TY - JOUR
T1 - Distributing hash families with few rows
AU - Colbourn, Charles J.
AU - Dougherty, Ryan E.
AU - Horsley, Daniel
PY - 2019/12/31
Y1 - 2019/12/31
N2 - Column replacement techniques for creating covering arrays rely on the construction of perfect and distributing hash families with few rows, having as many columns as possible for a specified number of symbols. To construct distributing hash families in which the number of rows is less than the strength, we examine a method due to Blackburn and extend it in three ways. First, the method is generalized from homogeneous hash families (in which every row has the same number of symbols) to heterogeneous ones. Second, the extension treats distributing hash families, in which only separation into a prescribed number of parts is required, rather than perfect hash families, in which columns must be completely separated. Third, the requirements on one of the main ingredients are relaxed to permit the use of a large class of distributing hash families, which we call fractal. Constructions for fractal perfect and distributing hash families are given, and applications to the construction of perfect hash families of large strength are developed.
AB - Column replacement techniques for creating covering arrays rely on the construction of perfect and distributing hash families with few rows, having as many columns as possible for a specified number of symbols. To construct distributing hash families in which the number of rows is less than the strength, we examine a method due to Blackburn and extend it in three ways. First, the method is generalized from homogeneous hash families (in which every row has the same number of symbols) to heterogeneous ones. Second, the extension treats distributing hash families, in which only separation into a prescribed number of parts is required, rather than perfect hash families, in which columns must be completely separated. Third, the requirements on one of the main ingredients are relaxed to permit the use of a large class of distributing hash families, which we call fractal. Constructions for fractal perfect and distributing hash families are given, and applications to the construction of perfect hash families of large strength are developed.
KW - Covering
KW - Distributing hash family
KW - Fractal hash family
KW - Perfect hash family
UR - http://www.scopus.com/inward/record.url?scp=85074470045&partnerID=8YFLogxK
U2 - 10.1016/j.tcs.2019.10.014
DO - 10.1016/j.tcs.2019.10.014
M3 - Article
AN - SCOPUS:85074470045
SN - 0304-3975
VL - 800
SP - 31
EP - 41
JO - Theoretical Computer Science
JF - Theoretical Computer Science
ER -