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Algorithmic methods for covering arrays of higher index

Author

Listed:
  • Ryan E. Dougherty

    (United States Military Academy)

  • Kristoffer Kleine

    (SBA Research)

  • Michael Wagner

    (SBA Research)

  • Charles J. Colbourn

    (Arizona State University)

  • Dimitris E. Simos

    (SBA Research)

Abstract

Covering arrays are combinatorial objects used in testing large-scale systems to increase confidence in their correctness. To do so, each interaction of at most a specified number t of factors is represented in at least one test; that is, the covering array has strength t and index 1. For certain systems, the outcome of running a test may be altered by variability of the interaction effect or by measurement error of the test result. To improve the efficacy of testing, one can ensure that each interaction of t or fewer factors is represented in at least $$\lambda $$ λ tests. When $$\lambda > 1$$ λ > 1 , this leads to covering arrays of higher index. We explore two algorithmic methods for constructing covering arrays of higher index. One is based on the in-parameter-order algorithm, and the other employs a conditional expectation paradigm. We compare these two by performing experiments on real-world benchmarks and on uniform parameter sets.

Suggested Citation

  • Ryan E. Dougherty & Kristoffer Kleine & Michael Wagner & Charles J. Colbourn & Dimitris E. Simos, 2023. "Algorithmic methods for covering arrays of higher index," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-21, January.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00947-x
    DOI: 10.1007/s10878-022-00947-x
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    References listed on IDEAS

    as
    1. Charles J. Colbourn & Daniel W. McClary, 2008. "Locating and detecting arrays for interaction faults," Journal of Combinatorial Optimization, Springer, vol. 15(1), pages 17-48, January.
    2. Ryan E. Dougherty & Charles J. Colbourn, 2020. "Perfect Hash Families: The Generalization to Higher Indices," Springer Optimization and Its Applications, in: Andrei M. Raigorodskii & Michael Th. Rassias (ed.), Discrete Mathematics and Applications, pages 177-197, Springer.
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