Reconstructing point patterns from incomplete nonmetric representations

A method is developed for reconstructing point patterns using incomplete nonmetric information. This information consists of a rank-order list of interpoint distances for a P-point pattern. Nonmetric, in this context, means that a distance is not designated by its length in units, but simply by its rank in the list, the largest designated as having a rank of one. The list is incomplete because less than the full complement of P(P-1)/2 distances is included. The method builds on an algorithm developed for metric representations, and this algorithm is briefly discussed. Results are presented indicating that while the amount of information required increases as the number of points increases. The percentage of the distances that have to be ranked decreases