Suppose I have a sparse $M \times N$ matrix $A$ and I define the "width" of each row $i$ to be:
$$w_i \equiv r(A_i) - l(A_i),$$ where $r(A_i)$ is the index of the rightmost nonzero element of row $i$ of $A$, and $l(A_i)$ is the index of the leftmost nonzero element of row $i$ of $A$.
I want to find a permutation of the columns of $A$ such that $W = \frac{1}{M} \sum_{i = 1}^M w_i$ is minimized. I know there are algorithms that deal with the bandwidth, but that deals with both the rows and columns of $A$. Is there any work on dealing with just the width (sometimes called the profile)?
