Group construction of covering arrays

作者: Karen Meagher , Brett Stevens

DOI: 10.1002/JCD.20035

关键词: Software testingGroup (mathematics)Algebraic methodSet (abstract data type)Orthogonal arrayMathematicsCombinatoricsDiscrete mathematicsExtension (predicate logic)Transversal designNetwork testing

摘要: A covering array t-CA (n, k, g) is a k × n on set of g symbols with the property that in each t × n subarray, every t × 1 column appears at least once. This paper improves many best known upper bounds n for arrays, 2-CA g + 1 ≤ k ≤ 2g, g = 3 · · · 12 by construction which these cases produces n = k (g − 1) + 1. The an extension algebraic method used Chateauneuf, Colbourn, and Kreher uses group action array. © 2004 Wiley Periodicals, Inc. J Combin Designs 13: 70–77, 2005.

参考文章(18)
Brett Stevens, Lucia Moura, Eric Mendelsohn, Lower Bounds for Transversal Covers Designs, Codes and Cryptography. ,vol. 15, pp. 279- 299 ,(1998) , 10.1023/A:1008329410829
P.C Denny, Search and Enumeration Techniques for Incidence Structures Department of Computer Science, The University of Auckland, New Zealand. ,(1998)
Brett Stevens, Eric Mendelsohn, Efficient software testing protocols conference of the centre for advanced studies on collaborative research. pp. 22- ,(1998)
Esther Seiden, Rita Zemach, On Orthogonal Arrays Annals of Mathematical Statistics. ,vol. 37, pp. 1355- 1370 ,(1966) , 10.1214/AOMS/1177699280
Brett Stevens, Eric Mendelsohn, New recursive methods for transversal covers Journal of Combinatorial Designs. ,vol. 7, pp. 185- 203 ,(1999) , 10.1002/(SICI)1520-6610(1999)7:3<185::AID-JCD3>3.0.CO;2-3
Daniel J. Kleitman, Joel Spencer, Families of k-independent sets Discrete Mathematics. ,vol. 6, pp. 255- 262 ,(1973) , 10.1016/0012-365X(73)90098-8
M. Chateauneuf, D. L. Kreher, On the state of strength-three covering arrays Journal of Combinatorial Designs. ,vol. 10, pp. 217- 238 ,(2002) , 10.1002/JCD.10002
D.M. Cohen, S.R. Dalal, J. Parelius, G.C. Patton, The combinatorial design approach to automatic test generation IEEE Software. ,vol. 13, pp. 83- 88 ,(1996) , 10.1109/52.536462
P. ERDÓS, CHAO KO, R. RADO, INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS Quarterly Journal of Mathematics. ,vol. 12, pp. 313- 320 ,(1961) , 10.1093/QMATH/12.1.313
Kari J. Nurmela, Upper bounds for covering arrays by tabu search Discrete Applied Mathematics. ,vol. 138, pp. 143- 152 ,(2004) , 10.1016/S0166-218X(03)00291-9