Place join algorithm

Fig. 2 Scheme for incremental construction (top line) and place-and-join (bottom line) systematic search algorithms... 

Hierarchical algorithms are characterized by the construction of a tree-like structure. A single linkage algorithm starts with placing in the first cluster the two nearest points. At the next stage, a third point joins the already formed cluster of two if its shortest distance to the members of the first cluster is smaller than to any other point. 

According to Section 6.5, in this case the joining of trajectories of the bottom and the intermediate sections is similar to the intermediate split in two-section columns, and the joining of trajectories of the top and the intermediate sections takes place according to the split with one distributed component. Therefore, the calculation of section trajectories should be carried out according to the general algorithm described in Section 7.3 for two-section columns at the intermediate split and at the split with a distributed component (Fig. 7.13b). The distillation trajectory for the column under consideration may be presented as follows ... 

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