TY - JOUR
T1 - Subspace restrictions and affine composition for covering perfect hash families
AU - Colbourn, Charles J.
AU - Lanus, Erin
N1 - Funding Information:
∗Thanks to Ryan Dougherty, Kaushik Sarkar, and Violet Syrotiuk for useful discussions, and to two anonymous referees for helpful comments. †Research of CJC was supported in part by the National Science Foundation under Grant No. 1421058. E-mail addresses: colbourn@asu.edu (Charles J. Colbourn), elanus@asu.edu (Erin Lanus)
PY - 2020
Y1 - 2020
N2 - Covering perfect hash families provide a very compact representation of a useful family of covering arrays, leading to the best asymptotic upper bounds and fast, effective algorithms. Their compactness implies that an additional row in the hash family leads to many new rows in the covering array. In order to address this, subspace restrictions constrain covering perfect hash family so that a predictable set of many rows in the covering array can be removed without loss of coverage. Computing failure probabilities for random selections that must, or that need not, satisfy the restrictions, we identify a set of restrictions on which to focus. We use existing algorithms together with one novel method, affine composition, to accelerate the search. We report on a set of computational constructions for covering arrays to demonstrate that imposing restrictions often improves on previously known upper bounds.
AB - Covering perfect hash families provide a very compact representation of a useful family of covering arrays, leading to the best asymptotic upper bounds and fast, effective algorithms. Their compactness implies that an additional row in the hash family leads to many new rows in the covering array. In order to address this, subspace restrictions constrain covering perfect hash family so that a predictable set of many rows in the covering array can be removed without loss of coverage. Computing failure probabilities for random selections that must, or that need not, satisfy the restrictions, we identify a set of restrictions on which to focus. We use existing algorithms together with one novel method, affine composition, to accelerate the search. We report on a set of computational constructions for covering arrays to demonstrate that imposing restrictions often improves on previously known upper bounds.
KW - Affine composition
KW - Covering array
KW - Covering perfect hash family
KW - Subspace restriction
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U2 - 10.26493/2590-9770.1220.3a1
DO - 10.26493/2590-9770.1220.3a1
M3 - Article
AN - SCOPUS:85070578718
SN - 2590-9770
VL - 1
JO - Art of Discrete and Applied Mathematics
JF - Art of Discrete and Applied Mathematics
IS - 2
M1 - 3a1
ER -