Irregular applications, which rely on pointer-based data structures, are often difficult to parallelize. The inputdependent nature of their execution means that traditional parallelization techniques are unable to exploit any latent parallelism in these algorithms. Instead, we turn to optimistic parallelism, where regions of code are speculatively run in parallel while runtime mechanisms ensure proper execution. The performance of such optimistically parallelized algorithms is often dependent on the schedule for parallel execution; improper choices can prevent successful parallel execution. We demonstrate this through the motivating example of Delaunay mesh refinement, an irregular algorithm, which we have parallelized optimistically using the Galois system. We apply several scheduling policies to this algorithm and investigate their performance, showing that careful consideration of scheduling is necessary to maximize parallel performance. 1