Figure 1.

Example of a hierarchical decomposition. According to a simple binary tree, it is shown how each node defines a subset of tasks (a block in the corresponding kernel matrix on the left). Here, the decomposition is shown for only one path: The subset defined by the root node contains all tasks, the subset defined by the left inner node contains t₁ and t₂ and the subset defined by the leftmost leaf only contains t₁. Accordingly, each of the remaining nodes defines a subset S_i that contains all descendant tasks.