## Abstract

We consider the problem of routing in networks employing all optical routing technology. In these networks, messages travel in optical form and switching is performed directly on the optical signal. By using different wavelengths, several messages may use the same edge concurrently, However, messages assigned the same wavelength must use disjoint paths, or else be routed at separate rounds. No buffering at intermediate nodes is available. Thus, routing in this setting entails assigning wavelengths, paths, and time slots for the different messages. For arbitrary bounded degree networks, we show that any permutation can be routed efficiently in one round using at most O(log^{2}n/β^{2}) wavelengths, where β is the edge expansion of the network. This improves a quadratic factor on previous results, and almost matches the ω(l/β^{2}) existential lower bound. We consider two of the more popular architectures for parallel computers. For bounded dimension arrays we give the first per-instance approximation algorithm. Given a limited number of wavelengths and a set of messages to be routed, the algorithm approximates to within polylogarithmic factors the optimal number of rounds necessary to route all messages. Previous results for arrays give only worst-case performance. Finally, we show that on the hypercube any permutation can be routed using only a constant number of wavelengths. The previous known bound was O(logre).

Original language | English |
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Title of host publication | Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 |

Publisher | Association for Computing Machinery |

Pages | 567-576 |

Number of pages | 10 |

ISBN (Electronic) | 0898713498 |

State | Published - 22 Jan 1995 |

Externally published | Yes |

Event | 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 - San Francisco, United States Duration: 22 Jan 1995 → 24 Jan 1995 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### Conference

Conference | 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 |
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Country/Territory | United States |

City | San Francisco |

Period | 22/01/95 → 24/01/95 |

### Bibliographical note

Funding Information:T Laboratory for Computer Science, Cambridge, MA, 02138, aumannQtheory .lcs .mit edu. Supported by a Wolfson postdoctoral fellowship and DARPA contract N00014-92-J-1799. tWork done while at MIT Laboratory for Computer Science, supported by ARPA/Army contract DABT63-93-C-0038. Present address: Department of Computer Science, University Toronto, Toronto, Ontario lA4, rabaniQcs.toronto .edu.

### Funding

T Laboratory for Computer Science, Cambridge, MA, 02138, aumannQtheory .lcs .mit edu. Supported by a Wolfson postdoctoral fellowship and DARPA contract N00014-92-J-1799. tWork done while at MIT Laboratory for Computer Science, supported by ARPA/Army contract DABT63-93-C-0038. Present address: Department of Computer Science, University Toronto, Toronto, Ontario lA4, rabaniQcs.toronto .edu.

Funders | Funder number |
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ARPA/Army | DABT63-93-C-0038 |

MIT Laboratory for Computer Science | |

Defense Advanced Research Projects Agency | N00014-92-J-1799 |