### Abstract

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 ia 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 I's are above and left to the (non-prescribed) O'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.

Original language | English |
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Pages (from-to) | 57-70 |

Number of pages | 14 |

Journal | Acta Cybernetica |

Volume | 12 |

Issue number | 1 |

Publication status | Published - Jan 1 1995 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Software
- Computer Science (miscellaneous)
- Computer Vision and Pattern Recognition
- Management Science and Operations Research
- Information Systems and Management
- Electrical and Electronic Engineering

### Cite this

*Acta Cybernetica*,

*12*(1), 57-70.