The Computational Complexity of Finding Subdesigns in Combinatorial Designs

Charles J. Colbourn; Marlenc J. Colbourn; Douglas R. Stineon

doi:10.1016/S0304-0208(08)72975-X

The Computational Complexity of Finding Subdesigns in Combinatorial Designs

Charles J. Colbourn, Marlenc J. Colbourn, Douglas R. Stineon

Research output: Contribution to journal › Article

1 Scopus citations

Abstract

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(v^logd 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.

Original language	English (US)
Pages (from-to)	59-65
Number of pages	7
Journal	North-Holland Mathematics Studies
Volume	114
Issue number	C
DOIs	https://doi.org/10.1016/S0304-0208(08)72975-X
State	Published - Jan 1 1985
Externally published	Yes

Fingerprint

ASJC Scopus subject areas

Mathematics(all)

Cite this

Colbourn, C. J., Colbourn, M. J., & Stineon, D. R. (1985). The Computational Complexity of Finding Subdesigns in Combinatorial Designs. North-Holland Mathematics Studies, 114(C), 59-65. https://doi.org/10.1016/S0304-0208(08)72975-X

@article{18df0f0573ad46a0a57ddbfbb3d9aa47,

title = "The Computational Complexity of Finding Subdesigns in Combinatorial Designs",

abstract = "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.",

author = "Colbourn, {Charles J.} and Colbourn, {Marlenc J.} and Stineon, {Douglas R.}",

year = "1985",

month = jan

day = "1",

doi = "10.1016/S0304-0208(08)72975-X",

language = "English (US)",

volume = "114",

pages = "59--65",

journal = "North-Holland Mathematics Studies",

issn = "0304-0208",

publisher = "Elsevier",

number = "C",

}

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.

UR - http://www.scopus.com/inward/record.url?scp=77956929987&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956929987&partnerID=8YFLogxK

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 -

Access to Document

10.1016/S0304-0208(08)72975-X