Point pattern reconstruction with less than complete information

Point patterns can be reconstructed based on interpoint distance information using multidimensional scaling. However, the number of interpoint distances, n(n-1)/2 for an n point pattern, becomes excessive as n becomes large. In this paper reconstruction of point patterns based on incomplete interpoint distance information is demonstrated. Three different techniques are investigated, (1) repeated use of multidimensional scaling (MDS), (2) an evolutionary algorithm using mutation and selection, and (3) a combined strategy alternating between the first two. While various degrees of success were achieved with all three, the third proved the most promising, with good reconstructions achieved using close to the theoretical minimum information for patterns consisting of fourteen points