The Computational Complexity of Finding Subdesigns in Combinatorial Designs

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

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)59-65
Number of pages7
JournalNorth-Holland Mathematics Studies
Volume114
Issue numberC
DOIs
StatePublished - 1985
Externally publishedYes

Fingerprint

Combinatorial Design
Computational Complexity
Polynomial time
Maximal Order
Block Design
NP-complete problem
Design

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The Computational Complexity of Finding Subdesigns in Combinatorial Designs. / Colbourn, Charles; Colbourn, Marlenc J.; Stineon, Douglas R.

In: North-Holland Mathematics Studies, Vol. 114, No. C, 1985, p. 59-65.

Research output: Contribution to journalArticle

Colbourn, Charles ; Colbourn, Marlenc J. ; Stineon, Douglas R. / The Computational Complexity of Finding Subdesigns in Combinatorial Designs. In: North-Holland Mathematics Studies. 1985 ; Vol. 114, No. C. pp. 59-65.
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