# Drop cost and wavelength optimal two-period grooming with ratio 4

1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
4 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We study grooming for two-period optical networks, a variation of the traffic grooming problem for 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 ADMs) for any $n,v$ and $C=4$ and $C' \in \{1,2,3\}$. 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.
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Reports

Cited literature [34 references]

https://hal.inria.fr/inria-00432801
Contributor : Ignasi Sau Valls <>
Submitted on : Tuesday, November 17, 2009 - 12:46:17 PM
Last modification on : Tuesday, November 17, 2020 - 11:18:04 PM
Long-term archiving on: : Thursday, June 17, 2010 - 8:41:02 PM

### Files

RR-7101.pdf
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### Identifiers

• HAL Id : inria-00432801, version 1
• ARXIV : 0911.3475

### Citation

Jean-Claude Bermond, Charles J. Colbourn, Lucia Gionfriddo, Gaetano Quattrocchi, Ignasi Sau Valls. Drop cost and wavelength optimal two-period grooming with ratio 4. [Research Report] RR-7101, INRIA. 2009, pp.24. ⟨inria-00432801⟩

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