TY - JOUR

T1 - Optical grooming with grooming ratio nine

AU - Colbourn, Charles

AU - Ge, Gennian

AU - Ling, Alan C H

N1 - Funding Information:
We thank the reviewers for their careful reading and helpful comments. The research of the second author was supported by the National Outstanding Youth Science Foundation of China under Grant No. 10825103 , National Natural Science Foundation of China under Grant No. 10771193 , Specialized Research Fund for the Doctoral Program of Higher Education, Program for New Century Excellent Talents in University, and Zhejiang Provincial Natural Science Foundation of China under Grant No. D7080064 .

PY - 2011

Y1 - 2011

N2 - Grooming uniform all-to-all traffic in optical ring networks with grooming ratio C requires the determination of graph decompositions of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The minimum drop cost is determined for grooming ratio 9. Previously this bound was shown to be met when n≡0(mod9) with two exceptions and eleven additional possible exceptions for n, and also when n≡1(mod9) with one exception and one possible exception for n. In this paper it is shown that the bound is met for all n≡2,5,8(mod9) with four exceptions for n∈8,11,14,17 and one possible exception for n=20. Using this result, it is further shown that when n≡3,4,6,7(mod9) and n is sufficiently large, the bound is also met.

AB - Grooming uniform all-to-all traffic in optical ring networks with grooming ratio C requires the determination of graph decompositions of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The minimum drop cost is determined for grooming ratio 9. Previously this bound was shown to be met when n≡0(mod9) with two exceptions and eleven additional possible exceptions for n, and also when n≡1(mod9) with one exception and one possible exception for n. In this paper it is shown that the bound is met for all n≡2,5,8(mod9) with four exceptions for n∈8,11,14,17 and one possible exception for n=20. Using this result, it is further shown that when n≡3,4,6,7(mod9) and n is sufficiently large, the bound is also met.

KW - Block designs

KW - Combinatorial designs

KW - Group-divisible designs

KW - Optical networks

KW - Traffic grooming

KW - Wavelength-division multiplexing

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U2 - 10.1016/j.disc.2010.09.013

DO - 10.1016/j.disc.2010.09.013

M3 - Article

AN - SCOPUS:79953771682

SN - 0012-365X

VL - 311

SP - 8

EP - 15

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1

ER -