The.Algorithm.Design.Manual.Springer-Verlag.1998

Bandwidth Reduction
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Bandwidth Reduction
Input description: A graph G=(V,E), representing an matrix M of zero and nonzero elements.
Problem description: Which permutation p of the vertices of V minimizes the length of the longest edge
when the vertices are ordered on a line, i.e. minimizes ?
Discussion: Bandwidth reduction lurks as a hidden but important problem for both graphs and matrices,
and it is important to see how it arises so as to properly recognize it. Applied to matrices, it permutes the
rows and columns of a sparse matrix so as to minimize the distance b of any nonzero entry from the
center diagonal. This is important in solving linear systems, because Gaussian elimination (see Section
) can be performed in on matrices of bandwidth b. This is a big win over the general
algorithm if b