As I recall there are (or at least used to be) lots of computationally hard problems in searching for flights. I think it is already somewhat tricky to enumerate all the reasonable routes between two destinations (and back) (and sometimes there are C shaped plans of A->B, then days later B-> C), and then airlines have complex fee structures combining date, time, class (ie fare), loyalty programme memberships, legs, whole route, current demand, etc such that determining the price for a single route is somewhat tricky and searching for the fastest /cheapest route is also not easy (and crucially not reducible: if you have the cheapest flight from A to B, the cheapest return from A to B may not include it)

But maybe the landscape of airline booking/pricing has changed since I got this impression.