Article ID: | iaor2000459 |
Country: | Netherlands |
Volume: | 82 |
Issue: | 1/2 |
Start Page Number: | 125 |
End Page Number: | 158 |
Publication Date: | Jun 1998 |
Journal: | Mathematical Programming |
Authors: | Burkard Rainer E., Woeginger Gerhard J., Rote Gnter, ela Eranda |
Keywords: | programming: quadratic |
This paper investigates a restricted version of the Quadratic Assignment Problem (QAP), where one of the coefficient matrices is an Anti-Monge matrix with non-decreasing rows and columns and the other coefficient matrix is a symmetric Toeplitz matrix. This restricted version is called the Anti-Monge–Toeplitz QAP. There are three well-known combinatorial problems that can be modeled via the Anti-Monge–Toeplitz QAP: (P1) The ‘Turbine Problem’, i.e. the assignment of given masses to the vertices of a regular polygon such that the distance of the center of gravity of the resulting system to the center of the polygon is minimized. (P2) The Traveling Salesman Problem on symmetric Monge distance matrices. (P3) The arrangement of data records with given access probabilities in a linear storage medium in order to minimize the average access time. We identify conditions on the Toeplitz matrix