Nonconstructive advances in polynomial-time complexity (Q1098635)

The following decision problem is defined: Gate matrix layout (GML): Instance: A Boolean matrix M and an integer k; Question: Can we permute the columns of M such that if in each row we change to * every 0 lying between the row's leftmost and rightmost 1, then no column contains more than k 1's and *'s ? The main result of the paper is that the fixed-k version of GML is solvable in polynomial time. The proof is nonconstructive and is based on a result of \textit{N. Robertson} and \textit{P. D. Seymour} [SIAM J. Algebraic Discrete Methods 6, 300-305 (1985; Zbl 0565.05045)].