The Minimum Platforms problem finds the minimum number of platforms required for a railway station so that no train has to wait, assuming arrival and departure schedules are fixed.

Sort arrival and departure events independently in ascending order. Process events chronologically: if arrival, increment platform count; if departure, decrement platform count.

The peak number of overlapping train intervals represents the minimum platforms required at any instant in the global schedule.

Proof by sweep-line: a railway station cannot hold more trains than the peak overlapping count without collision, so at least Peak platforms are required.