FIG. 3.

Simulation time for various bin widths and number of bins. In this example, M = 10⁷ and every propensity = 10⁻⁷ (the propensity sum equals one). The dashed line corresponds to the theoretical optimal bin width $W=\sqrt{2}$ that minimizes the total search depth. The solid line corresponds to W = 16, which is the target bin width used in practice. The algorithm performs well over a fairly wide range of bin widths and number of bins. As the problem size increases, the optimal number of bins increases roughly proportional to $\sqrt{M}$.