## Algorithms in Combinatorial Design TheoryThe scope of the volume includes all algorithmic and computational aspects of research on combinatorial designs. Algorithmic aspects include generation, isomorphism and analysis techniques - both heuristic methods used in practice, and the computational complexity of these operations. The scope within design theory includes all aspects of block designs, Latin squares and their variants, pairwise balanced designs and projective planes and related geometries. |

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### Contents

1 | |

Chapter 2 Performance of subset generating aorithms | 49 |

Chapter 3 The computational complexity of finding subdesigns in combinatorial designs | 59 |

a survey | 67 |

Chapter 5 Algorithms to find directed packings | 137 |

Chapter 6 Four orthogonal onefactorizations on ten points | 143 |

Chapter 7 A problem of lines and intersections with an application to switching networks | 151 |

Chapter 8 A census of orthogonal Steiner triple systems of order | 165 |

Chapter 10 A survey of results on the number of t v k λ designs | 209 |

Chapter 11 Directing cyclic triple systems | 221 |

Chapter 12 Constructive enumeration of incidence systems | 227 |

Chapter 13 Construction procedures for tdesigns and the existence of new simple 6designs | 247 |

Chapter 14 Tables of parameters of BIBDs with r 41 including existence enumeration and resolvability results | 275 |

Chapter 15 On the existence of strong Kirkman cubes of order 39 and block size 3 | 309 |

Chapter 16 Hillclimbing algorithms for the construction of combinatorial designs | 321 |

Chapter 9 Derived Steiner triple systems of order 15 | 183 |

### Common terms and phrases

1-factorizations 2-colourable Annals of Discrete automorphism group balanced incomplete block BIBDs block designs C.J. Colbourn chromatic index column combinatorial design combinatorial design theory Combinatorial Theory complete Computer Science constructive enumeration contains cyclic define denote determine difference triples Discrete Mathematics disjoint Double coset elements embedding example exists geometry given Graph Theory Hence hill-climbing algorithm hypergraph incidence systems incomplete block designs integer intersection graphs invariant Journal of Combinatorial k-subsets K.T. Phelps Kirkman Kirkman triple systems Latin background Latin squares Lemma lines mate matrix Mendelsohn NE1 H Neighbours nested nodes nonisomorphic NP-complete one-factorizations orbit pair of orthogonal pairwise parallel classes parameters partial colouring partial design partial STS partition permutation polynomial predicate problem proposition repeated blocks resolvable Room squares Rosa solutions starter blocks Steiner systems Steiner triple systems Stinson strong starter STS(v subdesign subsets symmetric systems of order t-designs techniques Theorem vertices