### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### 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

**Partial covering arrays : Algorithms and asymptotics.** / Sarkar, Kaushik; Colbourn, Charles; De Bonis, Annalisa; Vaccaro, Ugo.

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

*Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings.*vol. 9843, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9843, Springer Verlag, pp. 437-448, 27th International Workshop on Combinatorial Algorithms, IWOCA 2016, Helsinki, Finland, 8/17/16. https://doi.org/10.1007/978-3-319-44543-434

}

TY - GEN

T1 - Partial covering arrays

T2 - Algorithms and asymptotics

AU - Sarkar, Kaushik

AU - Colbourn, Charles

AU - De Bonis, Annalisa

AU - Vaccaro, Ugo

PY - 2016

Y1 - 2016

N2 - 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)vt 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.

AB - 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)vt 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.

UR - http://www.scopus.com/inward/record.url?scp=84984914877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84984914877&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-44543-434

DO - 10.1007/978-3-319-44543-434

M3 - Conference contribution

AN - SCOPUS:84984914877

SN - 9783319445427

VL - 9843

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

SP - 437

EP - 448

BT - Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings

PB - Springer Verlag

ER -