Covering Arrays of Strength Four and Software Testing

  • Yasmeen AkhtarEmail author
  • Soumen Maity
  • Reshma C. Chandrasekharan
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 139)


A covering array \(t-\text{ CA }(n,k,g)\), of size n, strength t, degree k, and order g, is a \(k\times n\) array on g symbols such that every \(t\times n\) subarray contains every \(t\times 1\) column on g symbols at least once. Covering arrays have been studied for their applications on software testing, hardware testing, drug screening, and in areas where interactions of multiple parameters are to be tested. We define the coverage measure \(\mu _t(A)\) of an array A by the ratio between the number of distinct t-tuples contained in the column vectors of A and the total number of t-tuples given by \({\left( {\begin{array}{c}k\\ t\end{array}}\right) }g^t\). Given fixed values of tkg, and n, our objective is to construct an array A of size atmost n having largest possible coverage measure. This problem is called covering arrays with budget constrains. In this article, we present an algebraic construction method for strength four covering arrays with budget constraints.


Covering arrays Combinatorics Group action Software testing 



The first author gratefully acknowledges support from the Council of Scientific and Industrial Research (CSIR), India, during the work under CSIR senior research fellow scheme.


  1. 1.
    Chateauneuf, M.A., Colbourn, C.J., Kreher, D.L.: Covering arrays of strength three. Des. Codes Crypt. 16, 235–242 (1999)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Cohen, D.M., Dalal, S.R., Fredman, M.L., Patton, G.C.: The AETG system: an approach to testing based on combinatorial design. IEEE Trans. Softw. Eng. 23(7), 437–443 (1997)CrossRefGoogle Scholar
  3. 3.
    Colbourn, C.: Covering Array Tables for t=2,3,4,5,6.
  4. 4.
  5. 5.
    Hartman, A., Raskin, L.: Problems and algorithms for covering arrays. Discret. Math. 284, 149–156 (2004)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Hartman, A.: Software and hardware testing using combinatorial covering suites. Graph Theory, Comb. Algorithms: Interdisc. Appl. (Kluwer Academic Publishers) 34, 237–266 (2006)Google Scholar
  7. 7.
    Kaner, C., Falk, J., Nguyen, H.Q.: Testing Computer Software, 2nd edn. Wiley, New York (1999)Google Scholar
  8. 8.
    Maity, S.: 3-Way software testing with budget constraints. IEICE Trans. Inf. Syst. E-95-D(9), 2227–2231 (2012)Google Scholar
  9. 9.
    Maity, S., Nayak, A.: Improved test generation algorithms for pair-wise testing. In: Proceedings of 16th IEEE International Symposium on Software Reliability Engineering, pp. 235–244. Chicago (2005)Google Scholar
  10. 10.
    Meagher, K., Stevens, B.: Group construction of covering arrays. J. Comb. Des. 13(1), 70–77 (2005)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Richard, K.D., Wallace, D.R., Gallo, A.M.: Software fault interactions and implications for software testing. IEEE Trans. Softw. Eng. 30(6), 418–421 (2004)Google Scholar
  12. 12.
    Robinson, D.J.S.: A course in the theory of groups, 2nd edn. Springer, Heidelberg (1995)Google Scholar
  13. 13.
    Yilmaz, C., Cohen, M., Porter, A.: Covering arrays for efficient fault characterisation in complex configuration spaces. IEEE Trans. Softw. Eng. 32(1), 20–34 (2006)CrossRefGoogle Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  • Yasmeen Akhtar
    • 1
    Email author
  • Soumen Maity
    • 1
  • Reshma C. Chandrasekharan
    • 1
  1. 1.Indian Institute of Science Education and ResearchPuneIndia

Personalised recommendations