RECONSTRUCTION OF 2-VALUED MATRICES FROM THEIR 2 PROJECTIONS

A matrix is said to be two-valued if its elements assume at most two d ifferent values. We studied the problem of reconstructing a two-valued matrix from its marginals-that is, from its row sums and column sums- but without any knowledge of the value pair on hand. Provided at least one of these marginals is nonconstant, only finitely many (though pos sibly many) value pairs can lead to a valid reconstruction. Our consid erations lead to an efficient algorithm for calculating all possible s olutions, each with its own value pair. Special attention is given to uniqueness pairs-that is, value pairs to which there corresponds preci sely one matrix having the correct marginals. Unless both marginals ar e constant, there can be no more than two uniqueness pairs. (C) 1998 J ohn Wiley & Sons, Inc.