Browsing by Author "Ling, Alan C. H."

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MINIMIZING SONET ADMs IN UNIDIRECTIONAL WDM RINGS WITH GROOMING RATIO SEVEN
(2008)
Colbourn, Charles J.
;
Fu, Hung-Lin
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Ge, Gennian
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Ling, Alan C. H.
;
Lu, Hui-Chuan
In order to reduce the number of add-drop multiplexers (ADMs) in SONET/WDM networks using wavelength add-drop multiplexing, certain graph decompositions can be used to form a "grooming" that specifies the assignment of traffic to wavelengths. When traffic among nodes is all-to-all and uniform, the drop cost of such a decomposition is the sum, over all graphs in the decomposition, of the number of vertices of nonzero degree in the graph. The number of ADMs required is this drop cost. The existence of such decompositions with minimum cost, when every pair of sites employs no more than 1/7 of the wavelength capacity, is determined within an additive constant. Indeed when the number n of sites satisfies n equivalent to 1 (mod 3) and n not equal 19, the determination is exact; when n equivalent to 0 (mod 3), n not equivalent to 18 (mod 24), and n is large enough, the determination is also exact; and when n equivalent to 2 ( mod 3) and n is large enough, the gap between the cost of the best construction and the cost of the lower bound is independent of n and does not exceed 4.
THE EXISTENCE OF r x 4 GRID-BLOCK DESIGNS WITH r=3, 4
(2009)
Zhang, Rucong
;
Ge, Gennian
;
Ling, Alan C. H.
;
Fu, Hung-Lin
;
Mutoh, Yukiyasu
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 elements i and j in V occur exactly once in the same row or in the same column of an array in A. This design originated from the use of DNA library screening. In this paper, we show the existence of r x 4 grid-block designs with r = 3, 4. We settle completely for the case of r = 4 and almost completely for the case of r = 3, leaving 15 orders undetermined.