Upper bounds on the size of covering arrays

Kaushik Sarkar, Charles Colbourn

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

Covering arrays find important application in software and hardware interaction testing. For practical applications it is useful to determine or bound the minimum number of rows, CAN(t; k; v), in a covering array for given values of the parameters t; k, and v. Asymptotic upper bounds for CAN(t; k; v) have been established using the Stein-Lovász-Johnson strategy and the Lovász local lemma. A series of improvements on these bounds is developed in this paper. First an estimate for the discrete Stein-Lovász-Johnson bound is derived. Then using alteration, the Stein-Lovász-Johnson bound is improved upon, leading to a two-stage construction algorithm. Bounds from the Lovász local lemma are improved upon in a different manner, by examining group actions on the set of symbols. Two asymptotic upper bounds on CAN(t; k; v) are established that are tighter than the known bounds. A two-stage bound is derived that employs the Lovász local lemma and the conditional Lovász local lemma distribution.

Original languageEnglish (US)
Pages (from-to)1277-1293
Number of pages17
JournalSIAM Journal on Discrete Mathematics
Volume31
Issue number2
DOIs
StatePublished - 2017

Keywords

  • Conditional expectation algorithm
  • Covering array
  • Lovász local lemma

ASJC Scopus subject areas

  • Mathematics(all)

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