### Abstract

We study grooming for two-period optical networks, a variation of the traffic grooming problem for wavelength division multiplexed (WDM) ring networks introduced by Colbourn, Quattrocchi, and Syrotiuk. In the two-period grooming problem, during the first period of time there is all-to-all uniform traffic among n nodes, each request using 1/C of the bandwidth; and during the second period there is all-to-all uniform traffic only among a subset V of v nodes, each request now being allowed to use 1/C′ of the bandwidth, where C′ < C. We determine the minimum drop cost (minimum number of add-drop multiplexers (ADMs)) for any n,v and C = 4 and C′ ∈ {1,2,3}. To do this, we use tools of graph decompositions. Indeed the two-period grooming problem corresponds to minimizing the total number of vertices in a partition of the edges of the complete graph K_{n} into subgraphs, where each subgraph has at most C edges and where furthermore it contains at most C′ edges of the complete graph on v specified vertices. Subject to the condition that the two-period grooming has the least drop cost, the minimum number of wavelengths required is also determined in each case.

Original language | English (US) |
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Pages (from-to) | 400-419 |

Number of pages | 20 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 24 |

Issue number | 2 |

DOIs | |

State | Published - 2010 |

### Keywords

- Design theory
- Graph decomposition
- Optical networks
- SONET ADM
- Traffic grooming

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*SIAM Journal on Discrete Mathematics*,

*24*(2), 400-419. https://doi.org/10.1137/080744190