By Clifford A Pickover
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The rectangles are sorted into two lists; one using their lower bounds in that dimension and one using their upper bounds. For each list, all possible splits to two groups are considered and the sums of the margins of the MBRs for each group pair are summed. The intuition is that if we split across the “longest” axis, the resulting nodes will be more quadratic. After the split dimension is chosen, the best distribution along that axis is chosen, this time considering minimum overlap between the resulting groups (and minimum area as a second criterion, in the case of ties).
Right: tree structure and distribution of points to leaf nodes. 1, are appropriate for indexing points, not objects with extended geometry. Most PAMs define space decompositions of disjoint partitions, which are sufficient for clustering points into disk blocks. However, while a point is guaranteed to be assigned to a unique partition, a spatial object with extended geometry may overlap with more than one partition. For instance, the grid file decomposes the space using an orthogonal grid, each point is assigned to exactly one cell, and adjacent cells are organized to disk pages.
Each leaf node corresponds to a disk page, storing the points that are included in the corresponding partition. In this example, we assume that a disk block can store at most 3 points, so regions with more than 3 points should recursively be repartitioned. The root node has four children corresponding to the top-left, bottom-left, top-right, and bottom-right quadrants of the whole space. Note that the bottom-left and top-right quadrants have at most 3 points, so they do not need to be repartitioned.