Journal of Statistical Theory and Practice

, Volume 7, Issue 4, pp 630–649 | Cite as

Resolvable Covering Arrays

  • Charles J. ColbournEmail author


Two powerful recursive constructions of covering arrays of strengths three and four use difference covering arrays (DCAs). However, what is required in these constructions is not the algebraic structure of differences in a group, but rather that the DCAs produce covering arrays that are resolvable. Both constructions are strengthened by using resolvable covering arrays in place of DCAs. Many new difference covering arrays are found by computational methods, and resolvable covering arrays that do not arise from DCAs are produced. Improvements for bounds on covering array numbers are shown to be substantial.


Interaction faults Locating array Covering array 

AMS Subject Classification



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  1. Cohen, M. B., C. J. Colbourn, and A. C. H. Ling. 2008. Constructing strength three covering arrays with augmented annealing. Discrete Math. 308, 2709–2722.MathSciNetCrossRefGoogle Scholar
  2. Colbourn, C. J. 2008. Strength two covering arrays: Existence tables and projection. Discrete Math. 308, 772–786.MathSciNetCrossRefGoogle Scholar
  3. Colbourn, C. J. 2011a. Covering array tables.∼ccolbou/src/tabby.
  4. Colbourn, C. J., 2011b. Covering arrays and hash families. In Information security and related combinatorics, NATO Peace and Information Security, 99–136. Amsterdam, The Netherlands: IOS Press.Google Scholar
  5. Colbourn, C. J., and J. H. Dinitz. 1996. Making the MOLS table. In Computational and constructive design theory, ed. W. D. Wallis, 67–134. Dordrecht, The Netherlands: Kluwer.CrossRefGoogle Scholar
  6. Colbourn, C. J., and J. H. Dinitz. 2001. Mutually orthogonal Latin squares: A brief survey of constructions. J. Stat. Plan. Inference, 95, 9–48.MathSciNetCrossRefGoogle Scholar
  7. Colbourn, C. J., S. S. Martirosyan, Tran Van Trung, and R. A. WalkerII. 2006. Roux-type constructions for covering arrays of strengths three and four. Des. Codes Cryptogr., 41, 33–57.MathSciNetCrossRefGoogle Scholar
  8. Hartman, A. 2005. Software and hardware testing using combinatorial covering suites. In Interdisciplinary applications of graph theory, combinatorics, and algorithms, ed. M. C. Golumbic and I. B. A. Hartman, 237–266. Norwell, MA, Springer.CrossRefGoogle Scholar
  9. Hedayat, A. S., N. J. A. Sloane, and J. Stufken. 1999. Orthogonal arrays. New York, NY, Springer-Verlag.CrossRefGoogle Scholar
  10. Ji, L., and J. Yin. 2010. Constructions of new orthogonal arrays and covering arrays of strength three. J. Combin. Theory Ser. A, 117(3), 236–247.MathSciNetCrossRefGoogle Scholar
  11. Li, Y., L. Ji, and J. Yin. 2009. Covering arrays of strength 3 and 4 from holey difference matrices. Des. Codes Cryptogr., 50(3), 339–350.MathSciNetCrossRefGoogle Scholar
  12. Lobb, J. R., C. J. Colbourn, P. Danziger, B. Stevens, and J. Torres-Jimenez. 2012. Cover starters for strength two covering arrays. Discrete Math.; 312, 943–956.MathSciNetCrossRefGoogle Scholar
  13. Meagher, K., and B. Stevens. 2005. Group construction of covering arrays. J. Combin. Des., 13, 70–77.MathSciNetCrossRefGoogle Scholar
  14. Nie, C., and H. Leung. 2011. A survey of combinatorial testing. ACM Comput. Surveys, 43(2), #11.CrossRefGoogle Scholar
  15. Niskanen, S., and P. R. J. Östergård. 2003. Cliquer user’s guide, version 1.0. Technical Report Tech. Rep. T48, Communications Laboratory, Helsinki University of Technology, Espoo, Finland.Google Scholar
  16. Srivastava, J. N., and D. V. Chopra. 1973. Balanced arrays and orthogonal arrays. In Asurvey of combinatorial theory (Proc. Internat. Sympos., Colorado State Univ., Fort Collins, Colo., 1971), 411–428. Amsterdam, the Netherlands: North-Holland.CrossRefGoogle Scholar
  17. Stevens, B., A. C. H. Ling, and E. Mendelsohn. 2002. A direct construction of transversal covers using group divisible designs. Ars Combin., 63, 145–159.MathSciNetzbMATHGoogle Scholar
  18. Yin, J. 2003. Constructions of difference covering arrays. J. Combin. Theory Ser. A, 104(2), 327–339.MathSciNetCrossRefGoogle Scholar
  19. Yin, J. 2005. Cyclic difference packing and covering arrays. Des. Codes Cryptogr., 37(2), 281–292.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2013

Authors and Affiliations

  1. 1.School of Computing, Informatics and Decision Systems EngineeringArizona State UniversityTempeUSA

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