Parameterized Algorithms for the Matrix Completion Problem
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:16561665, 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 fixedparameter tractable with respect to all aforementioned parameters. We complement these results with a lowerbound result for the unbounded domain case that rules out fixedparameter tractability w.r.t. some of the parameters under consideration.
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