Matrix Assignments and an Associated Min Max Problem

We are concerned with an algorithm for determining p which is more efficient than the obvious one of generating the n\ possible assignments then straightforwardly selecting p. A method for demonstrating an assignment containing p. is also of concern, but such a method is easily evolved using the tools necessary to determine p. Before proceeding we define a nonzero column of a set of r rows of A as a column which contains at least one nonzero element.