Scaling function for weighted stochastic backtracking. The curves by the proposed scaling function, slot
= noise/(x + noise), are plotted, where x is the score difference between the optimal and the other backtracking path (i.e. x = hmax - h
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 slotmax = 1, while damped slot sizes (< 1) are assigned to the non-optimal DP paths (x > 0).