### 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 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 597-608 |

Number of pages | 12 |

Volume | 7777 |

DOIs | |

State | Published - 2013 |

### Publication series

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

Volume | 7777 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 7777, 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

**Randomized post-optimization for t-restrictions.** / Colbourn, Charles; Nayeri, Peyman.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 7777, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7777, pp. 597-608. https://doi.org/10.1007/978-3-642-36899-8-30

}

TY - GEN

T1 - Randomized post-optimization for t-restrictions

AU - Colbourn, Charles

AU - Nayeri, Peyman

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - covering array

KW - disjunct matrix

KW - frameproof code

KW - hash family

UR - http://www.scopus.com/inward/record.url?scp=84875994354&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875994354&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-36899-8-30

DO - 10.1007/978-3-642-36899-8-30

M3 - Conference contribution

AN - SCOPUS:84875994354

SN - 9783642368981

VL - 7777

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 597

EP - 608

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -