Because 0 precedes 1, node 3 will ask node 0 to find the successor of 1. In turn, node 0 will infer from its finger table that 1's successor is the node 1 itself, and return node 1 to node 3. In general, a Chord lookup proceeds in multiple hops around the identifier ring. Each hop eliminates at least half of the remaining distance to the desired successor. This means that the hops early in a query's path travel long distances in identifier space, and later hops travel small distances.
Lookups take a number of hops proportional to the log of the number of nodes in the system.
A new node r can initialize its finger table by querying an existing node for the respective successors of the lower endpoints of the k intervals in r 's table. Nodes whose routing information is invalidated by r 's addition are determined using r ' s predecessor table.