Playing the Melody on the Drums
OK, so if you haven't had the pleasure of listening to Ari play a melody, here is a great place to start.  This is the most extreme/literal melodic drumming possible, an evolution of the earlier Jeff Hamilton post.  Notice how Ari makes the phrases of this thorny bop melody breath.  Also in the drum/bass solo notice the constant references back to the hits on the bridge. 

One more.  Check out how clearly the melody comes out, and how he even modulates up a half step in the final A section!  He also quotes the famous Lee Morgan solo at length and trades melodic ideas with the guitar player.  Just beautiful playing.

New Role for a Drummer
Ari has found a unique way to tap into both songs of jazz (read the post "The Two Songs of Jazz" for more on this idea which I reference frequently on this blog).  By taking complete responsibility for the pre-composed song at the top, as well as by taking the first solo and clearly shaping the song of his improvisation on the pre-composed song, he has demonstrated to a certain extent that the drums can function as a sort of melody instrument.  In any case, his playing is closer to a melody instrument than any other drummer I have ever heard.  That is not to say that I think he is the "best" drummer, or even my favorite.  But you have to respect how he uses his phenomenal technique to bring the music out, rather then just resorting to typical jazz drumming aerobics.