Finding exact solutions to the bandwidth minimization problem
Given an \(m\times m\) sparse symmetric matrix, the authors consider the problem of finding the permutation of rows and columns which minimizes the bandwidth. The problem is known to be NP-complete; therefore no polynomial algorithm in \(m\) is likely to exist. They present two algorithms which exhaustively enumerate all permutations, trying to discard as early as possible those which cannot lead to an optimal ordering.
scientific article; zbMATH DE number 1333223