## Abstract

The paper deals with on-line routing in WDM (wavelength division multiplexing) optical networks. A sequence of requests arrives over time, each is a pair of nodes to be connected by a path. The problem is to assign a wavelength and a path to each pair, so that no two paths sharing a link are assigned the same wavelength. The goal is to minimize the number of wavelengths used to establish all connections. We consider trees, trees of rings, and meshes topologies. We give on-line algorithms with competitive ratio Ω(log n) for all these topologies. We give a matching Ω(log n) lower bound for meshes. We also prove that any algorithm for trees cannot have competitive ratio better than Ω(log n/log logn). We also consider the problem where every edge is associated with parallel links. While in WDM technology, a fiber link requires different wavelengths for every transmission, SDM (space division multiplexing) technology allows parallel links for a single wavelength, at an additional cost. Thus, it may be beneficial in terms of network economics to combine between the two technologies (this is indeed done in practice). For arbitrary networks with Ω(log n) parallel links we give an on-line algorithm with competitive ratio Ω(logn).

Original language | American English |
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Title of host publication | Automata, Languages and Programming - 24th International Colloquium, ICALP 1997, Proceedings |

Editors | Pierpaolo Degano, Roberto Gorrieri, Alberto Marchetti-Spaccamela |

Publisher | Springer Verlag |

Pages | 516-526 |

Number of pages | 11 |

ISBN (Print) | 3540631658, 9783540631651 |

DOIs | |

State | Published - 1997 |

Externally published | Yes |

Event | 24th International Colloquium on Automata, Languages and Programming, ICALP 1997 - Bologna, Italy Duration: 7 Jul 1997 → 11 Jul 1997 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1256 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 24th International Colloquium on Automata, Languages and Programming, ICALP 1997 |
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Country/Territory | Italy |

City | Bologna |

Period | 7/07/97 → 11/07/97 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 1997.