TY - JOUR
T1 - Conditional expectation algorithms for covering arrays
AU - Colbourn, Charles
PY - 2014/8
Y1 - 2014/8
N2 - An efficient conditional expectation algorithm for gencrating covering arrays has established a number of the best known upper bounds on covering array numbers. Despite its theoretical efficiency, the method requires a large amount of storage and time. In order to extend the range of its application, we generalize the method to find covering arrays that are invariant under the action of a group, reducing the search to consider only orbit representatives of interactions to be covered. at the same time, we extend the method to construct a generalization of covering arrays called quilting arrays. The extended conditional expectation algorithm, as expected, provides a technique for generating covering and quilting arrays that reduces the time and storage required. Remarkably, it also improves on the best known bounds on covering array numbers in a variety of parameter situations.
AB - An efficient conditional expectation algorithm for gencrating covering arrays has established a number of the best known upper bounds on covering array numbers. Despite its theoretical efficiency, the method requires a large amount of storage and time. In order to extend the range of its application, we generalize the method to find covering arrays that are invariant under the action of a group, reducing the search to consider only orbit representatives of interactions to be covered. at the same time, we extend the method to construct a generalization of covering arrays called quilting arrays. The extended conditional expectation algorithm, as expected, provides a technique for generating covering and quilting arrays that reduces the time and storage required. Remarkably, it also improves on the best known bounds on covering array numbers in a variety of parameter situations.
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M3 - Article
AN - SCOPUS:84906237854
SN - 0835-3026
VL - 90
SP - 97
EP - 115
JO - Journal of Combinatorial Mathematics and Combinatorial Computing
JF - Journal of Combinatorial Mathematics and Combinatorial Computing
ER -