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 these have been carried out, the resulting matrix is triangular. The complexity of the problem was posed as an open question by Wilf [6] 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.