Erratum to: Supercomputing and grid computing on the verification of covering arrays

The Covering Arrays (CAs) are mathematical objects with minimal coverage and maximum cardinality that are a good tool for the design of experiments. A covering array is an N ×k matrix over an alphabet v s.t. each N ×k subset contains at least one time each combination from {0,1, . . . , v − 1}t , given a positive integer value t . The process of ensuring that a CA contains each of the v combinations is called verification of CA. In this paper, we present an algorithm for CA verification and its implementation details in three different computation paradigms: (a) sequential approach (SA); (b) parallel approach (PA); and (c) Grid approach (GA). Four different PAs were compared in their performance of verifying a matrix as a CA; the PA with the best performance was included in a different experimentation where the three paradigms, SA, PA, and GA were compared in a benchmark composed by 45 possible CA instances. The results showed the limitations of the different paradigms H. Avila-George ( ) · A. Carrión · V. Hernández Instituto de Instrumentación para Imagen Molecular (I3M), Centro mixto CSIC, Universitat Politècnica de València, CIEMAT, Camino de Vera S/N, 46022 Valencia, Spain e-mail: hiavgeo@posgrado.upv.es A. Carrión e-mail: abcarcol@i3m.upv.es V. Hernández e-mail: vhernandez@dsic.upv.es J. Torres-Jimenez Information Technology Laboratory, CINVESTAV-Tamaulipas, Km. 5.5 Carretera Victoria-Soto La Marina, 87130 Victoria Tamps, Mexico e-mail: jtj@cinvestav.mx N. Rangel-Valdez Universidad Politécnica de Ciudad Victoria, Parque Científico y Tecnológico de Tamaulipas, Av. Nuevas Tecnologias 5902, Carretera Victoria-Soto la Marina Km. 5.5, 87138 Cd. Victoria, Tamps., Mexico e-mail: nrangelv@upv.edu.mx H. Avila-George et al. when solving the verification of CA problem, and points out the necessity of a Grid approach to solve the problem when the size of a CA grows.

[1]  José Torres-Jiménez,et al.  New bounds for binary covering arrays using simulated annealing , 2012, Inf. Sci..

[2]  Tatsuhiro Tsuchiya,et al.  Using artificial life techniques to generate test cases for combinatorial testing , 2004, Proceedings of the 28th Annual International Computer Software and Applications Conference, 2004. COMPSAC 2004..

[3]  Dennis Shasha,et al.  Products of mixed covering arrays of strength two , 2006 .

[4]  José Torres-Jiménez,et al.  Verification of General and Cyclic Covering Arrays Using Grid Computing , 2010, Globe.

[5]  Robert L. Probert,et al.  A practical strategy for testing pair-wise coverage of network interfaces , 1996, Proceedings of ISSRE '96: 7th International Symposium on Software Reliability Engineering.

[6]  José Torres-Jiménez,et al.  Computation of Ternary Covering Arrays Using a Grid , 2004, AACC.

[7]  Alan W. Williams,et al.  Determination of Test Configurations for Pair-Wise Interaction Coverage , 2000, TestCom.

[8]  Madhan Shridhar Phadke,et al.  Quality Engineering Using Robust Design , 1989 .

[9]  K. Burr,et al.  Combinatorial Test Techniques : Table-based Automation , Test Generation and Code Coverage , 1998 .

[10]  D E Shasha,et al.  Using combinatorial design to study regulation by multiple input signals. A tool for parsimony in the post-genomics era. , 2001, Plant physiology.

[11]  Diana Adler.  Experimental Design For Combinatorial And High Throughput Materials Development , 2016 .

[12]  C. Colbourn,et al.  Heterogeneous Hash Families and Covering Arrays , 2010 .

[13]  Angelo Gargantini,et al.  Building T-wise Combinatorial Interaction Test Suites by Means of Grid Computing , 2009, 2009 18th IEEE International Workshops on Enabling Technologies: Infrastructures for Collaborative Enterprises.

[14]  Jeff Yu Lei,et al.  IPOG: A General Strategy for T-Way Software Testing , 2007, 14th Annual IEEE International Conference and Workshops on the Engineering of Computer-Based Systems (ECBS'07).

[15]  Jeff Yu Lei,et al.  A Survey of Binary Covering Arrays , 2011, Electron. J. Comb..

[16]  K.Z. Zamli,et al.  A strategy for Grid based t-way test data generation , 2008, 2008 First International Conference on Distributed Framework and Applications.

[17]  Christine T. Cheng.  The test suite generation problem: Optimal instances and their implications , 2007, Discret. Appl. Math..

[18]  B. Stevens,et al.  Covering arrays with mixed alphabet sizes , 2003 .

[19]  Nelson Rangel-Valdez,et al.  Construction of logarithm tables for Galois Fields , 2011 .

[20]  K. A. Bush.  Orthogonal Arrays of Index Unity , 1952 .

[21]  Charles J. Colbourn,et al.  A recursive construction for perfect hash families , 2009, J. Math. Cryptol..

[22]  Nelson Rangel-Valdez,et al.  Construction of Orthogonal Arrays of Index Unity Using Logarithm Tables for Galois Fields , 2012 .

[23]  Hülya Bayrak,et al.  ON THE CONSTRUCTION OF ORTHOGONAL ARRAYS , 2001 .

[24]  Johannes Elmsheuser,et al.  Ganga: A tool for computational-task management and easy access to Grid resources , 2009, Comput. Phys. Commun..

[25]  Gadiel Seroussi,et al.  Vector sets for exhaustive testing of logic circuits , 1988, IEEE Trans. Inf. Theory.

[26]  José Torres-Jiménez,et al.  Construction of Mixed Covering Arrays of Variable Strength Using a Tabu Search Approach , 2010, COCOA.

[27]  Violet R. Syrotiuk,et al.  Factor interaction on service delivery in mobile ad hoc networks , 2004, IEEE Journal on Selected Areas in Communications.

[28]  Kari J. Nurmela,et al.  Upper bounds for covering arrays by tabu search , 2004, Discret. Appl. Math..

[29]  D.M. Cohen,et al.  The Combinatorial Design Approach to Automatic Test Generation , 1996, IEEE Softw..

[30]  Jeff Yu Lei,et al.  Practical Combinatorial Testing: Beyond Pairwise , 2008, IT Professional.

[31]  Joel H. Spencer,et al.  Families of k-independent sets , 1973, Discret. Math..

[32]  G. Katona.  Two applications (for search theory and truth functions) of Sperner type theorems , 1973 .

[33]  Charles J. Colbourn,et al.  Binary Covering Arrays and Existentially Closed Graphs , 2009, IWCC.

[34]  C. Colbourn.  Combinatorial aspects of covering arrays , 2006 .

[35]  José Torres-Jiménez,et al.  A Heuristic Approach for Constructing Ternary Covering Arrays Using Trinomial Coefficients , 2010, IBERAMIA.

[36]  Charles J. Colbourn,et al.  The density algorithm for pairwise interaction testing , 2007, Softw. Test. Verification Reliab..

[37]  Ami Marowka,et al.  The GRID: Blueprint for a New Computing Infrastructure , 2000, Parallel Distributed Comput. Pract..

[38]  Myra B. Cohen,et al.  Covering arrays for efficient fault characterization in complex configuration spaces , 2004, IEEE Transactions on Software Engineering.

[39]  Jennifer Werfel,et al.  Orthogonal Arrays Theory And Applications , 2016 .

[40]  Yu-Wen Tung,et al.  Automating test case generation for the new generation mission software system , 2000, 2000 IEEE Aerospace Conference. Proceedings (Cat. No.00TH8484).

[41]  Myra B. Cohen,et al.  Augmenting simulated annealing to build interaction test suites , 2003, 14th International Symposium on Software Reliability Engineering, 2003. ISSRE 2003..

[42]  George B. Sherwood.  Optimal and near-optimal mixed covering arrays by column expansion , 2008, Discret. Math..