### Abstract

A covering array CA(N;t, k, v) is an N × k array with entries in {1,2,…, v}, for which everyN × 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(Formula presented.) of the N × t subarrays and (2) the rows of everyN × 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) |
---|---|

Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Theory of Computing Systems |

DOIs | |

State | Accepted/In press - May 27 2017 |

### Fingerprint

### Keywords

- Combinatorial design
- Covering arrays
- Orthogonal arrays
- Partial covering arrays
- Software interaction testing

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics

### Cite this

*Theory of Computing Systems*, 1-20. https://doi.org/10.1007/s00224-017-9782-9

**Partial Covering Arrays : Algorithms and Asymptotics.** / Sarkar, Kaushik; Colbourn, Charles; de Bonis, Annalisa; Vaccaro, Ugo.

Research output: Contribution to journal › Article

*Theory of Computing Systems*, pp. 1-20. https://doi.org/10.1007/s00224-017-9782-9

}

TY - JOUR

T1 - Partial Covering Arrays

T2 - Algorithms and Asymptotics

AU - Sarkar, Kaushik

AU - Colbourn, Charles

AU - de Bonis, Annalisa

AU - Vaccaro, Ugo

PY - 2017/5/27

Y1 - 2017/5/27

N2 - A covering array CA(N;t, k, v) is an N × k array with entries in {1,2,…, v}, for which everyN × 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(Formula presented.) of the N × t subarrays and (2) the rows of everyN × 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 everyN × 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(Formula presented.) of the N × t subarrays and (2) the rows of everyN × 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.

KW - Combinatorial design

KW - Covering arrays

KW - Orthogonal arrays

KW - Partial covering arrays

KW - Software interaction testing

UR - http://www.scopus.com/inward/record.url?scp=85019747937&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019747937&partnerID=8YFLogxK

U2 - 10.1007/s00224-017-9782-9

DO - 10.1007/s00224-017-9782-9

M3 - Article

SP - 1

EP - 20

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

ER -