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The Delegation Chain
In the algorithm, each person is responsible for some number of people. When you're one of these agents saying, "I'm going to go look for someone," you have no idea who in this crowd is an agent or somebody who delegated it to someone else. The bigger the lump is, the less likely the more likely it is that you end up reaching that lump. Every round, the giant one can only absorb one of the others. And now you suddenly have time which is about square root of n.