Optical grooming with grooming ratio nine

Charles Colbourn, Gennian Ge, Alan C H Ling

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)8-15
Number of pages8
JournalDiscrete Mathematics
Issue number1
StatePublished - 2011


  • Block designs
  • Combinatorial designs
  • Group-divisible designs
  • Optical networks
  • Traffic grooming
  • Wavelength-division multiplexing

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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