Obtaining a Triangular Matrix by Independent Row-Column Permutations

Abstract : Given a square (0, 1)-matrix A, we consider the problem of deciding whether there exists a permutation of the rows and a permutation of the columns of A such that after carrying out these permutations , the resulting matrix is triangular. The complexity of the problem was posed as an open question by Wilf [7] in 1997. In 1998, DasGupta et al. [3] seemingly answered the question, proving it is NP-complete. However , we show here that their result is flawed, which leaves the question still open. Therefore, we give a definite answer to this question by proving that the problem is NP-complete. We finally present an exponential-time algorithm for solving the problem.
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Guillaume Fertin, Irena Rusu, Stéphane Vialette. Obtaining a Triangular Matrix by Independent Row-Column Permutations. 26th International Symposium on Algorithms and Computation, Dec 2015, Nagoya, France. ⟨hal-01189621⟩

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