## Abstract

We address the problem of efficient circuit switching in wide area networks. The solution provided is based on finding optimal routes for lightpaths and semilightpaths. A lightpath is a fully optical transmission path, while a semilightpath is a transmission path constructed by chaining several lightpaths together, using wavelength conversion at their junctions. The problem thus is to find an optimal lightpath/semilightpath in the network in terms of the cost of wavelength conversion and the cost of using the wavelengths on links. In this paper, we first present an efficient algorithm for the problem which runs in time O(k^{2}n + km + kn log(kn)), where n and m are the number of nodes and links in the network, and k is the number of wavelengths. We then analyze that the proposed algorithm requires O(d^{2}nk_{0}^{2} + mk_{0} log n) time for a restricted version of the problem in which the number of available wavelengths for each link is bounded by k_{0} and k_{0} = o(n), where d is the maximum in-degree or out-degree of the network. It is surprising to have found that the time complexity for this case is independent of k. It must be mentioned that our algorithm can be implemented efficiently in the distributed computing environment. The distributed version requires O(kn) time and O(km) messages. Compared with a previous O(k^{2}n + kn^{2}) time algorithm, our algorithm has the following advantages. 1) We take into account the physical topology of the network which makes our algorithm outperform the previous algorithm. In particular, when k is small e.g., k = O(log n) and m = O(n), our algorithm runs in time O(n log^{2} n), while the previous algorithm runs in time O(n^{2} log n). 2) Since our algorithm has high locality, it can be implemented on the network distributively.

Original language | English |
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Pages (from-to) | 1571-1579 |

Number of pages | 9 |

Journal | IEEE Transactions on Communications |

Volume | 48 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sept 2000 |