Online computation and competitive analysis
Online computation and competitive analysis
SIAM Journal on Computing
The regenerator location problem
Networks - Network Optimization (INOC 2007)
Placing regenerators in optical networks to satisfy multiple sets of requests
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Optimizing regenerator cost in traffic grooming
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
On the complexity of the regenerator placement problem in optical networks
IEEE/ACM Transactions on Networking (TON)
Online optimization of busy time on parallel machines
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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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 $\Omega \left({{\log (|{E}|/d) \cdot \log d} \over{\log ({\log (|{E}|/d) \cdot \log d})}}\right)$ , 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 $\sqrt{l}/2$ 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.