Abstract
A recursive dynamic programming strategy is discussed for optimally reorganizing the rows and simultaneously the columns of ann ×n proximity matrix when the objective function measuring the adequacy of a reorganization has a fairly simple additive structure. A number of possible objective functions are mentioned along with several numerical examples using Thurstone's paired comparison data on the relative seriousness of crime. Finally, the optimization tasks we propose to attack with dynamic programming are placed in a broader theoretical context of what is typically referred to as the quadratic assignment problem and its extension to cubic assignment.
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Partial support for this research was provided by NIJ Grant 80-IJ-CX-0061.
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Hubert, L.J., Golledge, R.G. Matrix reorganization and dynamic programming: Applications to paired comparisons and unidimensional seriation. Psychometrika 46, 429–441 (1981). https://doi.org/10.1007/BF02293800
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DOI: https://doi.org/10.1007/BF02293800