Quoting TVNWZ (Reply 9):
*Well it's late. Maybe some night owl A-netters can shed some light on this overnight. I'm toast.* |

Based on what I did in my previous life long time ago

The task that res.nwa.com does (or better orbitz.com, which is used by res.nwa.com) faces is an

NP-hard problem, check here

http://www.itasoftware.com/careers/eng.php for a practical view

*There are 25,000,000 practical flight combinations for a round-trip between Boston and Los Angeles with one-day travel windows. Computing the price for any one of those ways is at least NP-hard. The availability data is changing at 100 Hz. Find the cheapest solution in 10 seconds or less....*
A math professor would write about

NP hard problems this

http://en.wikipedia.org/wiki/NP-hard
Anyway, mu hunch (and I'm really speculating) is they do use heuristics to find the "best price" trip and with "Number of flights to display" they let us manipulate for how long (think CPU cycles or time) this heuristic should run. While they might not find an optimal solution (if I remember correctly the trip via

MEM was $0.5 cheaper than the one via

MSP) they can tell usually that they are very close to the optimal solution (the cheapest trip) - in this case it was $0.5 difference or about 0.2%. So, thus they stop the search to conserve CPU cycles. We need to remember that there are many other people searching at the same time. This is

NP hard problem, which means that not using heuristics and trying to find an optimal solution might be computionally very exhaustive -> (in a very simple way) time to solve the problem grows faster than the complexity of the problem and is not limited by any know polynomial.

Point is you searched "by price" and that's what they did. You hoped that in the first 16 results would be a trip via

MEM and it was not there. However, your question should have been "give me the best price if I fly back via

MEM". In that case you need to set "Number of flights to display" to increase your chances or use multi-city option.