### Abstract

Search, test, and measurement problems in sparse domains often require the construction of arrays in which every t or fewer columns satisfy a simply stated combinatorial condition. Such t-restriction problems often ask for the construction of an array satisfying the t-restriction while having as few rows as possible. Combinatorial, algebraic, and probabilistic methods have been brought to bear for specific t-restriction problems; yet in most cases they do not succeed in constructing arrays with a number of rows near the minimum, at least when the number of columns is small. To address this, an algorithmic method is proposed that, given an array satisfying a t-restriction, attempts to improve the array by removing rows. The key idea is to determine the necessity of the entry in each cell of the array in meeting the t-restriction, and repeatedly replacing unnecessary entries, with the goal of producing an entire row of unnecessary entries. Such a row can then be deleted, improving the array, and the process can be iterated. For certain t-restrictions, it is shown that by determining conflict graphs, entries that are necessary can nonetheless be changed without violating the t-restriction. This permits a richer set of ways to improve the arrays. The efficacy of these methods is demonstrated via computational results.

Original language | English (US) |
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Title of host publication | Information Theory, Combinatorics, and Search Theory |

Subtitle of host publication | In Memory of Rudolf Ahlswede |

Editors | Harout Aydinian, Christian Deppe, Ferdinando Cicalese |

Pages | 597-608 |

Number of pages | 12 |

DOIs | |

State | Published - Apr 15 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7777 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Fingerprint

### Keywords

- covering array
- disjunct matrix
- frameproof code
- hash family

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Information Theory, Combinatorics, and Search Theory: In Memory of Rudolf Ahlswede*(pp. 597-608). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7777). https://doi.org/10.1007/978-3-642-36899-8-30