### Abstract

A covering array t-CA(n, k, g), of size n, strength t, degree k, and order g, is a (Formula presented.) array on g symbols such that every (Formula presented.) sub-array contains every (Formula presented.) column on g symbols at least once. Covering arrays have been studied for their applications to software testing, hardware testing, drug screening, and in areas where interactions of multiple parameters are to be tested. In this paper, we present an algebraic construction that improves many of the best known upper bounds on n for covering arrays 4-CA(n, k, 3). The t-coverage of a testing array (Formula presented.) is the number of distinct t-tuples contained in the column vectors of (Formula presented.) divided by the total number of t-tuples. If the testing array is a covering array of strength t, its t-coverage is 100%. The covering arrays with budget constraints problem is the problem of constructing a testing array of size at most n having largest possible coverage, given values of t, k, g and n. This paper also presents several testing arrays with high 4-coverage.

Original language | English (US) |
---|---|

Pages (from-to) | 1-17 |

Number of pages | 17 |

Journal | Graphs and Combinatorics |

DOIs | |

State | Accepted/In press - Dec 15 2017 |

### Fingerprint

### Keywords

- Coverage
- Covering arrays
- Projective general linear group
- Software testing

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### Cite this

*Graphs and Combinatorics*, 1-17. https://doi.org/10.1007/s00373-017-1861-9

**Improved Strength Four Covering Arrays with Three Symbols.** / Maity, Soumen; Akhtar, Yasmeen; Chandrasekharan, Reshma C.; Colbourn, Charles.

Research output: Contribution to journal › Article

*Graphs and Combinatorics*, pp. 1-17. https://doi.org/10.1007/s00373-017-1861-9

}

TY - JOUR

T1 - Improved Strength Four Covering Arrays with Three Symbols

AU - Maity, Soumen

AU - Akhtar, Yasmeen

AU - Chandrasekharan, Reshma C.

AU - Colbourn, Charles

PY - 2017/12/15

Y1 - 2017/12/15

N2 - A covering array t-CA(n, k, g), of size n, strength t, degree k, and order g, is a (Formula presented.) array on g symbols such that every (Formula presented.) sub-array contains every (Formula presented.) column on g symbols at least once. Covering arrays have been studied for their applications to software testing, hardware testing, drug screening, and in areas where interactions of multiple parameters are to be tested. In this paper, we present an algebraic construction that improves many of the best known upper bounds on n for covering arrays 4-CA(n, k, 3). The t-coverage of a testing array (Formula presented.) is the number of distinct t-tuples contained in the column vectors of (Formula presented.) divided by the total number of t-tuples. If the testing array is a covering array of strength t, its t-coverage is 100%. The covering arrays with budget constraints problem is the problem of constructing a testing array of size at most n having largest possible coverage, given values of t, k, g and n. This paper also presents several testing arrays with high 4-coverage.

AB - A covering array t-CA(n, k, g), of size n, strength t, degree k, and order g, is a (Formula presented.) array on g symbols such that every (Formula presented.) sub-array contains every (Formula presented.) column on g symbols at least once. Covering arrays have been studied for their applications to software testing, hardware testing, drug screening, and in areas where interactions of multiple parameters are to be tested. In this paper, we present an algebraic construction that improves many of the best known upper bounds on n for covering arrays 4-CA(n, k, 3). The t-coverage of a testing array (Formula presented.) is the number of distinct t-tuples contained in the column vectors of (Formula presented.) divided by the total number of t-tuples. If the testing array is a covering array of strength t, its t-coverage is 100%. The covering arrays with budget constraints problem is the problem of constructing a testing array of size at most n having largest possible coverage, given values of t, k, g and n. This paper also presents several testing arrays with high 4-coverage.

KW - Coverage

KW - Covering arrays

KW - Projective general linear group

KW - Software testing

UR - http://www.scopus.com/inward/record.url?scp=85038096110&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038096110&partnerID=8YFLogxK

U2 - 10.1007/s00373-017-1861-9

DO - 10.1007/s00373-017-1861-9

M3 - Article

AN - SCOPUS:85038096110

SP - 1

EP - 17

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

ER -