Partial Covering Arrays

Algorithms and Asymptotics

Kaushik Sarkar, Charles Colbourn, Annalisa de Bonis, Ugo Vaccaro

Research output: Contribution to journalArticle

2 Citations (Scopus)

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)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.

Original languageEnglish (US)
Pages (from-to)1-20
Number of pages20
JournalTheory of Computing Systems
DOIs
StateAccepted/In press - May 27 2017

Fingerprint

Covering Array
Software testing
Biological systems
Computer hardware
Polynomials
Partial
Testing
Software Testing
Probabilistic Methods
Randomized Algorithms
Asymptotically Optimal
Biological Systems
Polynomial time
Covering
Hardware
Upper bound
Subset
Requirements
Interaction

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

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

In: Theory of Computing Systems, 27.05.2017, p. 1-20.

Research output: Contribution to journalArticle

Sarkar, Kaushik ; Colbourn, Charles ; de Bonis, Annalisa ; Vaccaro, Ugo. / Partial Covering Arrays : Algorithms and Asymptotics. In: Theory of Computing Systems. 2017 ; pp. 1-20.
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