### Abstract

In a problem arising in grooming for two-period optical networks, it is required to decompose the complete graph on n vertices into subgraphs each containing at most C edges, so that the induced subgraphs on a specified set of v ≤ n vertices each contain at most C′ ≤ C edges. The cost of the grooming is the sum, over all subgraphs, of the number of vertices of nonzero degree in the subgraph. The optimum grooming is the one of lowest cost. An integer linear programming formulation is used to determine precise lower bounds on this minimum cost for all choices of n and v when 1 ≤ C′ < C ≤ 3. In most cases, this approach determines not only the bound but also the specific structure of any grooming that could realize the bound.

Original language | English (US) |
---|---|

Pages (from-to) | 299-306 |

Number of pages | 8 |

Journal | Networks |

Volume | 52 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2008 |

### Fingerprint

### Keywords

- Combinatorial designs
- Graph decomposition
- Linear programming duality
- Optical networks
- Traffic grooming

### ASJC Scopus subject areas

- Computer Networks and Communications
- Information Systems

### Cite this

*Networks*,

*52*(4), 299-306. https://doi.org/10.1002/net.20251

**Lower bounds for two-period grooming via linear programming duality.** / Colbourn, Charles; Quattrocchi, Gaetano; Syrotiuk, Violet.

Research output: Contribution to journal › Article

*Networks*, vol. 52, no. 4, pp. 299-306. https://doi.org/10.1002/net.20251

}

TY - JOUR

T1 - Lower bounds for two-period grooming via linear programming duality

AU - Colbourn, Charles

AU - Quattrocchi, Gaetano

AU - Syrotiuk, Violet

PY - 2008/12

Y1 - 2008/12

N2 - In a problem arising in grooming for two-period optical networks, it is required to decompose the complete graph on n vertices into subgraphs each containing at most C edges, so that the induced subgraphs on a specified set of v ≤ n vertices each contain at most C′ ≤ C edges. The cost of the grooming is the sum, over all subgraphs, of the number of vertices of nonzero degree in the subgraph. The optimum grooming is the one of lowest cost. An integer linear programming formulation is used to determine precise lower bounds on this minimum cost for all choices of n and v when 1 ≤ C′ < C ≤ 3. In most cases, this approach determines not only the bound but also the specific structure of any grooming that could realize the bound.

AB - In a problem arising in grooming for two-period optical networks, it is required to decompose the complete graph on n vertices into subgraphs each containing at most C edges, so that the induced subgraphs on a specified set of v ≤ n vertices each contain at most C′ ≤ C edges. The cost of the grooming is the sum, over all subgraphs, of the number of vertices of nonzero degree in the subgraph. The optimum grooming is the one of lowest cost. An integer linear programming formulation is used to determine precise lower bounds on this minimum cost for all choices of n and v when 1 ≤ C′ < C ≤ 3. In most cases, this approach determines not only the bound but also the specific structure of any grooming that could realize the bound.

KW - Combinatorial designs

KW - Graph decomposition

KW - Linear programming duality

KW - Optical networks

KW - Traffic grooming

UR - http://www.scopus.com/inward/record.url?scp=56749174908&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56749174908&partnerID=8YFLogxK

U2 - 10.1002/net.20251

DO - 10.1002/net.20251

M3 - Article

AN - SCOPUS:56749174908

VL - 52

SP - 299

EP - 306

JO - Networks

JF - Networks

SN - 0028-3045

IS - 4

ER -