Diagram of tree algorithm for one-component Smoluchowski coagulation calculations. (a) The dust property (here, mass) distribution is discretized into bins, and the bitree corresponds to the hierarchical grouping of the bins. (b) The tree algorithm assumes that the dust parameter space is a virtual metric space, where a distance is defined. To calculate coagulation using the tree, the algorithm first fixes one of the colliding dust aggregates, I-dust, and iterates through the other dust aggregate, II-dust, using the tree. For each level of grouping, the distance between the average of the II-dust bin and the I-dust bin D, the length of the grouped bin L, and the ratio of these two values θ are calculated. (c) The algorithm computes the coagulation (Eq. (34)) using the averaged II-dust bin with the largest bin width under the condition of θ < θ_c.