I haven’t done this in a while. Given two musicians, find the shortest path between them, a la “Six Degrees of Kevin Bacon”.
For example: take Joe Walsh and Mick Fleetwood, you can go: Joe Walsh -> Don Henley (both in the Eagles) -> Stevie Nicks (they did a duet) -> Mick Fleetwood (in Fleetwood Mac).
To be a valid link, the two musicians must have been a member of the same band or played together on at least one recorded and released song. Jamming together at Farm Aid doesn't count, nor does record production, nor does doing a cover song.
OK?
Simple.
So, try this: Trent Reznor to Luther Vandross.
I can do it with four steps in between. There might be fewer steps, and there are certainly ways to do it in more steps.
I'll turn on hidden comments until someone gets it.

Your rules are restrictive!! I can get there in two through Bowie (Reznor toured with Bowie, was in one of his videos and produced a couple remixes) and Vandross wrote a song for Bowie (Fascination on Young Americans). But none of those connections count, so back to the drawing board!
How about this though: Vandross sang backup for Bowie. Adrian Belew played on Bowie’s album Low. And Adrian Belew also played on Nine Inch Nails’s The Downward Spiral.
nice! i didn’t know Vandross sang backup for Bowie.
mine went: Reznor -> Belew -> Bowie -> Bing Crosby -> Sinatra -> Vandross
He was on the Young Americans album and even wrote a song for it. I like your chain as well, should have thought of the Bowie-Crosby-Sinatra thing.
I’m home sick today so have lots of time to waste!