Parallelizing graph algorithms on GPUs is challenging due to the irregular memory accesses and control-flow involved in graph traversals. In this work, we tame these challenges by injecting approximations. In particular, we improve memory coalescing by renumbering and replicating nodes, memory latency by adding edges among specific nodes brought into shared memory, and thread-divergence by normalizing degrees across nodes assigned to a warp. Using a suite of graphs with varied characteristics and five popular algorithms, we demonstrate the effectiveness of our proposed techniques. Our approximations for coalescing, memory latency and thread-divergence lead to mean speedups of 1.3×, 1.41× and 1.06× achieving accuracies of 83%, 78% and 84%, respectively. © 2019 Copyright held by the owner/author(s).