Dr George Mertzios george.mertzios@durham.ac.uk
Associate Professor
Antonio Fernàndez Anta
Editor
Giuseppe Lipari
Editor
Matthieu Roy
Editor
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.
Presentation Conference Type | Conference Paper (Published) |
---|---|
Conference Name | 15th International Conference on Principles of Distributed Systems (OPODIS) |
Publication Date | Dec 1, 2011 |
Deposit Date | Dec 8, 2011 |
Publicly Available Date | Mar 6, 2012 |
Pages | 4-17 |
Series Title | Lecture notes in computer science |
Series Number | 7109 |
Series ISSN | 0302-9743,1611-3349 |
Book Title | Principles of distributed systems, OPODIS 2011, 15th International Conference, 13-16 December 2011, Toulouse, France ; proceedings. |
DOI | https://doi.org/10.1007/978-3-642-25873-2_2 |
Keywords | Online algorithms, Optical networks. |
Public URL | https://durham-repository.worktribe.com/output/1157490 |
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/ |
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The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-25873-2_2
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