On the complexity of the regenerator placement problem in optical networks

Placement of regenerators in optical networks has attracted the attention of recent research works in optical networks. In this problem, we are given a network with an underlying topology of a graph G and with a set of requests that correspond to paths in G. There is a need to put a regenerator every certain distance, because of a decrease in the power of the signal. In this paper, we investigate the problem of minimizing the number of locations to place the regenerators. We present analytical results regarding the complexity of this problem, in four cases, depending on whether or not there is a bound on the number of regenerators at each node, and depending on whether or not the routing is given or only the requests are given (and part of the solution is also to determine the actual routing). These results include polynomial time algorithms, NP-completeness results, approximation algorithms, and inapproximability results.