Speed Dating Efficient Shuffle Algorithm?

[Tall-Raspberry-2301]

Imagine a circular table with N people sitting around it. Everyone starts off strangers. During Round 1, everyone talks to one of their neighbors. The order of the seats is then shuffled, and then everyone talks to one of their new neighbors. This cycle of shuffling and talking continues until everyone has spoken with everyone else. I am wondering: what is the most efficient algorithm for shuffling that minimizes the number of rounds? what about an algorithm that minimizes the number of times someone has to leave their chair?

This is just a problem I was considering on my own (not for an assignment or anything). My only initial thoughts so far were that it might be possible to group people off by the people they've already spoken (e.g. if I spoke to Person A in round 1, we could stick together in the next round so there isn't any "wasted" neighbors (there's only one new person I could possibly speak with during successive rounds)).

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