Since the optical reach (the distance an optical signal can travel before its quality degrades to a level that necessitates regeneration) ranges from 500 to 2000 miles, regeneration of optical signals is essential to establish lightpaths of lengths greater than the optical reach. In a translucent optical networfc,theoptical signal is regenerated at selected nodes of the network before the signal quality degrades below a threshold. Given the optical reach of the signal, to minimize the overall network design cost, the goal of the regenerator placement problem is to find the minimum number of regenerators necessary in the network, so that every pair of nodes is able to establish a lightpath (either transparent or translucent) between them. In this paper, we study the regenerator placement problem and prove that the problem is NP-complete. We formulate the regenerator placement problem as a Connected Dominating Set problem in a Labeled Graph (LCDS) and provide a procedure for computing it. We evaluate the effectiveness of our approach using a number of networks.