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Geographic routing based on greedy forwarding at node level and planar graph routing at overlay level is more efficient than both being performed at node level, especially when topology changes frequently. Overlay graphs based on geographic clusters constructed for wireless networks, modeled as 2D graphs, are generally nonplanar and planar graph routing applied on such overlay graphs may fail. Existing planarization algorithms create planar overlay graphs, when the network graphs obey assumptions like Unit Disk Graph (UDG) property. However, in real wireless networks due to radio range irregularities they fail to create connected planar graphs for connected network graphs. We propose a new planarization algorithm for overlay graphs based on the localized link removal and addition based planarization algorithm. Theoretical analysis shows that planarized graphs created by our algorithm are always planar and connected for connected UDG modeled networks. Evaluation of our algorithm on Log Normal Shadowing model, a realistic wireless model, shows that our algorithm creates connected networks in almost all simulations. Moreover, the probability of getting planar graphs is really high compared to the existing planarization algorithms.