Geographic routing scheme (such as Greedy perimeter stateless routing) makes use of location information to forward packets greedily. Nodes need to keep only this location information in stateless routing. When the greedy forwarding fails, routing switches to perimeter forwarding based on either planar graph (GG and RNG) or cross link detection protocol approaches. However, it has drawback in terms of cost and computational overheads. We propose a coverage-tree heuristic based routing instead of face routing in geographic routing schemes when greedy forwarding fails. We prove that the coverage tree based routing problem is NP hard by reduction using minimum rooted spanning tree of depth 2 (RST 2). We also show that coverage-tree based geographic routing problem is APX hard and not approximable with a factor of (1-∈)lnn for any fixed (Formula Presented.). Our proposed scheme of coverage-tree heuristics based geographic routing is (Formula Presented.)-approximation algorithm, a polynomial time algorithm using minimum distance topology knowledge. On performance comparison using simulation, our proposed scheme outperforms with the competitive schemes in term of success rate, network overhead and success rate against varying node density. © 2014, Springer Science+Business Media New York.