The problem with the mod N approach is that if the number of nodes N changes, most of the keys will need to be moved from one node to another. For example, say hash(key) = 123456. If you initially have 10 nodes, that key starts out on node 6 (because 123456 mod 10 = 6). When you grow to 11 nodes, the key needs to move to node 3 (123456 mod 11 = 3), and when you grow to 12 nodes, it needs to move to node 0 (123456 mod 12 = 0). Such frequent moves make rebalancing excessively expensive. We need an approach that doesn’t move data around more than necessary.
