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Zbl 0894.68107
McKay, Brendan D.
Isomorph-free exhaustive generation. (English)
[J] J. Algorithms 26, No.2, 306-324 (1998). ISSN 0196-6774

Summary: We describe a very general technique for generating families of combinatorial objects without isomorphs. It applies to almost any class of objects for which an inductive construction process exists. In one form of our technique, no explicit isomorphism testing is required. In the other form, isomorph testing is restricted to within small subsets of the entire set of objects. A variety of different examples are presented, including the generation of graphs with some hereditary property, the generation of Latin rectangles and the generation of balanced incomplete block designs. The technique can also be used to perform unbiased statistical analysis, including approximate counting, of sets of objects too large to generate exhaustively.

MSC 2000:: *68R10 Graph theory in connection with computer science

Keywords: exhaustive generation

Cited in: Zbl 1117.05054

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