Figure 2

Scaling function for weighted stochastic backtracking. The curves by the proposed scaling function, slot _i = noise/(x + noise), are plotted, where x is the score difference between the optimal and the other backtracking path (i.e. x = h_max - h _i in Equation 7). In the figure, dotted line, solid line, and dashed line indicate the curves for noise = 10⁴, noise = 0.3, and noise = 10^-4, respectively (noise = 10⁴ and noise = 10^-4 are drawn as examples of two extreme cases). For any noise > 0, the optimal path (x = 0) has slot_max = 1, while damped slot sizes (< 1) are assigned to the non-optimal DP paths (x > 0).