Reconstruction of Unique Binary Matrices with Prescribed Elements

  A. Kuba

 Summary

 The reconstruction of a binary matrix from its row and column sum vectors is considered when some elements of the matrix may be prescribed and the matrix is uniquely determined from these data. It is shown that the uniqueness of such a matrix is equivalent to the impossibility of selecting certain sequences from the matrix elements. The unique matrices are characterized by several properties. Among others it is proved that their rows and columns can be permutated such that the 1's are above and left to the (non-prescribed) 0's. Furthermore, an algorithm is given to decide if the given projections and prescribed elements determine a binary matrix uniquely, and, if the answer is yes, to reconstruct it.

 Gyenizse Pal 1996. Szeptember 3. Kedd 12:53:34 MET DST