound result for the unbounded domain case that rules out fixed-parameter tractability w.r.t. some of the parameters under consideration.} }
Endnote
%0 Conference Paper %T Parameterized Algorithms for the Matrix Completion Problem %A Robert Ganian %A Iyad Kanj %A Sebastian Ordyniak %A Stefan Szeider %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-ganian18a %I PMLR %P 1656--1665 %U https://proceedings.mlr.press/v80/ganian18a.html %V 80 %X We consider two matrix completion problems, in which we are given a matrix with missing entries and the task is to complete the matrix in a way that (1) minimizes the rank, or (2) minimizes the number of distinct rows. We study the parameterized complexity of the two aforementioned problems with respect to several parameters of interest, including the minimum number of matrix rows, columns, and rows plus columns needed to cover all missing entries. We obtain new algorithmic results showing that, for the bounded domain case, both problems are fixed-parameter tractable with respect to all aforementioned parameters. We complement these results with a lower-bound result for the unbounded domain case that rules out fixed-parameter tractability w.r.t. some of the parameters under consideration.
APA
Ganian, R., Kanj, I., Ordyniak, S. & Szeider, S.. (2018). Parameterized Algorithms for the Matrix Completion Problem. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:1656-1665 Available from https://proceedings.mlr.press/v80/ganian18a.html.

Related Material