What is "subpaving"

In mathematics, a subpaving is a set of nonoverlapping box of R. A subset X of R can be approximated by two subpavings X and X such that X ⊂ X ⊂ X. The three figures on the right show an approximation of the set X = {(x, x) ∈ R | x + x + sin(x + x) ∈ [4,9]} with different accuracies. The set X corresponds to red boxes and the set X contains all red and yellow boxes.

Combined with interval-based methods, subpavings are used to approximate the solution set of non-linear problems such as set inversion problems. Subpavings can also be used to prove that a set defined by nonlinear inequalities is path connected , to provide topological properties of such sets , to solve piano-mover's problems or to implement set computation .