Partial covering arrays: Algorithms and asymptotics

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

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


A covering arrayCA(N; t, k, v) is an N × k array with entries in {1,2,…,v}, for whichevery N × t subarray containseach t-tuple of {1,2,…,v}tamong 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)vtlog k) is not too far from being asymptotically optimal. Sensible relaxations of the covering requirement arise when (1) the set {1,2,…,v}tneed only be contained among the rows ofat least(1 − ϵ) (Formula present) of the N × t subarrays and (2) the rows ofevery N × t subarray need only contain a (large)subsetof {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)1470-1489
Number of pages20
JournalTheory of Computing Systems
Issue number6
StatePublished - May 27 2018


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics


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