Mertzios, G.B. and Shalom, M. and Wong, P.W.H. and Zaks, S. (2011) 'Online regenerator placement.', in *Principles of distributed systems, OPODIS 2011, 15th International Conference, 13-16 December 2011, Toulouse, France ; proceedings.* Berlin, Heidelberg: Springer, pp. 4-17. Lecture notes in computer science. (7109).

## Abstract

Connections between nodes in optical networks are realized by lightpaths. Due to the decay of the signal, a regenerator has to be placed on every lightpath after at most d hops, for some given positive integer d. A regenerator can serve only one lightpath. The placement of regenerators has become an active area of research during recent years, and various optimization problems have been studied. The first such problem is the Regeneration Location Problem (Rlp), where the goal is to place the regenerators so as to minimize the total number of nodes containing them. We consider two extreme cases of online Rlp regarding the value of d and the number k of regenerators that can be used in any single node. (1) d is arbitrary and k unbounded. In this case a feasible solution always exists. We show an O(log|X| ·logd)-competitive randomized algorithm for any network topology, where X is the set of paths of length d. The algorithm can be made deterministic in some cases. We show a deterministic lower bound of W([(log(|E|/d) ·logd)/(log(log(|E|/d) ·logd))])log(Ed)logdlog(log(Ed)logd) , where E is the edge set. (2) d = 2 and k = 1. In this case there is not necessarily a solution for a given input. We distinguish between feasible inputs (for which there is a solution) and infeasible ones. In the latter case, the objective is to satisfy the maximum number of lightpaths. For a path topology we show a lower bound of Öl/2l2 for the competitive ratio (where l is the number of internal nodes of the longest lightpath) on infeasible inputs, and a tight bound of 3 for the competitive ratio on feasible inputs.

Item Type: | Book chapter |
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Additional Information: | This work was supported in part by the Israel Science Foundation grant No. 1249/08 and British Council Grant UKTELHAI09 Proceedings published as: Principles of Distributed Systems: 15th International Conference, OPODIS 2011, Toulouse, France, December 13-16, 2011. Event url: http://www.opodis.net/ |

Keywords: | Online algorithms, Optical networks. |

Full text: | PDF - Accepted Version (179Kb) |

Status: | Peer-reviewed |

Publisher Web site: | http://dx.doi.org/10.1007/978-3-642-25873-2_2 |

Publisher statement: | The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-25873-2_2 |

Record Created: | 21 Feb 2012 13:05 |

Last Modified: | 31 Mar 2015 13:12 |

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