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Parameterized Algorithms for the Matrix Completion Problem
Robert Ganian · Iyad Kanj · Sebastian Ordyniak · Stefan Szeider

Wed Jul 11 06:10 AM -- 06:20 AM (PDT) @ A5
in Ranking and Preference Learning 1 »

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.

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Author Information

Robert Ganian (TU Wien)
Iyad Kanj (DePaul University, Chicago)
Sebastian Ordyniak (University of Sheffield)
Stefan Szeider (TU Wien)

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