Permuted max-algebraic eigenvector problem is NP-complete Original Research Article

Let acircled plusb=max(a,b) and acircle times operatorb=a+b for image and extend these operations to matrices and vectors as in conventional linear algebra. The following eigenvector problem has been intensively studied in the past: Given image find all image (eigenvectors) such that Acircle times operatorx=λcircle times operatorx for some image The present paper deals with the permuted eigenvector problem: Given image and image is it possible to permute the components of x so that it becomes a (max-algebraic) eigenvector of A? Using a polynomial transformation from BANDWIDTH we prove that the integer version of this problem is NP-complete.