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(disclaimer: I work at Google, but no relationship with the Flights team other than as an individual user)

Funny story: just last week I was booking a complicated multi-city trip with 5 legs, multiple countries, etc. I tried several times via united.com, and it wasn't showing me any flights available in one of the legs (which I knew they had a codeshare agreement).

I went back to Google Flights, chose all my flights, selected "Book with United", and was able to finish the reservation on united.com (!), with all the flights properly populated, including codeshares.

It's remarkable that the integration between Google Flights and the airlines is better than even the airlines' websites themselves.

I’m not too surprised by this. The function of every form, wizard, walk-thru, or guided app is to end up with a blob of data to post to the backend. While the blob could be relatively simple, e.g. iCal for recurring event, the UI can be extremely complicated because every valid combination must be achievable but all invalid combinations must be blocked. Google Flights UI is better than United at coming up with the right data blob to post. Once the blob is created, United final page and backend have no problem parsing and posting it.

Sounds like a P/NP-type problem. It's quite a hard problem to calculate all possible permutations of routings and schedules across 5 cities ("NP"), and United's system clearly isn't up to snuff for it, while Google's is.

But validating and pricing any single itinerary is a trivially easy problem ("P"), so United can handle that no problem. It can't come up with the itinerary, but given a particular one, it will sell it to you.

On multi-city trips, usually the UI allows the user to select each leg individually, so it is a very trivial problem (i.e., the same as 5 one way trips).

So no, there's no special magic here.

I found out that Google Flights just have smaller time margins between flights. Might be something to look out for.

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