Trying to find the cheapest airfare between two cities? That's a problem that even advanced mathematics and super computers can't solve. There are so many different fare options available, that, according to the article Behind the Fiendish Complexities of Airfare Pricing from Wired magazine, the <airline pricing> system is so complex that the problem of finding the cheapest airfare between two cities is considered mathematically unfathomable. According to a paper from the Society for Industrial and Applied Mathematics provided by ITA, "the problem of finding the cheapest airfare from point A to point B is unsolvable."
However, all hope is not lost! Well you may not agree with mileage running, you can learn a thing or two from these road warriors who spend their time looking for ways to maximize their airline miles through the lowest fare. In the article We Love to Fly and It Shows: Inside the World of Mileage Running, the author provides this tip for finding cheap flights, which I've used in the past to find the best deals:
Best of luck!