Multiintervals

Multiintervals are a concept used in various fields, including mathematics, computer science, and statistics, to represent and manipulate collections of intervals. A multiinterval can be thought of as a set containing zero or more disjoint intervals. For example, a multiinterval could be the union of the intervals [1, 3] and [5, 7], denoted as {[1, 3], [5, 7]}.

The formal definition of a multiinterval can vary depending on the context. In some applications, it might be defined as a set of ordered pairs of real numbers, where each pair represents the start and end of an interval, and these intervals are non-overlapping. In other contexts, it might be represented as a list or array of interval objects.

Operations on multiintervals include union, intersection, and difference. The union of two multiintervals results in a new multiinterval that encompasses all the points present in either of the original multiintervals. Intersection yields a multiinterval containing only the points common to both. The difference operation removes the points of one multiinterval from another.

Multiintervals find applications in areas such as scheduling, where they can represent available or busy time slots, and in data analysis, where they might delineate ranges of interest or uncertainty. Their ability to represent complex sets of ranges efficiently makes them a useful tool for various computational problems.