Interval Trees

Used for scheduling and planning.

Problem: Need data structure that determines if any of a stored set of intervals overlaps a given interval. We want to perform all associated operations in O(lg n) time.

Define a closed interval object i as [t₁, t₂] such that , low(i) =t₁, and high(i) = t₂.

Overlap(i₁, i₂)
1 $\;\;\;\;\;$if low(i₁) $\leq$ high(i₂) and low(i₂) $\leq$ high(i₁)
2 $\;\;\;\;\;$then return True
3 $\;\;\;\;\;$else return False

Does [2, 7] overlap [5, 8]? Yes. 2 is less than 8, and 5 is less than 7, points 6, 7 common to both.