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1. Kaski, Petteri. Algorithms for Classification of Combinatorial Objects.

Degree: 2005, Helsinki University of Technology

URL: http://lib.tkk.fi/Diss/2005/isbn9512277271/

A recurrently occurring problem in combinatorics is the need to completely characterize a finite set of finite objects implicitly defined by a set of constraints. For example, one could ask for a list of all possible ways to schedule a football tournament for twelve teams: every team is to play against every other team during an eleven-round tournament, such that every team plays exactly one game in every round. Such a characterization is called a classification for the objects of interest. Classification is typically conducted up to a notion of structural equivalence (isomorphism) between the objects. For example, one can view two tournament schedules as having the same structure if one can be obtained from the other by renaming the teams and reordering the rounds. This thesis examines algorithms for classification of combinatorial objects up to isomorphism. The thesis consists of five articles – each devoted to a specific family of objects – together with a summary surveying related research and emphasizing the underlying common concepts and techniques, such as backtrack search, isomorphism (viewed through group actions), symmetry, isomorph rejection, and computing isomorphism. From an algorithmic viewpoint the focus of the thesis is practical, with interest on algorithms that perform well in practice and yield new classification results; theoretical properties such as the asymptotic resource usage of the algorithms are not considered. The main result of this thesis is a classification of the Steiner triple systems of order 19. The other results obtained include the nonexistence of a resolvable 2-(15, 5, 4) design, a classification of the one-factorizations of k-regular graphs of order 12 for k ≤ 6 and k = 10, 11, a classification of the near-resolutions of 2-(13, 4, 3) designs together with the associated thirteen-player whist tournaments, and a classification of the Steiner triple systems of order 21 with a nontrivial automorphism group.

Research reports / Helsinki University of Technology, Laboratory for Theoretical Computer Science, ISSN 1457-7615; 94

Subjects/Keywords: classification algorithm; isomorphism; isomorph rejection; near-resolvable design; one-factorization; orderly algorithm; regular graph; resolvable design; Steiner triple system

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APA (6^{th} Edition):

Kaski, P. (2005). Algorithms for Classification of Combinatorial Objects. (Thesis). Helsinki University of Technology. Retrieved from http://lib.tkk.fi/Diss/2005/isbn9512277271/

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Kaski, Petteri. “Algorithms for Classification of Combinatorial Objects.” 2005. Thesis, Helsinki University of Technology. Accessed October 23, 2020. http://lib.tkk.fi/Diss/2005/isbn9512277271/.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Kaski, Petteri. “Algorithms for Classification of Combinatorial Objects.” 2005. Web. 23 Oct 2020.

Vancouver:

Kaski P. Algorithms for Classification of Combinatorial Objects. [Internet] [Thesis]. Helsinki University of Technology; 2005. [cited 2020 Oct 23]. Available from: http://lib.tkk.fi/Diss/2005/isbn9512277271/.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Kaski P. Algorithms for Classification of Combinatorial Objects. [Thesis]. Helsinki University of Technology; 2005. Available from: http://lib.tkk.fi/Diss/2005/isbn9512277271/

Not specified: Masters Thesis or Doctoral Dissertation