I am interested in the complexity of the following problem:
Given an $m\times n$ binary matrix $M$, can we permute its rows/columns to obtain a triangular matrix?
I am also interested in the case where "triangular" is replaced by unitriangular.
It says here that Wilf (1997) has studied the first problem in "On Crossing Numbers, and some Unsolved Problems". However I don't have access to it, nor can I find it on his website.
Does anyone know of a reference, or if there has been any subsequent work?
Clarification: I am asking whether there exist two permutation matrices $P,Q$ such that $PMQ$ is triangular. Equivalently, one may freely swap both the rows and columns of $M$.
Background: Since an algorithm has been spelt out in detail, I'll briefly explain my motivation.
Each finite (order-theoretic) lattice $L$ has an associated "poset of irreducibles" which may be viewed as the relation $R \subseteq J(L) \times M(L)$ between the join/meet-irreducibles where $R(j,m) \iff j \nleq_L m$. In Theorem 11 of Primes, Irreducibles and Extremal Lattices, Markowsky proves that $R$ is lower or upper unitriangularisable iff $L$ has length $|M(L)|$ or $|J(L)|$ respectively.