Browsing by Author "Jimbo, M"

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A resolvable r x c grid-block packing and its application to DNA library screening
(2004-12-01)
Mutoh, Y
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Jimbo, M
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Fu, HL
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應用數學系
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Department of Applied Mathematics
For a nu-set V, let A be a collection of r x c arrays with elements in V. A pair (V, A) is called an r x c grid-block packing if every two distinct points i and j in V occur together at most once in the same row or in the same column of arrays in A. And an r x c grid-block packing (V, A) is said to be resolvable if the collection of arrays A can be partitioned into sub-classes R-1, R-2,..., R-t such that every point of V is contained in precisely one array of each class. These packings have originated from the use of DNA library screening. In this paper, we give some constructions of resolvable r x c grid-block packings and give a brief survey of their application to DNA library screening.
Decomposing complete graphs into K-r x K-c's
(2004-02-01)
Fu, HL
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Hwang, FK
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Jimbo, M
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Mutoh, Y
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Shiue, CL
We consider the problem of decomposing a complete graph into the Cartesian product of two complete graphs K, and K, This problem originated from the clone library screening. We give a general method of constructing such decompositions using various sorts of combinatorial designs. In particular, for r = 3 and c = 3, we show that such a decomposition exists for all n satisfying some simple necessary conditions. (C) 2002 Elsevier B.V. All rights reserved.
The existence of 2x4 grid-block designs and their applications
(2003)
Mutoh, Y
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Morihara, T
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Jimbo, M
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Fu, HL
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應用數學系
Fu, Hwang, Jimbo, Mutoh, and Shiue [J. Statist. Plann. Inference, to appear] introduced the concept of a grid-block design, which is defined as follows: For a v- set V, let A be a collection of r x c arrays with elements in V. A pair ( V, A) is called an r x c grid-block design if every two distinct points i and j in V occur exactly once in the same row or in the same column. This design has originated from the use of DNA library screening. They gave some general constructions and proved the existence of 3 x 3 grid-block designs. Meanwhile, the existence of 2 x 3 grid-block designs was shown by Carter [ Designs on Cubic Multigraphs, Ph. D. thesis, McMaster University, Hamilton, ON, Canada, 1989] by decomposing K-v into cubic graphs. In this paper, we show the existence of 2 x 4 grid-block designs.