### Abstract

A covering array CA(N; t, k, v) is an N ×k array with entries in {1, 2, … , v}, for which every N × t subarray contains each t-tuple of {1, 2, … , v}^{t} among its rows.Covering arrays find application in interaction testing, including software and hardware testing, advanced materials development, and biological systems.A central question is to determine or bound CAN(t, k, v), the minimum number N of rows of a CA(N; t, k, v).The well known bound CAN(t, k, v) = O((t − 1)v^{t} log k) is not too far from being asymptotically optimal.Sensible relaxations of the covering requirement arise when (1) the set {1, 2, … , v}^{t} need only be contained among the rows of at least (1 − ϵ)(^{k} _{t}) of the N × t subarrays and (2) the rows of every N × t subarray need only contain a (large) subset of {1, 2, … , v}^{t}.In this paper, using probabilistic methods, significant improvements on the covering array upper bound are established for both relaxations, and for the conjunction of the two.In each case, a randomized algorithm constructs such arrays in expected polynomial time.

Original language | English (US) |
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Title of host publication | Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings |

Publisher | Springer Verlag |

Pages | 437-448 |

Number of pages | 12 |

Volume | 9843 |

ISBN (Print) | 9783319445427 |

DOIs | |

State | Published - 2016 |

Event | 27th International Workshop on Combinatorial Algorithms, IWOCA 2016 - Helsinki, Finland Duration: Aug 17 2016 → Aug 19 2016 |

### 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 | 9843 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 27th International Workshop on Combinatorial Algorithms, IWOCA 2016 |
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Country | Finland |

City | Helsinki |

Period | 8/17/16 → 8/19/16 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings*(Vol. 9843, pp. 437-448). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9843). Springer Verlag. https://doi.org/10.1007/978-3-319-44543-434