Comment by jgautsch

Interval trees or ordered segment sets are the "correct" answer but sometimes you can accept constraints in your domain that radically simplify– for example, with equipment availability and time slots, you may have a fixed window and allow for slots to only fall on 5 minute marks. With those 2 constraints in place, a simple bitmask becomes a viable way to represent a schedule. Each bit represents 5 minutes, and 1=avail 0=unavail