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

Jean Claude Bermond, Charles Colbourn, Lucia Gionfriddo, Gaetano Quattrocchi, Ignasi Sau

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 Kn 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 languageEnglish (US)
Pages (from-to)400-419
Number of pages20
JournalSIAM Journal on Discrete Mathematics
Volume24
Issue number2
DOIs
StatePublished - 2010

Fingerprint

Wavelength
Costs
Complete Graph
Subgraph
Traffic Grooming
Bandwidth
Traffic
Graph Decomposition
Ring Network
Division ring or skew field
Optical Networks
Vertex of a graph
Period of time
Partition
Subset

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Drop cost and wavelength optimal two-period grooming with ratio 4. / Bermond, Jean Claude; Colbourn, Charles; Gionfriddo, Lucia; Quattrocchi, Gaetano; Sau, Ignasi.

In: SIAM Journal on Discrete Mathematics, Vol. 24, No. 2, 2010, p. 400-419.

Research output: Contribution to journalArticle

Bermond, Jean Claude ; Colbourn, Charles ; Gionfriddo, Lucia ; Quattrocchi, Gaetano ; Sau, Ignasi. / Drop cost and wavelength optimal two-period grooming with ratio 4. In: SIAM Journal on Discrete Mathematics. 2010 ; Vol. 24, No. 2. pp. 400-419.
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