Reducing the bandwidth of non-symmetric matrix
The following article discusses various approaches to reducing the bandwidth of unsymmetric matrices.

J.K. Reid, J. A. Scott: Reducing the total bandwidth of a sparse unsymmetric matrix, SIAM Journal on Matrix Analysis and Applications 28(3):805&ndash;821. 

The technical report version of the article is available here:

J. K. Reid and J. A. Scott, Reducing the total bandwidth of a sparse unsymmetric matrix, Technical Report RAL-TR-2005-001, STFC Rutherford Appleton Laboratory. http://www.numerical.rl.ac.uk/reports/rsRAL2005001.pdf