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In this paper, we presented a fully distributed algorithm to compute a planar subgraph of the underlying wireless connectivity graph. We considered the idealized unit disk graph model in which nodes are assumed to be connected if and only if nodes are within their transmission range. The main contribution of this work is a fully distributed algorithm to extract the connected, planar graph for routing in the wireless networks. The communication cost of the proposed algorithm is O(d log d) bits, where d is the degree of a node. In addition, this paper also presented a geometric routing algorithm and established its lower bound. The algorithm is fully distributed and nodes know only the position of other nodes and can communicate with neighboring nodes in their transmission range.