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We introduce a challenging problem in establishing and initially configuring or bootstrapping a Free Space Optical (FSO) network. In such networks, it is assumed that each communication node is a base station, including a router and wireless optical communications hardware, and its number of transceivers is limited. In addition, the FSO networks are characterized by narrow beam, directional links (e.g., operating at 1550 nm) and support up to Gbps data rates. The problem of initially configuring the transceivers to form a connected topology is NP-complete because of the transceiver limitation. What makes this problem even more challenging is the need to configure the transceiver in a "distributed" fashion, because a node can have only direct knowledge of its neighbors. We have developed a fully distributed approximation algorithm, which constructs a spanning tree with maximal node degree at most one larger than that in the optimal solution. Due to its distributed nature, this algorithm outperforms known serial algorithms. For a graph with 200 nodes generated in some randomized model, speed-ups greater than 6 have been demonstrated.