TY - JOUR
T1 - The Computational Complexity of Finding Subdesigns in Combinatorial Designs
AU - Colbourn, Charles J.
AU - Colbourn, Marlenc J.
AU - Stineon, Douglas R.
PY - 1985/1/1
Y1 - 1985/1/1
N2 - Algorithms for determining the existence of subdesigns in a combinatorial design are examined. When λ=1, the existence of a subdesign of order d in a design of order v can be determined in O(vlogd time. The order of the smallest subdesign can be computed in polynomial time. In addition, determining whether a design has a subdesign of maximal possible order (a “head”) requires polynomial time. When λ>1, the problems are apparently significantly more difficult: we show that deciding whether a block design has any non-trivial subdesign is NP-complete.
AB - Algorithms for determining the existence of subdesigns in a combinatorial design are examined. When λ=1, the existence of a subdesign of order d in a design of order v can be determined in O(vlogd time. The order of the smallest subdesign can be computed in polynomial time. In addition, determining whether a design has a subdesign of maximal possible order (a “head”) requires polynomial time. When λ>1, the problems are apparently significantly more difficult: we show that deciding whether a block design has any non-trivial subdesign is NP-complete.
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U2 - 10.1016/S0304-0208(08)72975-X
DO - 10.1016/S0304-0208(08)72975-X
M3 - Article
AN - SCOPUS:77956929987
VL - 114
SP - 59
EP - 65
JO - North-Holland Mathematics Studies
JF - North-Holland Mathematics Studies
SN - 0304-0208
IS - C
ER -