To start us off, here's what Qwerty said:
I believe they bought Overture more for PPC than to get ahold of AV and ATW (which Overture owned), but they've got them, and it makes sense for them to use them. Maybe not right away, but I think eventually we'll see ATW's index ranked by INK's algo (so hopefully a lot of the trash in there will go away), and maybe AV's image search, which I find much better than Google's.
I've been saying for a long time (July of 2002 is the first time I said it - over in WMW) that all signs show that Yahoo really wants to be out of the search business altogether. The problem is that they really haven't been able to afford to be out of it - that is, until now.
October's purchase of Overture was the key to it all. The purchase of INK was important, but just having crawled search capabilities does not a search provider make. (Even Google uses the DMOZ as part of their search service).
You'll notice that with all of the purchases and partnerships Yahoo! has made over the past half decade or so, they instantly slap their brand on it (like eGroups/groups.yahoo.com or the partnership that gave us Yahoo!/SBC High Speed Internet). The exceptions to this rule have been when the purchases are in the search sector. Visit an INK site and you'll be hard pressed to find the word Yahoo! anywhere. Visit the Overture site and you can see it on the corporate page, but that is it. They simply are not looking to put their name on search services - it would, afterall, dillute their brand by having Yahoo! plastered all over the place on MSN (using INK), AllTheWeb, AltaVista, all the sites using Overture, and so on.
It's far better that they use the "Overture" brand (or one of the other brands) for search, and the Yahoo brand for the plethora of things you will find on the Yahoo site. (the same way that ABC is owned by Disney, but maintains its own separate entity.) It makes sense, then, that Yahoo would provide a whole line of services on their site with "Search Services provided by Overture."
Yahoo, back when INK was first purchased, never really said exactly what they were going to do with it, but insinuations were made that it would be developed into a corporate search solution - and they most assuredly never said that it would be used for serving their own Yahoo! Search results.
That's not to say that the INK algo won't be incorporated, in part, into the results generated by AlltheWeb or AV. (And if you look at the AV results right now, there are some signs that they may already be experimenting with this).
To be truly prepared for what's to come from Yahoo, I do think it would be a mistake to ignore Inktomi completely, but at the end of the day it is what we see coming off AV or AllTheWeb that we'll need to comprehend to rank well at Yahoo. (I believe that AllTheWeb is the "experimental" engine and that AV is the "public consumption" version - though I may have that backwards... )
Yahoo might also use INK to provide a "middle level" of results in their new plans. (i.e. When you search you get "Directory Sites" "Overture PPC" "INK PFI" and then the "free inclusion backfill" coming off ATW/AV. I have a feeling that wouldn't go over very well as there would be just too much fluff up top before you got to the generic results.
So, my conclusion (though it can be, by no means, considered fact) is that we're going to have to really have our brains wrapped around the notion of ranking well with AllTheWeb/AV - and I'll see if I can find which is the experimental one - one of them will give us foreshadowing of "things to come" and the other will give us a look at "what is"). If any of the INK technologies are used in the generic results, that will show up on the experimental engine first and INK will never be used (as an entity) to provide Yahoo's generic search results.