I'm writing a semi-automatic scheduling application. Given some existing bookings and some resource requirements, it needs to find the times at which a new event can be scheduled. A human user will then evaluate the results and choose one of the options. It does not need to optimise a timetable for multiple events and hence it is not the usual NP-Hard timetabling problem.
The system has a number of resources (trainers, rooms, equipment) each of which has a type (e.g. French teacher, seminar room, projector...). Resources are booked for events each of which has a start and end time.
Now, say I need to schedule a 2 hour long French class using a projector in a seminar room, what are the times that at least one resource of each required resource type is available?
In order to limit the problem space, it's acceptable to consider only 9am-5pm, Mon-Fri at 15 minute intervals for the next 90 days. Total number of resources in of the order of 1000.
How can I do this without having to compare every resource with every other resource?