TY - JOUR
T1 - The Computational Complexity of Finding Subdesigns in Combinatorial Designs
AU - Colbourn, Charles J.
AU - Colbourn, Marlenc J.
AU - Stineon, Douglas R.
N1 - Funding Information:
The authors would like to thank the Natural Sciences and Engineering Research Council of Canada and Simon Fraser University for supporting the Workshop on Latin Squares held at Simon Fraser, .My-August 1983, during which this research was done. Research of the authors is funded by *NSERC Canada under grants numbered A5047 (CJC), A5483 (MJC), and U0217 (DRS).
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 -