Generalized Triad Design Algorithms
This thesis mainly focuses on the development of a triad design on v objects, TD(v), which is a way of arranging distinct triples on v objects with some properties. Previous studies on TD(v) reported its existence when v≡1 or 5 (mod 6) and TD(7) was developed by using a brute-force method. In this s...
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| Format: | Thesis |
| Language: | eng |
| Published: |
2012
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| Subjects: | |
| Online Access: | https://etd.uum.edu.my/2976/1/Tareq_Mohammad_Abu_Saa.pdf |
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| Summary: | This thesis mainly focuses on the development of a triad design on v objects, TD(v), which is a way of arranging distinct triples on v objects with some properties. Previous studies on TD(v) reported its existence when v≡1 or 5 (mod 6) and TD(7) was developed by using a brute-force method. In this study, generalized and new algorithms for developing TD(v) for any v = 6n + 1 or v = 6n + 5 were developed. In general, the first part of the thesis develops two new techniques to solve the problems above. In addition, new constructions for the starter of a compatible factorization on v objects, a SCF(v), and new algorithms for a CF(v) was developed. The second part of the thesis develops three new techniques for building algorithms of the TD(v), TD(v) = CF(v) where is the completion of the CF(v). Furthermore, a starter triad design, STD(v) = SCF(v) and many remarkable theorems were proved. Additionally, a new technique for STD(v) algorithms, known as the “Generalized Interval Method - GIM” was constructed, by analyzing the pattern of the triples in the STD(v) using the intervals number and the components of triples. This technique, finally listed TD(6n + 1) and TD(6n + 5) by repeated addition of 1 (mod v) from the STD(v). |
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