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- W2996901643 abstract "We provide a number of algorithmic results for the following family of problems: For a given binary m x n matrix A and a nonnegative integer k, decide whether there is a simple binary matrix B which differs from A in at most k entries. For an integer r, the simplicity of B is characterized as follows.- Binary r-Means: Matrix B has at most r different columns. This problem is known to be NP-complete already for r=2. We show that the problem is solvable in time 2^{O(k log k)}*(nm)^O(1) and thus is fixed-parameter tractable parameterized by k. We also complement this result by showing that when being parameterized by r and k, the problem admits an algorithm of running time 2^{O(r^{3/2}* sqrt{k log k})}(nm)^O(1), which is subexponential in k for r in o((k/log k)^{1/3}).- Low GF(2)-Rank Approximation: Matrix B is of GF(2)-rank at most r. This problem is known to be NP-complete already for r=1. It is also known to be W[1]-hard when parameterized by k. Interestingly, when parameterized by r and k, the problem is not only fixed-parameter tractable, but it is solvable in time 2^{O(r^{3/2}* sqrt{k log k})}(nm)^O(1), which is subexponential in k for r in o((k/log k)^{1/3}).- Low Boolean-Rank Approximation: Matrix B is of Boolean rank at most r. The problem is known to be NP-complete for k=0 as well as for r=1. We show that it is solvable in subexponential in k time 2^{O(r2^r * sqrt{k log k})}(nm)^O(1)." @default.
- W2996901643 created "2020-01-10" @default.
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- W2996901643 date "2018-01-01" @default.
- W2996901643 modified "2023-10-16" @default.
- W2996901643 title "Parameterized Low-Rank Binary Matrix Approximation" @default.
- W2996901643 doi "https://doi.org/10.4230/lipics.icalp.2018.53" @default.
- W2996901643 hasPublicationYear "2018" @default.
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