Let S denote a set of n intervals Ii = [xi, yi], 1 ≤ i ≤ n, xi, yi ∈ ℕ, xi <yi, where xi denotes the coordinate of the left endpoint and yi denotes the coordinate of the right endpoint. The length |Ii| of an interval is defined as yi - xi. Let Ii = [xi, yi] and Ij = [xj, yj] be two intervals. Their overlap length |Ii ⋂ Ij| is given by: